Reprinted  with  the  permission  of  the  American  Telephone
and  Telegraph  Company,  New  York

Devoted  to  the  Scientific  and  Engineering  Aspects
of  Electrical  Communication

MODERN  industry  is  characterized  by  the  extent  to  which
scientific  research  and  technique  based  on  precise  study  have
contributed  to  its  progress.  So  complete  has  been  the  adaptation
of  and  reliance  on  scientific  research  in  many  industries  that  it  is
difficult  at  this  time  to  visualize  the  state  of  affairs  of  two  or  three
decades  ago,  when  substantially  all  industry  on  its  technical  side  was
dependent  for  advancement  on  cut-and-try,  rule-of-thumb,  methods
of  development.  Today  in  many  industries  the  management  would
not  think  of  embarking  on  a  new  project  without  consulting  their
research   engineers.

Many  industries  have  proved  the  benefits  to  be  derived  from  the
utilization  of  that  organized  knowledge  provided  both  in  the  fields
of  the  physical  sciences  and  in  those  newer  fields  which  have  to  do
with  psychology  and  economics.  There  are  still  greater  numbers  of
industrial  organizations  where  the  adoption  of  scientific  methods  has
been  slow.  However,  the  time  will  undoubtedly  come  when  every  in-
dustry will  recognize  the  aid  it  can  derive  from  scientific  research
in  some  form  as  it  now  recognizes  its  dependence  for  motive  power
on  steam  or  electricity  rather  than  on  muscular  activity.

Upwards  of  one  hundred  years  ago  there  was  adopted  in  earnest
by  scientific  men,  principally  in  university  laboratories,  the  program
of  searching  deeper  into  the  unknown,  to  discover  new  principles  and
new  relationships  of  a  kind  which  had  at  the  time  very  little  apparent
practical  interest  to  mankind  as  a  whole.

Out  of  this  work,  and  in  time,  have  grown  entirely  new  industries.
From  the  fact  that  these  industries  sprang  directly  from  the  research
laboratory,  it  was  inevitable  that  they  should  be  conspicuous  because
of  the  number  of  their  men  trained  in  the  methods  of  scientific  re-
search. Equally  inevitable  was  it  that  these  new  fields  of  endeavor,
originating  as  they  did  and  being  staffed  as  they  were,  should  be  the
ground  where  industrial  research  would  find  its  first  and  largest
development.  And  not  the  least  of  the  advantages  which  obtained
in  these  newer  industries  was  the  absence  of  age-long  traditions  tend-
ing to  ultra-conservatism  as  to  new  undertakings,  and  more  par-
ticularly as  to  the  employment  of  the  new  types  of  mind.

The  results  up  to  the  present  indicate  clearly  that  the  electrical
and  chem.ical  fields  in  industry  as  we  know  them  today,  are  the  places
where  the  greatest  advances  have  been  made  in  the  utilization  of
research  methods  and  research  men.  Other,  older  and  more  basic
industries  are  rapidly  following  the  general  path  marked  out  by  the
successes  already  obtained  in  these  fields.  Hence,  it  is  expected  that
shortly  all  industrial  activities  will  be  based  on  the  results  obtained
by  trained  investigators,  using  the  tools  of  modern  scientific  in-
vestigation.

Just  as  applied  electricity  is  a  leading  exemplar  of  the  benefits  to
be  obtained  by  an  intelligent  use  of  scientific  knowledge,  so  electrical
communication  of  intelligence  is  a  leading  exemplar  in  the  field  of
applied  electricity.  This  branch  of  applied  electricity  is  a  pioneer
among  those  recognizing  the  practical  value  of  scientific  research.
It  is  interesting  to  note  that  electrical  communication  is  credited
with  having  organized  a  research  laboratory  prior  to  the  first  university
course    in   electrical   engineering.

More  than  ever  before,  the  communication  engineer  must  seek
exact  solutions  of  his  problems.  If  his  results  do  not  always  attain
the  certainty  he  desires,  the  reason  is  the  absence  of  complete  knowl-
edge with  regard  to  one  or  more  essential  facts.  But  true  knowledge
of  what  things  limit  the  solution  of  a  problem  is  frequently  more
than  half  the  battle  of  obtaining  the  missing  facts.  Sometimes  these
unknown  facts  can  be  obtained  by  a  search  through  the  remoter
parts  of  the  vast  scientific  storehouses  which  have  been  built  in  times
past.     Frequently,  however,  the  search  discloses  the  entire  absence

of  the  thing  sought  for,  and  new  researches  are  begun  with  definite
ends  in  \'\e\\.  Thus  it  has  come  about  that  the  communication
engineer  has  become  an  original  investigator  and  is  extending  the
boundaries  of  human  knowledge  and  supplementing  the  advances  of
pure  science  to  find  solutions  for  his  various  and  sundry  problems.

Hence,  while  well  equipped  physical  and  chemical  laboratories  are
still  a  necessary  part  of  the  communication  engineer's  equipment,  he
is  equally  active  in  pushing  his  investigations  in  many  other  direc-
tions. Questions  involved  in  the  making  of  proper  rate  schedules  and
adequate  fundamental  plans  for  new  construction  are  originating
profound  researches  in  such  fields  as  political  science,  psychology  and
mathematics.  A  casual  examination  of  recent  technical  literature
dealing  with  electrical  communication  would  show  articles  which
touch  upon  almost  every  branch  of  human  activity,  which  we  designate
as  science.

With  this  intense  and  growing  interest  in  the  proper  application  of
scientific  methods  to  the  solution  of  the  problems  of  electrical  com-
munication, it  is  natural  that  a  widespread  desire  should  have  arisen
for  a  technical  journal  to  collect,  print  or  reprint,  and  make  readily
available  the  more  important  articles  relating  to  the  field  of  the  com-
munication engineer.  These  articles  are  now  appearing  in  some
fifteen  or  twenty  periodicals  scattered  throughout  the  world  and  in
the  majority  of  instances  receive  their  first  and  last  printing  in  these
widely  separated  mediums.  The  need  already  felt  for  such  a  journal
will  grow  keener  as  new  developments  extend  the  scope  of  the  art  and
the  specialization  of  its  engineers  of  necessity  increases.  It  is  hoped
that  the  Bell  System  Technical  Journal  will  fill  this  need,  and
as  implied  above,  it  is  intended  that  the  range  of  subjects  treated  in
the  Journal  will  be  as  broad  as  the  science  and  technique  of  electrical
communication  itself.

While  many  of  the  articles  which  will  appear  in  the  Journal  will
be  original  presentations  of  some  phase  of  the  research  or  develop-
ment or  other  technical  work  of  the  Bell  System,  it  is  not  intended
that  the  Journal  should  be  the  sole  means  by  which  this  work  is
presented.  Just  as  in  the  past,  original  articles  and  papers  will  con-
tinue to  be  presented  before  various  societies  and  in  different  technical
and  non-technical  magazines.  Moreover,  the  Journal  will  reprint
articles  on  important  research  and  development  work  in  the  communi-
cation field  generally  so  that  the  results  of  such  work  may  be  given
greater  publicity  and  become  of  greater  value  to  communication
engineers.

Synopsis:  The  type  of  vacuum  tube  described  in  the  present  article  is
likely  to  become  one  of  the  most  remarkable  devices  of  modern  electrical
science.  Vacuum  tubes  capable  of  handling  small  amounts  of  power  have
been  extensively  used  during  the  past  few  years  as  telephone  repeaters
and  as  oscillators,  modulators,  detectors  and  amplifiers  in  radio  trans-
mission and  other  fields.  Practically  all  such  tubes  have  depended  upon
thermal  radiation  from  the  plates  to  dissipate  the  electrical  energy  which  in

the  device  necessarily  absorbs  during  its  operation.     With  present  methods  i^^

of  construction,  and  using  glass  for  the  containing  V^ulb,  a  fairly  definite
upper  limit  can  be  set  for  the  power  which  a  radiation  cooled  tube  can
handle;  as  the  author  points  out,  this  limit  gives  a  tube  capable  of  delivering
about  1  to  2  k.  w.  when  used  as  an  oscillator.

been  made  possible  by  a  new  and  striking  development  in  the  art  of  seal-
in?  metal  to  glass.  In  the  case  of  the  100  k.  w.  tube  the  seal  between  the
c>lindrical  copper  anode  and  glass  portion  is  3.5  inches  in  diameter.

The  remarkable  character  of  these  copper-in-glass  seals  is  evidenced
by  the  fact  that  they  do  not  depend  upon  a  substantial  equality  between
the  coefficient  of  expansion  of  the  metal  and  glass.  To  Mr.  W.  G.  Hous-
keeper  of  the  Bell  System  Research  Laboratory  at  the  Western  Electric
Company,  goes  the  credit  for  developing  the  copper-in-glass  seals.  As
the  article  brings  out,  Mr.  Houskeeper  has  also  invented  means  for  sealing
heavy  copper  wire  and  strip  through  glass  in  such  a  way  that  the  best
vacua  can  be  maintained  under  wide  changes  of  temperature. — pAlilor.

THE  development  of  wireless  telephony  and  the  use  of  continu-
ous wave  transmission  in  wireless  telegraphy  have  led  to  the
general  adoption  of  the  vacuum  tube  as  the  generator  of  high  fre-
quency currents  in  low  power  installations.

The  ordinary  form  of  vacuum  tube  is,  however,  ill  suited  for  the
handling  of  large  amounts  of  power,  and  at  the  large  wireless  stations
where  the  plant  is  rated  in  hundreds  of  kilowatts  either  the  arc  or
the  high  frequency  alternator  is  used.

The  undoubted  advantages  to  be  derived  from  the  use  of  vacuum
tubes,  especially  in  the  field  of  wireless  telephony  where  the  output
power  must  be  modulated  to  conform  to  the  intricate  vibration  pat-
tern of  the  voice,  has  led  to  a  demand  for  tubes  capable  of  handling
amounts  of  power  comparable  with  those  in  use  at  the  largest  stations.

That  the  development  of  such  tubes  was  of  great  importance  was
recognized  by  the  engineers  of  the  Bell  Telephone  System  in  the
early  days  of  the  vacuum  tube  art.     The  experiments  at  Arlington,

Virginia,  in  which  speech  was  first  transmitted  across  the  Atlantic
to  Paris  and  across  the  Pacific  to  Honolulu,  required  the  use  of  nearly
300  of  the  most  powerful  tubes  then  available,  each  capable  of  han-
dling about  25  watts,  and  the  difficulties  encountered  in  operating  so
many  tubes  in  parallel  gave  added  impetus  to  the  development  of
high  power  units.

It  is  the  object  of  the  present  paper  to  deal  with  the  various  steps
in  the  development  of  high  power  tubes  as  carried  out  in  the  Bell
System  research  laboratories  at  the  Western  Electric  Company.

The  usual  type  of  vacuum  tube  consists  of  an  evacuated  glass  vessel
in  which  are  enclosed  three  elements,  the  filament,  the  plate,  and  the
grid.  When  the  tube  is  in  operation  an  electron  current  flows  between
the  filament  which  is  heated  by  an  auxiliary  source  of  power  and  the
plate,  the  magnitude  of  this  current  being  controlled  by  the  grid.

The  passage  of  the  current  through  a  thermionic  tube  is  accompanied
by  the  dissipation  in  the  plate  of  an  amount  of  power  which  is  compa-
rable to  the  power  delivered  to  the  output  circuit  and  wrhich  manifests
itself  in  the  form  of  heat.  This  causes  the  temperature  of  the  plate
in  the  usual  type  of  tube  to  rise  until  the  rate  of  loss  of  heat  by  radia-
tion is  equal  to  the  power  dissipated.  Some  of  the  heat  liberated  by
the  plate  is  absorbed  by  the  walls  of  the  containing  vessel  which  con-
sequently rise  in  temperature.  These  factors,  together  with  a  con-
sideration of  the  size  of  plate  that  can  be  conveniently  suspended  inside
a  glass  bulb  and  the  size  of  glass  bulb  that  can  be  conveniently  worked,
set  a  limit  of  about  1  to  2  k.  w^  for  the  power  that  can  be  dissipated
in  the  plate  of  a  commercial  vacuum  tube  of  this  type.  The  plates
are  generally  constructed  of  molybdenum  or  some  other  refractory
metal  and  the  containing  vessel  made  of  hard  glass.

The  use  of  quartz  as  the  containing  vessel  offers  certain  advantages
which  tend  to  raise  the  power  limit  somewhat  and  this  material  has
been  used  for  power  tube  purposes  in  England.

It  is  apparent  then  that  in  the  development  of  vacuum  tubes  capa-
ble of  handling  large  amounts  of  power  means  other  than  radiation
must  be  used  for  removing  the  heat  dissipated  at  the  plate,  and
development  of  tubes  along  these  lines  was  undertaken  by  Dr.  E.  R.
Stoekle  and  Dr.  O.  E.  Buckley.

Dr.  Stoekle  had  already  worked  for  some  years  on  the  problem  of
removing  the  heat  dissipated  at  the  anode  of  a  thermionic  tube  by
making  the  anode  a  part  of  the  outside  wall  of  the  vessel  and  thus
making  it  possible  to  convey  the  heat  directly  away  from  it  by  means
of  circulating  water.  This  was  clearly  the  right  principle  but  as  is
obvious  to  those  who  are  familiar  with  these  devices,  great  difficulties

presented  themselves  in  the  mechanical  construction  of  large  tubes
in  which  vacuum  tight  joints  must  be  made  and  maintained  between
glass  and  large  masses  of  metal.  The  importance  of  the  problem,
however,  was  such  that  Stoekle  and  Buckley  pushed  on  in  the  face  of
difficulties  to  the  construction  of  tubes  which  could  handle  kilowatts
where  previous  tubes  could  only  handle  watts.

A  step  in  the  direction  of  overcoming  these  difficulties  was  made  by
Messrs.  Schwerin  and  Weinhart,  who  were  working  with  Dr.  Buckley
on  the  problem,  and  who  suggested  that  the  anode  might  be  made
in  the  form  of  a  tube  or  thimble  of  platinum  sealed  into  a  glass  vessel
and  kept  cool  by  passing  water  through  it.

This  suggestion  led  to  the  development  of  a  tube  which,  although
not  the  one  finally  adopted,  is  discussed  in  some  detail  since  it  was  the
first  one  to  be  pushed  to  such  a  point  as  to  give  promise  of  economical
commefcial  manufacture.

The  tube  is  shown  in  Fig.  1.  The  anode  consists  of  a  platinum
cylinder  A,  7"  long  and  .625"  wide,  which  is  scaled  into  the  center  of
the  glass  cylinder  B.  The  end  of  the  platinum  cylinder  remote  from
the  seal  is  closed.  The  anode  is  surrounded  by  the  grid  C  and  by
the  filament  D,  which  are  supported  by  the  glass  arbors  E.  The
current  for  the  filament  is  led  into  the  tube  through  the  platinum
thimbles  F.

The  anode  is  kept  cool  by  means  of  a  supply  of  water  passing  into
the  anode  through  the  tube  G  and  leaving  by  the  tube  H.

A  number  of  tubes  having  this  general  type  of  construction  were
made  up  and  it  was  found  possible  to  dissipate  as  much  as  15  k.  w.
in  the  anode.

As  soon  as  the  pressure  of  work  more  directly  connected  with  the
necessities  of  the  war  would  permit,  Mr.  W.  G.  Houskeeper  and  Dr.
M.  J.  Kelly  undertook  the  further  improvement  of  the  water-cooled
tube,  the  former  assuming  the  task  of  developing  the  mechanical
structure,  and  the  latter  that  of  determining  the  electrical  design  and
the  process  of  tube  exhaust.

Mr.  Houskeeper  adopted  into  the  construction  of  the  tube  a  remark-
able type  of  vacuum  seal  which  he  had  previously  developed.  These
seals  are  made  between  glass  and  metal  and  can  be  made  in  any  desired
size.  They  are  capable  of  withstanding  repeated  heating  and  cooling
over  wide  ranges  of  temperature,  from  that  of  liquid  air  to  350°  C,
without  cracking  and  without  impairment  of  their  vacuum  holding
properties.

It  is  no  exaggeration  to  say  that  the  invention  of  these  seals  has
made  possible  the  construction  of  vacuum  tubes,  capable  of  handling
in  single  units,  powers  of  any  magnitude  which  may  be  called  for  in
wireless  telegraph  and  telephone  transmission.

The  underlying  principle  connected  with  the  making  of  this  seal
consists  in  obtaining  an  intimate  connection  between  the  glass  and
metal,  either  by  chemical  combination  or  by  mere  wetting,  and  in  so
proportioning  the  glass  and  metal  portions  of  the  seal  that  the  stresses
produced  when  the  seal  is  heated  or  cooled  will  not  be  great  enough  to
rupture  either  the  glass  or  the  junction  between  the  glass  and  metal.

The  three  principal  types  of  seals  developed  by  Mr.  Houskeeper
are  known  as  the  ribbon  seal,  the  disc  seal  and  the  tube  seal.

If  a  copper  ribbon  is  directly  sealed  through  glass  it  is  found  that
the  glass  and  copper  adhere  along  the  flat  faces  of  the  seal  but  that
ruptures  occur  along  the  edges  as  shown  in  Fig.  2  (a).  This  is  due  to
the  fact  that  as  the  seal  cools  after  being  made,  the  glass  in  contact
with  metal  is  capable  of  resisting  the  shearing  and  tensile  stresses

that  occur  along  the  faces,  while  the  glass  wrapping  round  the  edges
of  the  ribbon  is  called  upon  to  withstand  much  greater  tensile  stresses
and  gives  way.  If  the  edges  of  the  ribbon  are  sharpened  as  shown  in
Fig.  2  (b),  a  tight  seal  results,  the  reason  being  that  the  forces  of

adhesion  between  the  glass  and  copper  acting  along  the  flat  contact
faces  are  sufficient  to  stretch  the  thin  copper  at  the  edge  and  prevent
its  drawing  away  when  cooled.  There  is  a  definite  relation  between
the  elastic  properties  of  the  metal  and  glass  and  the  angle  of  edge
that  can  be  used  for  a  successful  seal.

By  proper  shaping  of  the  metal  ribbon,  seals  have  been  successfully
made  up  to  very  large  sizes.  Some  of  these  are  shown  in  Fig.  3,  the
the  largest  in  the  photograph  being  about  1  in  width,  and  capable
of  successfully  conducting  a  current  of  150  to  200  amperes.

The  principles  involved  in  the  making  of  the  disc  seal  are  the  same
as  those  involved  in  making  the  ribbon  seal.  If  a  metal  disc  is  sealed
wholly  into  glass  the  edges  must  be  sharpened  or  the  glass  and  copper
break  away  from  each  other  as  in  the  case  of  the  ribbon  seal.

In  the  general  use  to  which  these  seals  are  put  there  is  no  necessity
for  having  the  glass  surround  the  circumference  of  the  copper  disc

and  the  necessity  for  sharpening  the  edge  is  obviated  by  allowing  the
glass  to  adhere  to  the  flat  portion  of  the  disc  only,  care  being  taken  to
prevent  its  flowing  around  the  edge.  It  is  necessary  to  have  a  ring
of  glass  on  both  sides  of  the  seal  in  order  to  equalize  the  bending  stresses

which  would  otherwise  tend  to  break  the  glass  and  copper  away  from
each  other.  Successful  disc  seals  have  been  made  with  copper  up  to
1-10"  thick.  There  is,  of  course,  a  certain  maximum  thickness  that
can  be  used  for  a  seal  of  a  given  diameter  and  it  is  preferable  to  keep
well  below  this  limit.

The  seals  shown  in  Fig.  4  close  the  ends  of  glass  tubes  to  the  other
ends  of  which  are  sealed  pilot  lamps  for  the  purpose  of  testing  the
vacuum.  Tubes  sealed  in  this  way  have  been  kept  a  number  of
years  without  any  impairment  of  the  vacuum.

The  third  type  of  seal  and  the  most  important  in  connection  with
the  present  problem  is  the  tube  seal  shown  in  Fig.  5.  This  furnishes
the  means  of  joining  metal  and  glass  tubes  end  to  end  and  is  used  in
the  water-cooled  tube  to  attach  the  anode  to  the  glass  cylinder  which

serves  to  insulate  the  other  tube  elements.  As  in  the  case  of  the
disc  seal,  it  can  be  made  either  with  the  edge  of  the  metal  not  in  con-
tact with  the  glass,  as  shown  at  A,  or  with  the  metal  sharpened  to  a
fine  edge  which  is  in  contact  with  the  glass.  The  glass  may  be
situated  either  inside  or  outside  of  the  metal,  see  B  and  C.

The  first  thermionic  tubes  in  which  these  seals  were  embodied  were
made  of. copper  and  were  designed  to  operate  at  10,000  volts  and  to
give  about  5  k.  w.  output.

A  photograph  of  one  of  these  tubes  is  shown  in  Fig.  6;  and  the
filament  grid  assembly  is  shown  in  Fig.  7.

The  anode  consists  of  a  copper  tube  1.5''  in  diameter  and  7.5  long.
A  copper  disc  is  wielded  to  one  end  forming  a  vacuum-tight  joint.
The  other  end  which  is  turned  down  to  a  knife  edge  is  fused  directly
to  a  glass  tube.

The  filament  grid  assembly  consists  of  two  lavite  discs  D  and  E,
spaced  b"  apart  by  a  seamless  steel  tube.  The  grid  F  is  made  in  the
form  of  a  helix,  and  is  held  in  position  by  allowing  the  ends  of  the  lon-
gitudinal wires,  to  which  the  turns  of  the  helix  are  welded,  to  pass
through  holes  in  the  lavite  blocks  D  and  E.  The  filament  G  is
mounted  between  hooks  fastened  to  the  lavite  blocks  and  is  kept
taut  by  the  springs  H.  The  grid  lead  is  shown  at  J,  and  the  filament
leads  at  K  K.  In  this  tube  platinum  seals  are  used  for  the  lead  wires.
The  use  of  the  springs  H  make  it  necessary  to  supply  the  filament
with  current  from  the  opposite  end  of  the  assembly  and  this  is  done
by  passing  the  current  through  the  steel  support  tube  and  returning
it  through  a  lead  passing  through  this  tube  and  insulated  from  it  by
a  quartz  tube.

The  whole  assembly  is  carried  by  two  supports  B  B.  These  sup-
ports are  welded  to  a  corrugated  nickel  collar  A  which  grips  the  glass
stem  C.

The  pumping  of  these  tubes  at  first  presented  considerable  difficulty,
chiefly  on  account  of  the  large  amount  of  occluded  gas  contained  by
the  metal  parts.  This  caused  the  time  of  pumping  of  the  tube  to  be
very  long  and  a  dangerous  warping  of  the  internal  structure  developed
owing  to  the  fact  that  during  exhaust  the  tube  elements  are  maintained
at  a  much  higher  temperature  than  they  are  subjected  to  during  nor-
mal operation.  The  trouble  was  overcome  by  heating  the  various
parts  of  the  tube  to  as  high  a  temperature  as  possible  in  a  vacuum
furnace,  prior  to  the  final  assembly,  and  thus  getting  rid  of  a  large
amount  of  the  occluded  gases.  The  anode  was  preheated  before
the  glass  seal  was  made  and  the  whole  filament  grid  assembly  was  pre-
heated just  before  it  was  mounted  on  the  glass  stem.  The  preheating
of  the  parts  brought  about  an  enormous  reduction  in  the  time  re-
quired for  pumping  and  gave  a  much  more  uniform  product.

Although  successful  from  the  standpoint  of  operation,  this  tube
had  several  undesirable  features  that  it  was  thought  well  to  eliminate.
In  the  first  place  the  welding  of  the  end  into  the  tube  was  not  particu-
larly desirable,  and  in  general  any  troubles  that  occurred  due  to  leaks
in  the  metal  could  be  traced  to  this  point.  Further,  in  the  assembly
of  the  tube  there  were  a  very  large  number  of  welds  to  be  made
which  constituted  points  of  weakness  at  the  high  temperature  neces-
sary for  the  evacuation  of  the  tubes.  It  was,  therefore,  decided  to
go  to  a  type  of  tube  in  which  the  anode  would  be  drawn  in  one  piece
and  in  which  as  many  welds  as  possible  would  be  eliminated  in  the
assembly  of  the  internal  elements.  At  the  same  time  it  was  considered
desirable  to  go  to  a  somewhat  larger  type  of  structure  in  which  high

tension  insulation  could  be  more  easily  provided  and  a  larger  tube
was,  therefore,  designed  capable  of  delivering  10  k.  w.  to  an  antenna
at  a  plate  voltage  of  10,000  volts.

The  anode  A  is  drawn  from  a  piece  of  sheet  copper  and  is  9"  long
and  2"  in  diameter.  The  copper  flare  B  is  turned  down  to  a  sharp
edge  and  a  glass  bulb  C  sealed  thereto.  The  grid  and  plate  assembly
is  shown  at  D.  The  structure  is  supported  by  four  molybdenum
rods,  which  are  threaded  and  secured  by  means  of  nuts  to  the  lavite
pieces  E  and  F.  The  filament  is  made  of  19.5"  of  .025  pure  tungsten
wire  purchased  from  the  General  Electric  Company  and  is  formed
and  secured  to  two  of  the  molybdenum  rods  at  G  and   H.     The

power  consumed  in  it  during  operation  is  .75  k.  w.  It  is  guided  by
the  hooks  J.  The  filament  leads  are  shown  at  K,  K  and  are  led
through  the  glass  by  the  copper  disc  seals  L,  L.     The  grid  is  a  molyb-

denum  helix  and  is  supported  by  the  molybdenum  rods  M  which  are
fixed  to  the  lavite  block  E  and  slide  on  the  outside  of  the  lavite  block
F.     The  whole  structure  is  mounted  on  the  flare  R  by  means  of  the

nickel  collar  N  and  the  support  rods  P.  The  grid  lead  is  brought
out  through  the  tube  Q.  The  tube  is  completed  by  sealing  together
the  flare  R  and  the  bulb  C.

In  this  tube  all  welds  except  those  in  the  collar  N  are  eliminated,
the  assembly  being  bolted  together.     The  drawing  of  the  anode  does

away  with  the  leaks  that  were  troublesome  in  the  older  tubes  and
the  manufacture  of  the  tube  can  be  carried  out  with  certainty.

With  this  tube  as  much  as  12  k.  w.  have  been  obtained  in  an  arti-
ficial antenna  working  at  12,000  volts.  This  power  was  obtained
at  a  frequency  of  600,000  cycles  corresponding  to  500  meters  wave
length.  The  difficulties  of  obtaining  this  amount  of  power  at  this
frequency  using  a  number  of  smaller  tubes  in  parallel,  are  obvious
to  anyone  who  is  acquainted  with  the  problem.  On  a  D.  C.  test  the
anode  w^as  found  to  be  capable  of  dissipating  26  k.  w\  when  cooled
with  water.

The  success  which  had  attended  the  development  of  a  tube  of  this
high  power  capacity  indicated  the  possibility  of  constructing  still
larger  tubes  and  it  was  decided  to  proceed  with  the  development  of  a
tube  capable  of  delivering  at  least  100  k.  w.  into  an  antenna.

The  development  proceeded  with  a  few  minor  alterations  along  the
lines  of  the  smaller  tube,  nominally  rated  at  10  k.  w.  and  the  100  k.  w.

tube  as  now  developed  is  shown  in  Figs.  10  and  11.  The  anode  which
is  made  of  a  piece  of  seamless  copper  tubing  closed  by  a  copper  disc
welded  into  the  end,  is  14"  long  and  3.5"  in  diameter.  The  filament  is
of  tungsten  and  is  .060"  in  diameter  and  63.5"  long.  The  current
required  to  heat  it  is  91  amperes  and  the  power  consumed  in  it  6  k.  w.

The  filament  leads  are  of  copper  red  one  eighth  of  an  inch  in  diameter
and  are  sealed  through  1"  copper  disc  seals.  The  grid  is  of  molyb-
denum and  is  wound  around  three  molybdenum  supports.

The  handling  of  the  parts  of  this  tube  during  manufacture  presents
a  task  of  no  mean  magnitude  and  numerous  fixtures  have  been  devised
to  assist  in  the  glass  working.  It  has  been  found  necessary  for  in-
stance to  suspend  the  anode  in  gimbals  during  the  making  of  the  tube
seal  owing  to  its  great  weight,  and  special  devices  have  been  made
to  hold  the  filament  grid  assembly  in  place  while  it  is  being  sealed  in,
otherwise  the  strains  produced  by  its  weight  cause  cracking  of  the  seal.

The  significance  of  this  development  in  the  radio  art  cannot  be
overestimated.  It  makes  available  tubes  in  units  so  large  that  only
a  very  few  would  be  necessary  to  operate  even  the  largest  radio  sta-
tions now  extant,  with  all  the  attendant  flexibility  of  operation  which
accompanies  the  use  of  the  vacuum  tube.

From  the  standpoint  of  wireless  telephony  the  development  of  these
high  power  tubes  gives  us  the  possibility  of  using  very  much  greater
amounts  of  power  than  have  ever  been  readily  available  before.  The
filaments  in  these  tubes  have  been  made  so  large  that  the  electron
emission  from  them  will  easily  take  care  of  the  high  peak  currents  ac-
companying the  transmission  of  modulated  power.

The  100  k.  w.  tube  by  no  means  represents  the  largest  tube  made
possible  by  the  present  development.  There  is  no  doubt  that  if  the
demand  should  occur  for  tubes  capable  of  handling  much  larger
amounts  of  power  they  could  be  constructed  along  these  same  lines.

Synopsis:  Direct  capacity,  direct  admittance  and  direct  impedance  are
defined  as  the  branch  constants  of  the  particular  direct  network  which  is
equivalent  to  any  given  electrical  system.  Typical  methods  of  measuring
these  direct  constants  are  described  with  especial  reference  to  direct  ad-
mittance; the  substitution  alternating  current  bridge  method,  due  to
Colpitts,  is  the  preferred  method,  and  for  this  suitable  variable  capacities
and  conductances  are  described,  and  shielding  is  recommended.  Propo.sed
methods  are  also  described  involving  the  introduction  of  electron  tubes
into  the  measuring  set,  which  will  reduce  the  measurement  to  a  single  setting
or  deflection.  This  gives  an  alternating  current  method  which  is  com-
parable with  Maxwell's  single  null-setting  cyclical  charge  and  discharge
method.  Special  attention  is  drawn  to  Maxwell's  remarkable  method
which  is  entirely  ignored  by  at  least  most  of  the  modern  text-books  and
handbooks.

THE  object  of  this  paper  is  to  emphasize  the  importance  of  direct
capacity  networks;  to  explain  various  methods  of  measuring
direct  capacities;  and  to  advocate  the  use  of  the  Colpitts  substitution
method  which  has  been  found  preeminently  satisfactory  under  the
wide  range  of  conditions  arising  in  the  communication  field.

About  thirty  years  ago  telephone  engineers  substituted  the  so-
called  "  mutual  capacity  "  measurement  for  the  established  "  grounded
capacity  "  measurement;  this  was  a  distinct  advance,  since  the  trans-
mission efficiency  is  more  closely  connected  with  mutual  capacity
than  with  grounded  capacity.  Mutual  capacity,  however,  can  give
no  information  respecting  crosstalk,  and  accordingly,  about  twenty
years  ago,  I  introduced  the  measurement  of  "  direct  capacity  "
which  enabled  us  to  control  crosstalk  and  to  determine  more  com-
pletely how  telephone  circuits  will  behave  under  all  possible  con-
nections.

For  making  these  direct  capacity  measurements  alternating  cur-
rents of  telephone  frequencies  were  introduced  so  as  to  determine
more  exactly  the  effective  value  of  the  capacity  in  telephonic  trans-
mission, and  to  include  the  determination  of  the  associated  effective
direct  conductances  which  immediately  assumed  great  importance
upon  the  introduction  of  loading.

Telephone  cables  and  other  parts  of  the  telephone  plant  present
the  problem  of  measuring  capacities  which  are  quite  impossible  to
isolate,  but  which  must  be  measured,  just  as  they  occur,  in  associa-
tion with  other  capacities;  and  these  associated  capacities  may  be
much   larger  than   the  particular  direct  capacity  which  it  is  neces-

1  This  article  is  also  appearing  in  the  August  issue  of  the  Journal  of  the  Optical
Society  of  America  and  Review  of  Scientific  Instruments.  An  appendix  is  added  here
giving  proofs  of  the  mathematical  results.

sary  to  accurately  measure,  and  have  admittances  overwhelmingly
larger  than  the  direct  conductance,  which  is  often  the  most  important
quantity.  This  is  the  interesting  problem  of  direct  capacity  measure-
ment, and  distinguishes  it  from  ordinary  capacity  measurements
where  isolation  of  the  capacity  is  secured,  or  at  least  assumed.

The  substitution  alternating  current  bridge  method,  suggested  to
me  in  1902  by  Mr.  E.  H.  Colpitts  as  a  modification  of  the  potentiometer
method,  has  been  in  general  use  by  us  ever  since  in  all  cases  where
accuracy  and  ease  of  manipulation  are  essential.

After  first  defining  direct  capacities  and  describing  various  methods
for  measuring  them,  this  paper  will  explain  how  this  may  all  be  general-
ized so  as  to  include  both  the  capacity  and  conductance  components
of  direct  admittances,  and  the  inductance  and  resistance  components
of  direct  impedances.

It  is  a  familiar  fact  that  two  condensers  of  capacities  Ci,  Ci,  when
in  parallel  or  in  series,  are  equivalent  to  a  single  capacity  (Ci  +  d)
or  Ci  C-i.l{C\  -f  C2),  respectively,  directly  connecting  the  two  terminals.
These  equivalent  capacities  it  is  proposed  to  call  direct  capacities.
The  rules  for  determining  them  may  be  stated  in  a  form  having  general
applicability,  as  follows:

Rule  I.  The  direct  capacity  which  is  equivalent  to  capacities  in
parallel  is  equal  to  their  sum.

Rule  2.  The  direct  capacity  between  two  terminals,  which  is
equivalent  to  two  capacities  connecting  these  terminals  to  a  con-
cealed branch-point,  is  equal  to  the  product  of  the  two  capacities
divided  by  the  total  capacity  terminating  at  the  concealed  branch-
point, i.e.,  its  grounded  capacity.

These  rules  may  be  used  to  determine  the  direct  capacities  of  any
network  of  condensers,  with  any  number  of  accessible  terminals  and
any  number  of  concealed  branch-points.  Thus,  all  concealed  branch-
points may  be  initially  considered  to  be  accessible,  and  they  are  then
eliminated  one  after  another  by  applying  these  two  rules;  the  final
result  is  independent  of  the  order  in  which  the  points  are  taken;  all
may,  in  fact,  be  eliminated  simultaneously  by  means  of  determinants^;
a  network  of  capacities,  directly  connecting  the  accessible  terminals,
without  concealed  branch-points  or  capacities  in  parallel,  is  the  final
result.  Fig.  1  shows  the  two  elementary  cases  of  direct  capacities
and  also,  as  an  illustration  of  a  more  complicated  system,  the  bridge

circuit,  with  three  corners  1,  2,  3  assumed  to  be  accessible,  and  the
fourth  inaccessible,  or  concealed.  Generalizing,  we  have  the  following
definition:

The  direct  capacities  of  an  electrical  system  with  n  given  accessible
terminals  are  defined  as  the  n{n  —  i)  /2  capacities  which,  connected
between  each  pair  of  terminals,  will  be  the  exact  equivalent  of  the  system,
in  its  external  reaction  upon  any  other  electrical  system  with  which  it  is
associated  only  by  conductive  connections  through  the  accessible  terminals.

The  total  direct  capacity  between  any  group  of  the  terminals  and  all
of  the  remaining  accessible  terminals,  connected  together,  is  called
the  grounded  capacity  of  the  group.

This  definition  of  direct  capacity  presents  the  complete  set  of  direct
capacities  as  constituting  an  exact,  symmetrical,  realizable  physical
substitute  for  the  given  electrical  system  for  all  purposes,  including
practical  applications.  Direct  capacities  are  Maxwell's  "  coefificients
of  mutual  induction,"  but  with  the  sign  reversed,  their  number  being
increased  so  as  to  include  a  direct  capacity  between  each  pair  of
terminals.

In  considering  direct  capacities  we  exclude  any  direct  coupling,
either  magnetic  or  electric,  from  without  with  the  interior  of  the
electrical  system,  since  we  have  no  concern  with  its  internal  structure;
we  are  restricted  to  its  accessible,  peripheral  points  or  terminals;
some  care  has  been  taken  to  emphasize  this  in  the  wording  of  the
definition.

Connecting  a  capacity  between  two  terminals  adds  that  capacity
to  the  direct  capacity  between  these  terminals,  and  leaves  all  other
direct  capacities  unchanged.  Connecting  the  terminals  of  two  distinct
electrical  systems,  in  pairs,  gives  a  system  in  which  each  direct  capacity
is  the  sum  of  the  corresponding  two  direct  capacities  in  the  individual
systems.  Joining  two  terminals  of  a  single  electrical  system  to  form
a  single  terminal  adds  together  the  two  direct  capacities  from  the  two
merged  terminals  to  any  third  terminal,  and  leaves  all  other  direct
capacities  unchanged,  with  the  exception  of  the  direct  capacity
between  the  two  merged  terminals,  which  becomes  a  short  circuit.
Combining  the  terminals  into  any  number  of  merged  groups  leaves
the  total  direct  capacity  between  any  pair  of  groups  unchanged,  and
short-circuits  all  direct  capacities  within  each  group.

These  several  statements  of  the  additive  property  of  direct  capaci-
ties show  the  simple  manner  in  which  direct  capacities  are  altered
under  some  of  the  most  important  external  operations  which  can  be
made  with  an  electrical  network,  and  explain,  in  part,  the  preeminent
convenience  of  direct  capacity  networks.

Since  the  additive  property  of  direct  capacities  is  sufficient  for
explaining  the  different  methods  of  measuring  direct  capacities  we
may  now,  without  further  general  discussion  of  direct  capacities,  pro-
ceed to  the  description  of  the  more  important  methods  of  measurement.

The  unknown  direct  capacity  is  shifted  from  one  side  of  the  bridge
to  the  other,  and  the  balance  is  restored  by  adjusting  the  capacity
standard  so  as  to  shift  back  an  equal  amount  of  direct  capacity.
The  method  is  therefore  a  substitution  method,  and  the  value  of  the
bridge  ratio  is  not  involved.  Both  the  standard  and  the  unknown
remain  in  the  bridge  for  both  settings,  so  that  the  method  involves
transposition  rather  than  simple,  ordinary  substitution.

Details  of  the  method  as  shown  by  Fig.  2  are  as  follows :  To  measure
the  direct  capacity  Cn  between  terminals  1  and  2  connect  one  terminal
(1)  to  corner  5*of  the  bridge,  and  adjust  for  a  balance  with  the  other
terminal  (2)  on  corner  (^  and  then  on  (?,  while  each  and  every  one  of
the  remaining  accessible  terminals  (3,  4,  .  .  .  )  of  the  electrical  system
is  permanently  connected  during  the  two  adjustments  to  either  corner
<^or  (?.  If  the  direct  capacities  in  the  standard  condenser  between
corners  CF  and  S)  are  C,  C"  in  the  two  balances,

where  C^  is  the  standard  condenser  reading  when  the  bridge  alone
is  balanced.

Two  settings  are  required  by  this  method  for  an  individual  direct
capacity  measurement,  but  in  the  systematic  measurement  of  all  the
direct  capacities  in  a  system  the  total  number  of  settings  tends  to
equal  the  total  number  of  capacities,  when  this  number  becomes  large.
The  number  of  settings  may  always  be  kept  equal  to  the  number  of
capacities  by  employing  an  equality  bridge  ratio,  and  using  the  ex-
pression for  the  direct  capacity  difference  given  above.  The  same
remarks  also  hold  for  the  group  of  direct  capacities  connecting  any
one  terminal  with  all  the  other  terminals.

In  general,  ground  is  placed  upon  corner  C  of  the  bridge,  but  is
transferred  to  corner  2),  if  it  is  connected  to  one  terminal  of  the  re-
quired direct  capacity.  The  arbitrary  distribution  of  the  other
terminals  between  corners  <^  and  (?  may  be  used  to  somewhat  control
the  amount  of  standard  capacity  required;  or  it  may  be  helpful  in
reducing  interference  from  outside  sources,  when  tests  are  made  upon
extended  circuits.  The  grounded  capacity  of  a  terminal  or  group  of
terminals  is  measured  by  connecting  the  group  to  (?,  and  all  of  the
remaining  terminals  together  to  2).

The  excess  of  one  direct  capacity  C\2  over  another  Cm  is  readily
determined  by  connecting  terminals  1  and  5  to  corner  ^,  terminals
3,  4,  7,  8,  .  .  .  to  corner  ^''or  d*,  and  then  balance  with  terminals  2
and  6  on  ^  and  C^,  respectively,  and  repeat,  with  their  connections
reversed.

The  required  direct  capacity  C12  is  balanced  against  one  of  its
associated  direct  capacities,  augmented  by  a  standard  direct  capacity

C ,  and  the  measurement  is  repeated  with  the  required  direct  capacity
and  standard  interchanged.  Let  R\  R"  be  the  resistances  required
in  arm  (?^  o[  the  bridge  for  the  first  and  second  balance,  then,  5
being  the  total  slide  wire  resistance  and  G\  the  grounded  capacity
of  terminal  1:*

This  ratio  method  requires  for  the  bridge  a  variable  or  slide  wire
resistance  and  a  constant  condenser,  and  it  may  be  employed  as  an
improvised  bridge,  when  sufficient  variable  capacity  is  not  available
for  the  Colpitts  method.     Not  being  a  substitution  method,  however,

greater  precautions  are  necessary  for  accurate  results.  There  must
be  no  initial  direct  capacity  in  arm  CS),  or  a  correction  will  be  re-
quired. Possibly  variable  capacity  ratio  arms  would  be  preferable
to  resistances.

Assuming  that  the  electron  tube  supplies  the  means  of  obtaining
an  invariable  true  negative  resistance,  Fig.  4  shows  a  method  which
determines  any  individual  direct  capacity  from  a  single  bridge  setting.
The  bridge  arms  are  replaced  by  a  Y  network  made  up  of  two  resist-

ances  R,  R  and  a  negative  resistance  —  R/2;  the  Y  has  then  a  null-
impedance  between  corner  ^  and  corners  ^,  (?  connected  together^.
The  three  terminals  1,  2,  3  of  the  network  to  be  measured  are  con-
nected to  corners  2),  6^,  6B  and  a  balance  obtained  by  adjusting  the
variable  standard  condenser  C .  Then  di  =  C  regardless  of  the
direct  capacities  associated  with  Cn  and  C\  since  these  capacities
either  are  short-circuited  between  corners  SB,  (2  ox  ^,(?  or  are  between
corners  58,  S)  and  thus  outside  of  the  bridge.

Correct  adjustment  of  the  negative  resistance  may  be  checked  by
observing  whether  there  is  silence  in  telephone  Ti  after  the  balance
has  been  obtained.  Assuming  invariable  negative  resistance,  this
test  need  be  made  only  when  the  bridge  is  set  up,  or  there  is  a  change
in  frequency.  The  bridge  may  be  given  any  ratio  Z1/Z2  by  employing
a  Y  made  up  of  impedances  Zi,  Z2,  and  —  Zi  Z2/(Zi  +  Z2).

Connect  the  terminals  between  which  the  direct  capacity  C12  is
required,  to  A,  B  and  the  remaining  accessible  terminals  of  this
electrical  system  to  D.  The  adjustable  standard  capacity  is  C  and
any  associated  direct  capacities  in  this  standard  are  shown  as  C",

C".  If  C\2  is  a  direct  capacity  to  ground,  interchange  C  and  C12.
Balancing  involves  the  following  repeated  cycle  of  operations:

1.  Make  connections  1,  2,  3  and  7  for  an  instant  (thus  charging
C12,  Ci3,  C",  C  and  discharging  the  electrometer).

2.  Make  connections  4,  5  and  then  6  (to  discharge  condensers  C13,
C" ,  mix  charges  of  C12,  C  with  polarities  opposed  and  connect
electrometer).

3.  Adjust  C  to  reduce  the  electrometer  deflection  when  the  cycle
is  again  repeated.

When  a  null  deflection  is  obtained  Cn  =  C;  the  required  direct
capacity  is  equal  to  the  standard  direct  capacity  irrespective  of  the
magnitudes  of  the  four  associated  direct  capacities.  If  all  capacities
are  free  of  leakage  and  absorption,  this  remarkable  method  accurately
compares  two  direct  capacities  by  means  of  a  single  null  setting,  and
it  requires  the  irreducible  minimum  amount  of  apparatus.

This  is  defined  as  the  direct  capacity  between  two  given  terminals
with  all  other  terminals  left  floating  and  ignored,  after  a  hypothetical
redistribution  of  the  total  direct  capacity  from  the  given  pair  of
terminals  to  every  third  terminal  which  balances  the  two  sides  of  the
pair.  The  balanced-terminal  capacity,  as  thus  defined,  is  equal  to
the  direct  capacity  between  the  pair  augmented  by  one-quarter  of

the  grounded  capacity  of  the  pair,  neither  of  which  is  changed  by  the
assumed  method  of  balancing.

As  illustrated  in  Fig.  6,  terminals  1,  2  are  the  given  pair  and  terminal
3  includes  all  others,  assumed  to  be  connected  together.  A  bridge
ratio  of  unity  is  employed,  and  the  entire  bridge  is  shielded  from
ground  with  the  exception  of  corners  (?,  2)  which  are  initially  balanced

Fig.  6 — Bridge  for   Determining   Hypothetical   Capacity   Between   Two  Terminals
with  Other  Terminals  Balanced  and  Ignored

to  ground  within  the  range  of  variable  condenser  /.  The  following
two  successive  balances  are  made:

1.  With  contacts  a,  a'  closed  and  h  open,  balance  is  secured  by
varying  condenser  /  (the  total  capacity  of  which  is  constant)
giving  the  reading  C  for  its  direct  capacity  in  parallel  with
terminals  1,  3.

2.  With  contacts  a,  a'  open  and  h  closed,  balance  is  obtained  by
varying  condenser  //,  obtaining  the  reading  C"  for  its  direct
capacity  in  (S'2).

If  Co,  C'l  are  the  corresponding  readings  without  the  network,  the
balanced-terminal  capacity  C\,  and  the  grounded  capacity  unbalance
of  the  given  pair  of  terminals  are:^

Any  failure  to  afljust  condenser  /  to  perfectly  balance  the  given
pair  of  terminals  will  decrease  the  measured  capacity  Ce,.  This  fact
may  be  utilized  to  measure  the  capacity  with  the  second  bridge  ar-
rangement alone  (contacts  a,  a'  open  and  b  closed)  by  adjusting  con-
denser /  so  as  to  make  the  reading  C"  of  condenser  II  a  maximum.
This  procedure  presents  no  difficulty,  since  the  correct  setting  for
condenser  /  lies  midway  between  its  two  possible  settings  for  a  balance
with  any  given  setting  of  condenser  //;  furthermore,  C"  is  not  sensi-
tive to  small  deviations  from  a  true  balance  in  C.

Balanced-terminal  capacity  is  of  practical  importance  as  a  measure
of  the  transmission  efficiency  to  be  expected  from  a  metallic  circuit,
if  it  is  subsequently  transposed  so  as  to  balance  it  to  every  other
conductor.  In  practice,  when  the  unbalance  of  the  section  of  open
wire  or  cable  pair,  which  is  being  measured,  is  relatively  small,  it  is
sufficient  to  set  condenser  /,  once  for  all,  to  balance  the  bridge  itself
and  ignore  the  unbalance  of  the  pair.  This  favors  an  unbalanced
pair,  however,  by  the  amount  [Gi  —  GiY/^  {On  -f  Geo)  where
Gi2  +  GcD  is  the  grounded  capacity  of  the  pair  augmented  by  that
of  the  bridge.^  For  rapid  working,  condenser  II  is  graduated  to  read
2C"  and  by  auxiliary  adjustment  Cg  is  made  zero,  so  that  the  re-
quired capacity  is  read  directly  from  the  balance.

Measurement  of  the  capacity  between  the  terminals,  taken  in
pairs  with  all  the  remaining  terminals  left  insulated  or  floating,  gives
n(n  —  l)/2  independent  results,  from  which  all  the  direct  capacities
may  be  derived  by  calculation  of  certain  determinants^.  Practically,
however,  we  are  in  general  interested  in  determining  individual  direct
capacities  from  the  smallest  possible  number  of  measurements,  and
the  first  step  is  naturally  to  connect  all  of  the  remaining  conductors
together,  so  as  to  reduce  the  system  to  two  direct  capacities  in  addi-
tion to  the  one  the  value  of  which  is  required.  Three  measurements
are  then  the  maximum  number  required,  and  we  know  that  two,  or
even  one,  is  sufficient  if  particular  devices  are  employed.

The  three  measurement  method  of  determining  direct  capacities
from  the  grounded  capacities  of  the  two  terminals  taken  separately
Gi,  Gi,  and  together  G12,  is  given  by  Maxwell.'"  If  d  =  €',  Gn  =
a  +  C\  and  G2  =  C"  +  C"\

which  indicates  a  method  by  which  large  grounded  capacities  can  be
balanced  against  three  variable  capacities,  only  one  of  which  need  be
calibrated,  and  that  one  need  be  no  larger  than  the  required  direct
capacity.

Two-setting  methods,  as  illustrated  by  the  Colpitts  and  potentio-
meter methods,  rest  upon  the  possibility  of  connecting  one  of  the
associated  direct  capacities  between  opposite  corners  of  the  bridge
where  it  is  without  influence  on  the  balance,  and  not  altering  any
associated  direct  capacity  introduced  into  the  working  arms  of  the
bridge.  Numerous  variations  of  these  methods  have  been  considered
which  may  present  advantages  under  special  circumstances.  Thus,
if  conductors  1,  2,  3  of  Fig.  7  are  in  commercial  operation,  and  it  is
not  permissible  to  directly  connect  two  of  them  together,  a  double
bridge  might  be  employed  with  a  testing  frequency  differing  from

that  of  operation.  A  telephone  is  shown  for  each  ear,  and  a  constant
total  direct  capacity  is  divided  between  the  three  branches  in  the
proportion  required  to  silence  both  telephones.

One-setting    methods    attained    ideal    simplicity    in    the    Maxwell
discharge  method,  but  we  found  it  necessary  to  use  alternating  current

methods,  and  here  negative  resistances  make  a  one-setting  method
at  least  theoretically  possible,  as  explained  above.  Of  possible  varia-
tions it  will  be  sufficient  to  refer  to  the  ammeter  method  Fig.  8.    Termi-

nals  1  and  2  of  the  required  direct  capacity  Cn  are  connected  to  the
voltmeter  and  ammeter  terminals,  respectively,  and  all  other  terminals
go  to  the  junction  point  at  3.     Then

provided  the  ammeter  actually  has  negligible  impedance.  The
method  is  well  adapted  for  rapid  commercial  testing.  The  ammeter
impedance  may  be  reduced  to  zero  by  a  variable  negative  impedance
device  (  —  Z),  adjusted  to  reduce  the  shunted  telephone  to  silence.

In  the  discussion  of  the  bridge,  it  has  been  assumed  that  the  several
pieces  of  apparatus  forming  the  six  branches  of  the  bridge  have  no
mutual  electrical  or  magnetic  reaction  upon  each  other,  except  as
indicated.  In  general,  however,  a  balance  will  be  upset  by  changes
in  position  of  the  pieces  of  apparatus,  or  even  by  movements  of  the
observer  himself,  whereas  these  motions  cannot  affect  any  of  the
mutual  reactions  which  have  been  explicitly  considered.  The  skillful
experimenter,  understanding  how  these  variations  are  produced  by
the  extended  electric  and  magnetic  fields,  will  anticipate  this  trouble
and  take  the  necessary  precautions,  possibly  without  slowing  down  his
rate  of  progress.

Where  hundreds  of  thousands  of  measurements  are  to  be  made,
however,  substantial  savings  are  effected  by  arranging  the  bridge  so
that  reliable  measurements  can  be  made  by  unskilled  observers,  and
here  it  is  necessary  to  shield  the  bridge  so  that  any  possible  movements
of  the  observer  and  of  the  apparatus  will  not  affect  the  results.  Mag-
netic fields  of  transformers  are  minimized  by  using  toroidal  coils
with  iron  cases.     Electrostatic  fields  are  shielded  by  copper  cases;

the  principles  of  shielding  were  explained  in  an  earlier  paper /^  Fig.  13
of  that  paper  showing  the  complete  shielding  of  the  balance  as  con-
structed for  the  measurement  of  direct  capacity  by  the  Colpitts
method.  Over  five  million  capacity  and  conductance  measurements
have  been  made  with  the  shielded  capacity  and  conductance  bridge
and  in  a  forthcoming  paper  Mr.  G.  A.  Anderegg  will  give  details  of
actual  construction  of  apparatus  and  of  methods  of  operation  as  well
as  some  actual  representative  results.

For  simplicity,  the  preceding  definitions  and  methods  of  measure-
ment have  been  described  in  terms  of  capacity,  but  everything  may  be
generalized,  with  minor  changes  only,  for  the  definition  and  measure-
ment of  direct  admittances  with  their  capacity  and  conductance
components.  The  essential  apparatus  change  is  the  addition,  in
parallel  with  the  variable  capacity  standards  employed,  of  a  variable
conductance  standard,  which  shifts  direct  conductance  from  one  side
of  the  bridge  to  the  other,  without  changing  the  total  reactance  and
conductance  in  the  two  sides  of  the  bridge.  This  may  be  practically
realized  in  a  great  variety  of  ways  as  regards  details,  which  it  will
suffice  to  illustrate  by  Fig.  9,  where  C ,  C" ,  C" ,  G' ,  G",  indicate  the

pig_  9 — Variable  Direct  Conductance  and  Capacity  Standard  for  Direct  Admittance

continuously  variable  capacity  and  conductance  standards  with
enough  step-by-step  extensions  to  secure  any  desired  range.

For  the  continuously  variable  conductance  standard  a  slide  wire  is
represented,  with  a  slider  made  up  of  two  hyperbolic  arcs  so  pro-
portioned that,  as  the  slider  is  moved  uniformly  in  a  given  oblique
direction,  conductance  is  added  uniformly  on  the  left  and  just  enough
of  the  wire  is  short-circuited  to  produce  an  equal  conductance  de-
crease on  the  other  side.  The  arcs  are  portions  of  the  hyperbola
xy  =  (L^  —  5^)74,  where  L,  S  are  the  total  length  of  the  wire  and  of
the  portion  to  be  traversed  by  the  slider,  and  the  coordinate  axes  are

the  slide  wire  and  the  direction  of  the  motion  of  the  slider  as  oblique
asymptotic  axes.'^  L  =  GS/g  =  4  G/p(G^  —  g^),  where  G  is  the
total  conductance  and  {G  =*=  g)/2  the  limiting  direct  conductance  on
either  side.

If  an  ordinary  slider  replaces  the  hyperbolic  arc  slider,  and  the
scale  reading  is  made  non-uniform  so  as  to  give  one-half  of  the  differ-
ence between  the  direct  conductances  C?  to  3)  and  C  to  3),  the  con-
ductance standard  will  still  give  absolutely  correct  results  with  the
Colpitts  method,  provided  the  bridge  ratio  is  unity.  This  simplifica-
tion in  connection  with  the  balancing  capacity  /  of  Fig.  6  would,
however,  not  be  strictly  allowable.  For  improvised  testing  we  have
found  it  sufficient  to  use  two  equal  resistances  {R)  with  a  dial  re-
sistance {r)  in  series  with  one  of  them,  and  take  the  defect  of  con-
ductance introduced  by  the  dial  resistance  as  equal  to  r/F?  or  to
10~2r,  10~V,  r,  micromho  according  as  R  was  made  10000,  3162,
or  1000  ohms. 13

For  a  step-by-step  conductance  standard.  Fig.  9  shows  a  set  of
10  equal  resistances,  connected  in  series  between  corners  ^,  (?,  to
the  junction  points  of  which  there  is  connected  a  parabolic  fringe  of
resistances,  the  largest  of  which  is  2.5  times  each  of  the  ten  resistances.
With  this  arrangement  the  direct  conductance  in  CFS)  may  be  ad-
justed by  ten  equal  steps,  beginning  with  zero,  whi'e  the  conductance
in  (?2)  is  decreased  by  equal  amounts  to  zero.  The  total  res'stance
required  for  this  conductance  standard  's  only  21/25  of  the  res'stance
required  to  make  a  single  isolated  conductance  equal  to  one  of  the
ten  conductance  steps;  the  ratio  may  be  reduced  to  1/2  by  doubl  ng
the  number  of  contacts, ^^  and  using  onsfringe  resistance  for  all  posi-
tions. Resistance  may  be  still  further  economized  by  using  as  high  a
total  conductance  as  is  permissible  in  the  bridge,  and  securing  the
required  shift  in  conductance  from  a  small  central  portion  of  the
parabolic  fringe.

Fig.  9  shows  the  variable  capacity  standards  as  well  as  the  variable
conductance  standards  and  a  few  practical  points  connected  with  the
capacity  standards  may  be  mentioned  here.

The  revolving  air  condenser  standard  has  two  fixed  plates  connected
to  <^  and  (?,  so  that  the  capacity  will  increase  as  rapidly  on  one  side
as  it  decreases  on  the  other  side.  Since  perfect  constancy  of  the  total
capacity  is  not  to  be  expected,  on  account  of  lack  of  perfect  mechanical
uniformity,    the   revolving   condenser   should    be   calibrated    to    read

one-half  of  the  difference  between  the  capacities  on  the  two  sides,  as
explained  above  in  connection  with  conductance.  The  capacity
sections  employed  to  extend  the  range  of  the  revolving  condenser
include  both  air  condensers  C  and  mica  condensers  C" ,  the  latter
being  calibrated  by  means  of  the  air  condensers  and  the  conductance
standard.

A  novel  feature  of  our  standard  air  condensers  is  a  third  terminal
called  the  leakage  terminal,  and  indicated  at  L  in  Figs.  4,  9.  Attached
to  it  are  plates  so  arranged  that  all  leakages  either  over,  or  through,
the  dielectric  supports  from  either  of  the  two  main  terminals,  must
pass  to  the  leakage  terminal.  There  can  be  no  leakage  directly
from  one  of  the  main  terminals  to  the  other.  There  is  thus  no  phase
angle  defect  in  the  standard  direct  capacity  due  to  leakage,  and  that
due  to  dielectric  hysteresis  in  the  insulating  material  is  reduced  to  a
negligible  amount  by  extending  the  leakage  plates  beyond  the  dielec-
tric, so  as  to  intercept  practically  all  lines  of  induction  passing  through
any  support.  This  leakage  terminal  is  connected  to  corner  C  of  the
bridge;  in  the  revolving  condensers,  it  is  one  of  the  fixed  plates.

The  reciprocal  of  a  direct  admittance  is  naturally  termed  a  direct
impedance;  substituting  impedance  for  capacity,  the  definition  of
direct  capacity,  given  above,  becomes  the  definition  of  direct  im-
pedance. The  complete  set  of  ciirect  impedances  constitutes  an  exact,
symmetrical,  physical  substitute  for  any  given  electrical  system.
Direct  impedances  are  often,  in  whole  or  in  part,  the  most  convenient
constants  since  many  electrical  networks  are  made  up  of,  or  ap-
proximate to,  directly  connected  resistances  and  inductances.  To
make  direct  impedance  measurements  which  will  not  involve  the
calculation  of  reciprocals,  we  naturally  employ  inductance  and  re-
sistance standards  in  series,  the  associated  direct  impedances  being
eliminated  as  with  direct  capacities.

It  has  been  necessary  to  preface  the  description  of  methods  of
measuring  direct  capacities  by  definitions  and  a  brief  discussion,  since
direct  capacities  receive  but  scant  attention  in  text-books  and  hand-
books. By  presenting  direct  capacities,  direct  admittances,  and
direct  impedances  as  alternative  methods  of  stating  the  constants  of
the  same  direct  network,  employed  as  an  equivalent  substitute  for
any  given  electrical  system,  it  is  believed  the  discussion  and  measure-

merit  of  networks  has  been  simplified.  In  another  paper  the  terminol-
ogy for  admittances  and  impedances  will  be  still  further  considered,
together  with  their  analytical  correlation.

In  explaining  the  different  methods  of  measuring  direct  capacities
it  is  necessary  to  start  with  a  clear  idea  of  what  direct  capacities  are,
and  to  make  use  of  the  additive  property,  but  it  is  not  necessary  to
go  into  any  comprehensive  discussion  of  direct  capacities.  Accord-
ingly, the  mathematical  treatment  of  direct  capacities  has  been  reserved
for  another  paper,  but  it  seems  desirable  to  append  to  the  present
paper  proofs  of  the  analytical  results  given  in  this  paper,  since  the
method  of  approach  giving  the  simplest  proof  is  not  always  perfectly
obvious.

(1)  Reducing  the  number  of  terminals  which  are  considered
accessible,  by  ignoring  terminals  p,  q,  r,  .  .  .  ,  changes  the  direct  and
grounded  capacities  from  (Qy,  G,)  to  (Qj ,  G,'),  the  latter  being  ex-
pressed in  terms  of  the  former  as  follows:

To  check  these  formulas  note  that  on  substituting  (G,-,  —  Gy)  for
Maxwell's  (9,-,-,  qij)  in  his  equations  (18)'*  the  coefficients  form  an
array  in  which  the  grounded  capacity  G,-  is  the  ith  element  in  the  main
diagonal  and  —  Cij  is  the  element  at  the  intersection  of  row  i,  column
j.  The  array  may  be  supposed  to  include  every  terminal  symmetrically
by  considering  the  earth's  potential  as  being  unknown  and  writing
down  the  redundant  equation  for  the  charge  on  the  earth.  Let  the
charge  be  zero  on  terminal  j  and  on  all  concealed  terminals;  let  there
be  a  charge  on  terminal  i  and  an  equal  and  opposite  charge  on  all  the
remaining  accessible  terminals,  connected  together  to  form  a  single
terminal  k.     Now  taking  the  potential  of  j  as  the  zero  of  reference

and  calculating  the  potentials  of  i  and  k  and  then  allowing  the  direct
capacity  between  j  and  k  to  become  infinite,  the  direct  capacity
between  terminals  i  and  j  is  dj  =  —  Lim  {Qk  Vk  /Vi).  This  gives
the  above  formula  for  C,-^,  with  —  C„-  as  a  special  case.  This  method
is  an  electrostatic  counterpart  of  the  ammeter  method  shown  in
Fig.  8  on  page  29.

If  there  is  but  one  ignored  terminal  the  determinant  solution  takes
on  a  simple  form  from  which  Rules  1  and  2  and  Fig.  1  may  be  checked.

If  all  but  two  terminals  are  ignored  the  equivalent  direct  network
is  reduced  to  a  single  direct  capacity.  When,  for  each  pair  of  termi-
nals, this  capacity  dj  is  known,  from  measurements  or  from  calcu-
lations, the  direct  capacities  between  the  terminals  may  be  derived
by  means  of  the  following  formulas

where  Dij  is  the  cofactor  of  the  element  in  row  i  column  j  of  the
determinant

which  has  zeros  in  the  main  diagonal,  a  border  of  ones  in  the  last
row  and  column,  while  the  other  elements  are  5^  =  1/C,-,-,  that  is,
the  reciprocals  of  the  given  capacities.  The  5's  form  a  complete
symmetrical  system  of  network  constants;  Maxwell's  coefficients  of
potential  pa  with  the  two  sufifixes  the  same  are  the  same  quantities,
but  he  employs  only  those  coefificients  of  this  type  which  are  associ-
ated with  the  earth,  his  system  being  completed  by  adding  the  co-
efficients with  different  suffixes.  By  starting  with  Maxwell's  results
the  above  formula  may  be  deduced,  but  more  direct  proofs,  both
physical  and  mathematical,  will  be  given  in  the  theoretical  paper
referred  to  at  the  end  of  the  present  paper.

The  purpose  of  this  section  of  the  appendix  is  achieved  if  the  de-
terminant solutions  are  made  so  clear  as  to  be  available  for  use  in
any  particular  case.

(2)  Starting  with  the  bridge  alone  balanced  at  reading  C**  the  other
two  settings  involve,  in  the  capacity  standard,  increases  in  the  direct

capacity  on  the  left  of  (C  —  C°)  and  (C"  —  C°),  with  equal  decreases
on  the  right.     Therefore

(3)  The  condition  of  equal  impedance  ratios  on  the  two  sides,  as
required  for  a  balance,  gives,  for  both  the  switches  up  and  down,

(4)  The  Y  of  Fig.  4  has  unusual  properties  because  the  total
conductance  connecting  the  concealed  branch-point  of  the  Y  to  the
three  bridge  corners  ^,  ^,  (?  is  zero.  Thus  the  conductance  between
any  one  corner  and  the  remaining  two  corners  joined  together  is  infinite,
or  in  other  words,  the  Y  acts  as  a  short  circuit  under  all  these  three
conditions.  On  the  other  hand,  if  corner  ^,  ^,  or  (F  is  left  floating
and  ignored  the  conductance  between  the  other  two  corners  is  2/R,
1/2R  or  2/R,  respectively,  and  the  Y  is  not  a  short  circuit.  These
statements  are  verified  at  once  by  applying  the  familiar  expressions
for  resistances  in  parallel  and  in  series.

On  account  of  the  unusual  behavior  of  the  Y,  even  when  taken
alone,  it  is  not  immediately  apparent  how  it  will  affect  the  operation
of  the  bridge  of  Fig.  4  with  direct  capacities  between  corners  ^S^
and  S^C  For  this  reason  it  is  highly  desirable  to  find  an  equivalent
network  the  behavior  of  which  is  more  readily  comprehended.  It  is
not  feasible  to  employ  the  delta  network  which  is  equivalent  to  the

Y  for  this  has  indeterminate  characteristics,  being  made  up  of  three
infinite  conductances,  only  two  of  which  have  the  same  sign.  We
may,  however,  make  use  of  the  Y  which  is  equivalent  to  the  original

Y  and  direct  capacities  C^b  and  Cbc  taken  together.  This  is  found  as
follows:  Any  admittance  delta  may  be  replaced  by  a  star  having  ad-
mittances equal  to  the  sum  of  the  products  of  the  delta  admittances
taken  in  pairs  divided  by  the  opposite  delta  admittance.  Applied  to  the
delta  of  Fig.  1,  we  find  that  the  star  that  is  equivalent  has  the  capacities

which,  upon  substituting  the  value  of  d,  is  the  sum  of  16  terms,  each
of  which  is  the  product  of  three  capacities,  every  combination  of  three
capacities  being  included  except  the  four  cases  in  which  the  three
capacities  would  form  a  closed  circuit.  By  allowing  the  capacities
to  be  complex  quantities,  any  admittances  are  covered  by  the  formulas.
If  G4  =  0

or  the  new  Y  arms  present  the  same  ratios  as  the  original  Y  arms
taken  alone;  that  is,  the  direct  capacities  C^b^  Cbc  of  Fig-  4  have
no  effect  on  the  bridge  ratio.  Thus  the  constancy  of  the  bridge  ratio
holds  for  all  null-impedance  bridges  regardless  of  the  ratio  Z1/Z2  and
of  the  nature  of  the  direct  admittances  from  corners  A  and  C  to  B.
If  G4  =  0  and  also  C24  =  C14  and  C\i  =  0,  then

Applying  this  to  Fig.  4,  which  is  possible  since  the  bridge  ratio  is
unity,  we  find  that  the  three  arms  of  the  equivalent  Y  may  be  con-
sidered as  being  made  up  of  resistances  and  capacities  in  parallel.
The  resistances  are  R,  R,  —R/2  and  the  associated  capacities  C,  C,
—  2C,  where  R  is  the  original  resistance  in  the  Y  and  C  is  one-half  the
sum  of  the  two  actual  direct  capacities  from  ^  to  f^and  from  -S^  to  (?.
The  equivalent  bridge  thus  obtained  has  ratio  arms  made  up  of
ordinary  resistances  and  capacities  and  therefore  Fig.  4  used  as  a
bridge  can  present  no  unexpected  characteristics;  the  negative
resistances  and  capacities  of  the  equivalent  Y  merely  affect  the  current
supplied  to  the  bridge.

An  ideal  transformer,  if  such  a  device  existed,  might  replace  the  Y,
for  it  would  maintain  a  constant  ratio  between  the  currents  in  the
two  windings  and  act  as  a  short  circuit  when  the  bridge  is  balanced.
To  determine  the  error  when  an  actual  transformer  with  impedances
Zp,  Zs,  Zps  is  employed,  take  the  general  expression  for  the  ratio
of  the  capacities  derived  above  which  is

Change  to  admittances  by  substituting  Y  for  C  and  G  throughout.
Assume  the  transformer  replaced  by  its  equivalent  conductance  star
so  that

Substituting  these  values  the  expression  for  the  actual  ratio  of  the
bridge  arms  becomes

(5)  When  the  bridge  alone  is  balanced  at  readings  Co  and  Co  ,
let  CcD  and  Geo  be  the  direct  capacity  between  corners  C  and  2)  and
the  total  direct  capacity  between  these  corners  and  ground.  Since
GcD  is  balanced,  the  effective  direct  capacity  between  corners  C,  2)
when  earth  is  ignored,  is  by  Fig.  1,  {Ccd  +  G^cd/4)-  Now  connect  the
three  terminals  1,  2,  3,  as  shown  with  direct  capacities  C12,  G\  —  C\i,
Gi  —  C12;  Gi,  Gi  being  the  grounded  capacities  of  terminals  1  and  2.
The  first  balance  with  the  reading  C  requires  the  equality  of  the
total  capacity  added  on  each  side,  i.e.,

For  the  second  balance  ground  may  again  be  considered  an  ignored
terminal,  and  since  terminals  1  and  2  have  been  balanced  to  ground,
and  their  total  direct  capacity  to  ground  is  G12  =  Gi  -\-  d  —  2Ci2,
the  effective  direct  capacity  added  to  the  bridge  between  corners
(?  and  2)isCb=  Cn  +  Gn/4:.  Equating  the  added  capacities  on  the
two  sides  of  the  bridge  when  balanced  at  the  reading  C",  we  obtain
G  =  2  (C"  -  C).

The  direct  capacity  between  (?  and  2),  when  ground  is  considered
an  accessible  terminal,  is  assumed  to  be  absolutely  independent  of
the  setting  of  the  condenser  /.  To  actually  meet  this  condition  will
require  some  attention  in  the  design  of  the  variable  condenser.

(6)  Here  the  bridge  itself  is  supposed  to  have  equal  direct  capaci-
ties from  corners  <?and  ^to  ground,  while  the  added  terminals  1  and  2
have  different  direct  capacities  to  ground,  the  difference  being
(Gi  —  G2),  while  the  total  direct  capacity  to  ground  is  {Gn  +  Geo)-
Now  two  capacities  in  series  may  be  replaced  by  their  product  divided

by  their  sum,  which  is  equal  to  one-fourth  of  the  sum  minus  the  square
of  the  difference  divided  by  four  times  the  sum.  The  correction
due  to  the  difference  is  thus  (G2  —  Gi)V4(Gi2  +  G'cd),  as  stated.

(7)  These  determinants  are  given  at  the  end  of  the  first  paragraph
of  this  appendix.  These  expressions  for  the  direct  capacity  are  of
more  special  interest  in  the  analytical  discussion  of  networks.

(8)  Assume  that  a  wire  resistance  is  to  be  employed  and  that  a
sliding  contact  is  to  intercept  such  an  amount  of  resistance  that  the
equivalent  conductance  will  vary  directly  with  the  motion  of  the
slider  carrying  the  contact  point.  Then  if  the  wire  is  straight  and  the
intercepted  portion  is  of  length  x  and  the  slider  motion  is  rectilinear
and  its  extent  is  y  the  relation  which  holds  between  them  is  xy  =  con-
stant, the  value  of  the  constant  depending  upon  the  units  employed.

In  the  paper  it  is  assumed  that  the  total  conductance  G,  the  total
shifted  conductance  g,  and  the  resistance  of  unit  length  of  the  slide
wire  p  are  given ;  the  total  length  of  wire  L  and  the  portion  traversed
by  the  slider  S  are  then  calculated.  The  arc  employed,  for  each
half  of  the  slider  of  Fig.  9,  extends  equally  both  ways  from  the  vertex
to  the  points  where  the  values  of  x  and  y  are  (L  ±  S)/2,  on  the  hyper-
bola xy  =  {U  —  5^)/4,  Substituting  for  L  and  5  the  values  given
in  the  paper,  it  will  be  found  that  this  range  of  x  actually  gives  the
range  of  conductance  {G  ±  g)/2,  as  required.

(10)  At  mid-point  the  total  conductance  due  to  the  five  resistances
(R)  on  each  side,  taken  in  parallel,  is  2/5R  and  to  give  this  same
conductance  an  end  fringe  must  have  the  resistance  2.5R.  Assume
a  parabolic  fringe  having  the  resistance  (5  —  nY  R/10  at  the  point
connected  to  C?  and  (?  by  resistances  nR  and  (10  —  n)R.  This  gives
a  Y  network  and  by  Fig.  1  the  equivalent  direct  conductances  are
(10  -  n)/25R,  n/25R,  (5  -  ny/250R  between  =0^,  ^(?,  d'C  re-
spectively. The  sum  of  the  first  two  is  constant  and  the  first  de-
creases by  equal  steps,  of  l/25i?  each,  to  zero  as  the  second  increases.
The  parabolic  fringe,  therefore,  gives  the  required  conductances.

The  total  resistance  in  the  chain  of  ten  resistances  is  lOi?,  in  the
fringe  Hi?,  and  in  the  largest  single  fringe  2.hR.  With  the  complete
fringe  the  total  required  is  (10  +  11)  i?  =  2\R\  with  a  single  fringe,
subdivided  as  required,  only  (10  +  2.5)  R  =  12.5R  is  required.
Compared  with  25R,  which  would  be  required  for  one  of  the  con-
ductance steps,  these  resistances  are  21/25  and  1/2.

THE  purpose  of  this  paper  is  to  present  a  simple  theoretical  treat-
ment of  those  features  of  the  Petersen  methcd  of  grounding  a
power  network  which  are  of  principal  interest  from  the  standpoint
of  inductive  effects  in  neighboring  communication  circuits.  In  this
method,  the  neutral  of  the  system  is  grounded  through  an  inductance
which  is  in  resonance,  at  the  fundamental  frequency,  with  the  total
direct  capacity  of  the  system  to  ground.  The  theory  of  the  behavior
of  a  power  system  thus  grounded  at  times  of  accidental  faults  to
earth  has  been  developed  by  Petersen  in  a  paper  published  in  1919,'
in  which  the  results  of  field  tests  and  of  operating  experience  with  an
installation  in  Germany  are  also  described.  The  methcd  has  also
found  application  in  other  places  in  Europe,  chiefly  in  Italy  and
Switzerland.  It  does  not  appear  in  any  of  these  cases  that  inductive
interference  was  a  factor  requiring,  or  at  any  rate  receiving,  consider-
ation. In  fact,  it  does  not  seem  that  either  Petersen  himself,  or  other
engineers  in  Europe  who  have  made  use  of  his  scheme,  have  considered
it  except  as  a  method  of  protecting  power  systems  from  the  effects  of
accidental  grounds.

The  features  of  the  method  that  are  of  interest  from  the  viewpoint
of  inductive  interference  relate  both  to  normal  operating  conditions
of  the  power  system  and  to  the  phenomena  which  occur  when  a  phase
of  the  system  is  grounded.  With  regard  to  the  former,  it  is  principally,
though  not  entirely,  the  effect  of  the  neutral  reactor  on  the  harmonics
of  frequencies  within  the  voice  range  that  require  examination;  with
respect  to  the  latter,  the  things  of  chief,  though  not  exclusive,  import-
ance, are  the  ground  currents  and  unbalanced  voltages  to  ground  of
fundamental  frequency,  which  are  possible  sources  of  disturbance
in  exposed  communication  circuits.

These  features,  particularly  those  concerned  with  effects  at  funda-
mental frequency,  are  more  or  less  closely  related  to  questions  of
primary  importance  from  the  standpoint  of  power  system  operation.
It  is  impossible  that  this  should  not  be  the  case.  Accidental  dis-
turbances of  a  character  which  may  interrupt  service  or  endanger
apparatus  or  equipment  in  a  power  system  may  produce  inductive

disturbances  in  neighboring  communication  circuits,  and  the  question
of  grounding  the  neutral,  in  whatever  manner,  or  of  leaving  it  isolated,
exists  because  of  its  bearing  on  the  avoidance  or  limitation  of  such
power  system  disturbances.  Thus  a  method  of  grounding  the  neutral,
or  any  other  method  of  power  system  operation  designed  to  limit  the
extent  or  the  severity  of  accidental  disturbances,  must  necessarily
possess  importance  with  respect  to  inductive  effects  in  exposed  com-
munication circuits.

It  does  not  seem  necessary,  therefore,  to  apologize  for  the  discussion,
in  the  first  section  of  the  paper,  of  the  behavior  of  the  power  system  at
times  of  faults  to  earth.  In  this  section,  an  explanation  is  given  of
the  principal  characteristic  effect  of  the  reactor  which  differs  in  some
respects  from  that  set  forth  by  Petersen  in  the  paper  already  referred
to.  The  matter  of  transient  over-voltage  on  a  non-grounded  phase
is  also  examined  in  this  section,  and  the  bearing  of  these  and  the
earlier  considerations  on  inductive  effects  is  discussed.

In  the  second  section  of  the  paper,  the  behavior  of  the  power  system
with  reactor  under  normal  operating  conditions  is  discussed  with
reference  to  noise  and  other  inductive  effects  in  neighboring  com-
munication circuits.

Referring  to  Fig.  1,  in  which,  and  in  the  following  discussion  it  is-
assumed  that  the  three  admittances  to  ground  are  equal,  the  ad-
mittance current  through  the  fault  from  the  two  sound  phases  is

Fig.  1 — Single-Phase  System  with  Neutral  Grounded  Through  Reactor.    Admittances
to  Ground  Assumed  Balanced

On  comparison  of  this  expression  with  the  above  equation  (1)  for
the  charging  current,  which  constitutes  the  fault  current  if  the  system
is  isolated,  it  is  seen  that,  if  the  losses  in  the  system  are  small,  the
effect  of  the  coil  is  to  reduce  the  magnitude  of  the  current  in  the  fault

unity.  Further,  as  equation  (2)  shows,  the  phase  of  the  fault  current
coincides  with  that  of  the  voltage  impressed  between  the  faulty  wire
and  ground  to  the  degree  of  approximation  here  used,  i.e.,  to  the
second  order  of  small  quantities.  (The  bracket  on  the  right-hand
side  of  (2),  if  written  in  full,  would  include  quadrature  terms  in  the
square  and  higher  even  powers  of  r„/uL„.)  With  the  system  isolated,
the  phase  displacement  is  nearly  90".

The  coincidence  in  phase  of  the  fault  current  and  the  voltage  im-
pressed by  the  transformer  on  the  faulty  wire,  together  with  the  small
magnitude  of  the  former,  are  very  farorable  to  the  suppression  of  the

arc.  Following  its  extinction,  there  is  a  further  action  of  the  resonant
system  consisting  of  the  coil  and  the  total  capacity  to  ground  which
acts  in  such  a  way  as  to  prevent  any  over-voltage  and  to  restore  the
normal  potentials  to  ground  gradually,  thus  tending  to  prevent  the
arc  from  restriking.     This  action  is  as  follows:

Fig.  2 — Vector  Diagram  Showing  Relations  of  Voltages  and  Currents  at  and  Follow-
ing Extinction  of  Arc

Referring  to  Fig.  2,  the  vectors  £io,  -E20,  -E30  represent  the  emfs.
impressed  between  lines  and  neutral  by  the  transformer  bank.  7^,
/„,  If  are  respectively  the  admittance  current  to  the  fault,  the  current
supplied  by  the  reactor  to  the  fault,  and  the  total  fault  current.  The
fault  is  assumed  to  be  on  phase  3.  The  arc  will  go  out  when  If  passes
through  zero.  At  this  instant,  £30  is  also  zero  and  /„  and  7^  have
nearly  their  maximum  values.  Their  instantaneous  values  are,  how-
ever, exactly  equal  and  opposite  in  the  sense  indicated  by  the  arrows
in  Fig.  1,  i.e.,  regarded  as  currents  fed  to  the  fault  by  the  two  parallel
circuits  (1)  coil-fault-faulty  wire-Eso  and  (2)  admittance  of  sound
phases-fault-faulty  wire-transformer  bank.  These  instantaneous
currents  are  exactly  equal  in  magnitude  and  are  in  the  same  direction
in  the  single  series  circuit  consisting  of  coil,  transformers,  admittance
to  ground  of  the  three  phases  in  parallel,  and  ground.  Thus  the
condition  in  this  series  resonant  circuit  at  the  instant  of  extinction
is  that  of  an  established  free  oscillation,  the  energy  of  the  oscillation
being  at  this  instant  wholly  electromagnetic.

The  voltage  across  the  reactor  due  to  the  current  7„,  in  the  direction
of  £30  (Fig.  1)  is  represented  in  Fig.  2  by  the  vector  £og-  This  is
180°  out  of  phase  with  E30  and  initially  of  the  same  amplitude.  At
the  instant  the  arc  goes  out,  both  are  practically  zero.  As  the  oscilla-
tion progresses,  Eq^  dies  away,  due  to  damping,  and  the  resultant

voltage  of  the  faulty  wire  to  ground,  viz.,  E?g  =  £30  +  £0,,  passes
gradually  back  to  the  normal  value  £30.  At  the  same  time  the  voltages
to  ground  of  the  two  sound  phases  (£ig,  E,g,)  return  to  their  normal
values  £10,  £20-  The  ends  of  the  three  vectors,  £3^,  £,,,  £?,,  may  be
thought  of  as  sliding  at  equal  rates  along  the  line  £30  and  the  dotted
lines  parallel  to  it.

The  efifectiveness  of  the  action  just  sketched  (it  has  been  assumed
that  the  frequency  of  the  series  resonant  circuit  is  accurately  that  of
the  system  fundamental),  of  course,  depends  on  the  accuracy  of  the
tuning  and  the  amount  of  damping.  If  the  free  period  of  the  resonant
circuit  differs  considerably  from  the  fundamental  period  of  the  system,
the  impressing  on  the  faulty  wire  of  a  voltage  to  ground  in  excess  of
normal  may  result,  especially  if  the  damping  is  small.  The  effect  of
inexact  tuning  is  discussed  by  Petersen  in  the  article  referred  to  above.
He  describes  some  experiments  in  which  the  capacity  of  the  power
system  to  ground  was  varied  some  15  or  20%,  each  way  from  the
value  corresponding  to  resonance,  without  apparent  effect  on  the
quenching  action  of  the  reactor.

To  simplify  the  following  theoretical  discussion  a  single  phase
system  is  treated.     This  is  represented  in  Fig.  3.     Referring  to  this

Fig.  3 — Three-phase  System  with  Neutral  Grounded  Through  Reactor,  with  Fault

figure,  when  one  phase  is  grounded  (represented  by  the  closing  of  the
switch  S),  the  following  equations,  in  which  D  denotes  differentiation
with  respect  to  time,  must  be  satisfied:

To  solve  the  equations,  the  cubic  equation  <!>  {D)  =  0  must  be  solved.
An  algebraic  solution  would  be  so  cumbersome  as  to  be  impracticable.
The  following  numerical  values  of  the  constants  have  therefore  been
inserted,  as  what  is  desired  is  a  numerical  solution  representing  the
effect  in  a  practical  case:

which  may  be  denoted  by  —a',  —a  -\-  jb,  —  a  —  jb  respectively.
The  resulting  equations  for  iig  and  i„  are

The  relations  between  the  two  sets  of  arbitrary  constants  may  be
obtained  by  inserting  these  solutions  in  the  following  differential
equation  connecting  iig  and  i„:

and  the  three  independent  arbitrary  constants  so  found  are  determined
by  the  following  conditions  when  ^  =  0  (it  is  assumed  that  breakdown

The  numerical  quantities  in  the  second  and  third  of  these  equations
are  respectively  the  total  current  supplied  to  the  sound  wire  and  the
total  charge  on  this  wire  at  the  instant  of  breakdown.  They  are
obtained  by  solving  the  network  of  Fig.  3,  with  switch  S  open  and
taking  instantaneous  values  when  the  impressed  e.  m.  f.  is  a  maximum.
The  resulting  expressing  for  iig  is

The  non-oscillatory  term  0.3  X  10~®e~^^"*'  is  seen  to  be  negligible
compared  to  the  others.

The  voltage  between  the  sound  wire  and  ground  is  obtained  by
dividing  the  above  result  by  g  =  0.37  X  10"^,  and  is

This  equation  is  plotted  for  about  13^  cycles  of  fundamental  frequency
in  Fig.  4.  The  non-oscillatory  term  is  negligible.  As  will  be  seen,
the  maximum  overvoltage  is  about  30%.

For  comparison  purposes,  the  voltage  to  ground  of  the  sound  phase
with  the  reactor  omitted  {i.e.,  with  the  system  isolated)  has  been  cal-
culated, using  the  same  constants  as  before.     The  result  is

This  is  practically  identical  with  the  earlier  result;  that  is,  the  voltage
to  ground  of  the  sound  phase  is  practically  the  same  with  the  reactor
as  with  the  system  isolated.

3.     Effects  with  Respect  to  Induction  in  Neighboring  Communication
Circuits

An  estimate  of  the  value  of  the  Petersen  coil  must  involve  a  com-
parison with  other  methods  of  grounding  the  neutral  (including
grounding  through  an  infinite  impedance,  i.e.,  the  isolated  system)  or
of  otherwise  limiting  the  effects  of  abnormal  occurrences  in  a  power
system.  As  regards  the  induction  of  fundamental  frequency  voltages
in  exposed  communication  circuits,  the  methods  of  chief  importance
in  such  a  comparison,  at  least  so  far  as  American  practice  is  con-
cerned, are  that  in  which  the  neutral  is  grounded  either  directly  or
through  a  low  resistance,  and  that  in  which  the  neutral  is  isolated.

When  accidental  grounds  occur  on  a  power  system  with  neutral
grounded  through  zero  or  a  low  impedance,  the  resulting  heavy  short
circuit  currents  to  ground  may  produce  severe  disturbances  in  ex-
posed communication  circuits.  Owing  to  the  fact  that  these  dis-
turbances are  produced  by  electromagnetic  induction  in  a  circuit
consisting  of  the  communication  conductor  as  one  side  and  the  earth
as  the  other,  they  cannot  be  avoided  by  enclosing  the  communication
conductors  in  lead-sheathed  cable,  even  when  this  is  placed  under-
ground.

With  the  Petersen  coil,  according  to  the  explanation  in  the  first  part
of  this  section,  the  neutral  current  of  fundamental  frequency  due  to  a
fault  to  ground  is  made  equal  to  the  charging  current  of  the  system
to  ground  with  one  phase  grounded,  and  this  is  generally  a  small
fraction^  — a  few  per  cent,  or  less — of  the  neutral  current  in  an  identi-
cal system  with  neutral  directly  grounded.

The  Petersen  coil  will  thus  in  many  cases  largely  prevent  the  electro-
magnetic inductive  effects  at  fundamental  frequency  which  appear
when  a  fault  to  ground  occurs  on  a  system  grounded  solidly  or  through

»  Exceptions  to  this  statement  exist  in  the  case  of  extensive  high  voltage  networks
where,  with  a  ground  on  one  phase,  the  charging  current  to  ground  with  isolated
neutral  may  be  of  the  same  order  of  magnitude  as  the  short  circuit  current  with  dead-
erounded  neutral  if  the  fault  is  remote  from  a  point  of  main  power  supply.

a  low  resistance.  There  will  appear,  however,  electrically^  induced
voltages  of  fundamental  frequency  substantially  identical  with  those
that  would  occur  with  neutral  isolated.  Where  the  communication
circuits  are  in  underground  cable,  these  voltages  are  of  inappreciable
magnitude,  and  with  aerial  cables  (with  metallic  sheaths)  their  effects
can  in  general  be  controlled  without  great  difficulty.  With  open
wire  communication  circuits,  electrically  induced  voltages  are  of
much  more  consequence.  They  may  in  some  cases  equal  or  exceed
the  voltages  which  would  be  induced  electromagnetically  with  dead-
grounded  neutral.  However,  except  perhaps  in  cases  of  long  ex-
posure to  high  voltage  power  circuits  at  close  separations,  their
effects  are  generally  much  less  severe  than  the  electromagnetic  effects,
because  of  the  smaller  amount  of  energy  transferred  to  the  disturbed
circuit.  This  is  in  general  accordance  with  experience  with  open
wire  circuits  exposed  to  power  circuits  of  moderate  voltage.  As  is
explained  in  the  next  paragraph,  the  use  of  a  Petersen  reactor  to  ground
the  neutral  may  be  expected  to  lessen  the  severity  of  inductive  effects
which  would  be  experienced  from  an  isolated  system,  by  preventing
additional  parts  of  the  power  system  from  becoming  involved.

As  compared  to  the  isolated  system,  the  use  of  the  Petersen  coil  in
the  connection  from  neutral  to  ground  may  be  expected  to  have  the
advantage,  according  to  the  theory  of  the  first  subdivision  of  this
section,  of  preventing  the  formation  of  an  "arcing  ground."  As  ex-
perience has  shown,  an  arcing  ground  in  an  isolated  system  is  fre-
quently the  cause  of  serious  disturbances  which  may  involve  portions
of  a  network  remote  from  the  location  of  the  original  trouble.  The
advantage  of  the  reactor  in  this  respect  is,  of  course,  a  fundamental
one  from  the  standpoint  of  power  operation.  It  is  in  general  of  pro-
portionate importance  from  the  inductive  interference  point  of  view,
at  least  where  a  power  network  is  involved  in  parallels  with  com-
munication circuits  at  several  places,  as  is  not  infrequenctly  the  case
near  large  cities.  A  breakdown  to  ground  in  the  power  network  on  a
different  phase  from  that  originally  involved,  and  in  a  different  locality,
may  lead  to  large  phase-to-phase  currents  in  the  earth,  from  the
second  fault  to  the  first,  or  to  a  ground  intentionally  placed  on  the
phase  first  involved,  in  order  to  short  circuit  the  arc.  The  inductive
effects  thus  become  electromagnetic  in  character,  and  the  inter-
ference produced  in  this  manner  may  be  severe.

'"Electrically"  is  used  here  and  elsewhere  in  this  paper  in  the  sense  in  which
"electrostatically"  is  perhaps  more  commonly  used.  The  phenomena  involved
are  not  static  and  the  latter  word  is  inappropriate  on  this  account.

overvoltage  on  a  sound  phase  at  the  instant  of  grounding  than  would
be  the  case  in  an  isolated  system  is,  of  course,  of  importance  in  this
connection.  This  has  been  examined  from  a  theoretical  standpoint
in  the  second  subdivision  of  this  section,  with  the  conclusion  that
there  is  no  material  difference  in  this  respect.

There  remains  the  method  of  grounding  in  which  a  high  resistance
is  employed  in  the  connection  from  neutral  to  ground.  By  "high  "  here
may  be  meant  the  "critical"^  resistance  or  one  of  smaller  magnitude,
but  still  so  large  that  in  the  event  of  a  solidly  grounded  phase,  the
sound  phases  are  brought  to  subtsantially  full  delta  voltage  above
ground.  There  are  probably  few  cases  where  electromagnetic  indu-
tive  effects  due  to  accidental  grounds  on  a  power  system  are  a  matter
of  importance,  in  which  a  neutral  resistance  small  enough  to  avoid
this  rise  of  voltage  on  the  sound  phases  would  be  effective  as  a  meas-
ure of  relief.  This  method  of  grounding  would  thus  not  avoid  the
electrically  induced  voltages  which  arise  when  the  reactor  is  used,
although  it  would  presumably  be  effective  in  preventing  the  spread
of  trouble  to  other  parts  of  the  power  system  if  positive  operation  of
selective  relays  is  secured.  Inasmuch  as  it  presents  fewer  difficulties
from  this  last  point  of  view  than  the  Petersen  reactor,  grounding
through  a  moderate  resistance  has  a  definite  advantage  over  the  latter
method  from  the  standpoint  of  inductive  effects  at  fundamental
frequency,  provided  sufficient  resistance  can  be  used  to  limit  the
electromagnetically  induced  voltages  to  tolerable  values.

Where  this  is  impracticable  from  the  standpoint  of  power  system
operation,  the  relative  merits  of  the  two  systems  would  have  to  be
decided  by  balancing  the  effective  suppression  of  the  transient  electro-
magnetic inductive  effects  by  means  of  the  reactor,  plus  the  expecta-
tion of  occasional  disturbances  continuing  over  the  intervals  neces-
sary for  the  location  and  disconnection  of  the  faulty  line,  against  the
imperfect  suppression  of  the  former  effects  by  means  of  the  resistor,
plus  the  limitation  to  very  brief  intervals  of  electrically  induced  dis-
turbances otherwise  the  same  as  with  the  reactor.  It  is  obvious  that
the  factors  controlling  such  a  decision  would  vary  widely  in  different
cases,  and  that  practical  experience  with  both  methods  would  be  of
great  value  in  estimating  their  relative  importance.  It  is,  of  course,
possible  that  future  development  may  remove  some  of  the  disad-
vantage at  which  the  Petersen  coil  now  finds  itself  in  respect  to  the
matter  of  relay  protection  for  interconnected  networks.  Such  de-
velopment would  presumably  be  of  importance  also  to  the  critical

*  Le.,  the  resistance  for  which  a  discharge  to  ground  passes  from  the  oscillatory
to  the  non-oscillatory  type.

resistance  which,  as  a  method  of  grounding  the  neutral,  would  gener-
ally suffice  to  prevent  interference  from  ground  currents  at  times  of
faults  to  ground,  but  which  apparently  presents  difficulties  from  the
relay  standpoint  similar  to  those  involved  in  the  use  of  the  Petersen
coil.

Referring  to  Fig.  5  (we  now  take  account  of  inequalities  in  the  ad-
mittances to  ground),

Fig.   5 — Three-phase  System  with   Neutral   Grounded  Through   Reactor.     Admit-
tances to  Ground  Not  Balanced.

where     F  =   Fi  +  F2  +  F3  =  total    direct    admittance    to    ground.
If  the  impressed  voltages  are  balanced

The  parenthesis  is  the  "  residual  admittance  "  ^  to  ground  and,  if
the    three    leakances    to    ground    are    equal,    it    can    vanish    only   if

'  Inductive  Interference  between  Power  and  Communication  Circuits,  California
Railroad  Commission,  p.  269.

the  three  direct  capacities  to  ground  are  the  same.  The  equation  is
equivalent  to

where  E^^  is  the  "  characteristic  residual  voltage  "  ®  of  the  (isolated)
system  and  is  equal  in  magnitude  to  3  £oi  times  the  ratio  of  the  residual
admittance  to  ground  to  the  total  admittance  to  ground.
We  have

r„  and  L„  being  the  resistance  and  inductance  of  the  earth  coil,  and
g  and  C  the  total  leakance  and  capacity  to  ground,  respectively.
Also,  for  resonance

If  in  this  equation  the  denominator  on  the  right  be  denoted  by  x
and   the  fractional  unbalance   of   the   admittance    to   ground   by  y

If  the  losses  in  the  system  (including  the  earth  coil)  are  small,  x  is
small  compared  to  1.     Thus  we  get,  for  the  absolute  value  of  V

and  the  absolute  value  of  the  residual  voltage  is  three  times  this,
approximately.

In  substance,  this  means  that,  at  fundamental  frequency  and  with
small  losses,  the  fractional  admittance  unbalance  should  be  kept  small
compared  to  the  ratio  of  the  resistance  to  the  reactance  of  the  coil,  if
unduly  high  voltages  to  ground  are  to  be  avoided.  (It  is  supposed
that  g'oiC  is  of  the  order  of  r„/wL„,  or  smaller — a  condition  probably
satisfied  even  with  the  best  practiable  design  of  coil,  except  under
very  wet  line  conditions.)  The  point  involved  here  is,  of  course,  an
important  one  from  the  standpoint  of  power  system  operation.  It
is  also  important  from  the  standpoint  of  electrically  induced  voltages
in  exposed  communication  circuits.  The  admittance  unbalance  can
be  kept  within  the  necessary  limits  by  suitable  power  circuit  trans-
positions.

The  absolute  magnitude  of  the  fundamental  frequency  neutral
current  is  obtained  from  the  expression  for  ]  F„  ]  by  dividing  by  the
coil  impedance  (or  directly  from  equation  (3),  and  is,  approximately,

For  a  system  with  dead-grounded  neutral  the  fundamental  frequency
residual  current  is  yEoiY  and  is  thus  smaller  than  that  just  found  for
the  case  of  the  reactor  in  the  ratio  of  j  x  |  to  1,  approximately.  It  is
evident,  how^ever,  that  the  magnitude  of  the  neutral  current  with
reactor  is  controllable  by  means  of  transpositions,  as  in  the  case  of
the  neutral  and  residual  voltages.  The  inductive  effects  of  this
current  should  be  of  small  consequence  with  an  amount  of  transposing
sufficient  to  keep  the  line  voltages  to  ground  within  limits  desirable
from  the  standpoint  of  power  system  operation.

In  the  following  discussion,  we  retain  the  assumption  of  lumped
constants,  so  that  the  results  are  not  applicable  to  extensive  networks
without  modification.

With  this  restriction,  at  harmonic  frequencies  other  than  the  third
or  one  of  its  odd  multiples,  the  above  approximate  equation  for  V„
becomes

m  being  the  order  and  £oi  the  voltage  of  the  harmonic  and  x  and  y
accented  to  denote  that  they  are  to  be  taken  for  the  frequency  in

question.  For  small  losses  x'  may  be  neglected  in  comparison  with
unity,  as  before,  giving

Thus,  even  for  the  fifth  harmonic,  the  right  hand  side  of  (5)  is  only
4  per  cent,  in  excess  of  the  value  it  would  have  if  the  neutral  were
isolated.

For  harmonics  whose  orders  are  not  divisible  by  three  the  residual
voltage  is  three  times  F„.  Thus  from  the  standpoint  of  noise  inter-
ference from  voltages,  a  system  grounded  through  a  Petersen  coil
behaves  practically  as  though  the  neutral  were  isolated,  so  far  as  these
harmonics  are  concerned.  As  with  the  fundamental,  power  circuit
transpositions  are  available  for  the  reduction  of  residual  voltages  of
these  frequencies.

Residual  currents  of  frequencies  belonging  to  this  series  of  har-
monics, which  are  not  present  at  the  ends  of  the  line  with  isolated
neutral,  are  introduced  by  grounding  through  the  reactor,  but  they
are  of  minor  importance,  as  may  be  judged  by  comparing  the  neutral
currents  with  the  reactor  and  with  dead  grounded  neutral.  With  the
reactor,  the  neutral  current  of  a  harmonic  of  order  m  not  a  multiple
of  3  is  found  from  (5)  to  be,  in  absolute  value,

Z„  being  the  coil  impedance  at  fundamental  frequency,  while  with
dead-grounded  neutral,  it  would  be

in  which  Y  is  the  total  admittance  to  ground  at  fundamental  fre-
quency. Thus  the  magnitude  of  the  neutral  current  with  the  reactor
is  approximately  l/(m^  —  1)  of  its  magnitude  with  dead-grounded
neutral.  The  noise  effects  of  residual  currents  of  these  magnitudes
will  generally  be  insignificant  compared  to  those  arising  from  other
sources,  particularly  if  the  power  circuit  capacities  to  ground  are  well
balanced.

in  which  the  symbols  for  coil  impedance  and  line  admittance  are
accented  to  denote  that  they  refer  to  the  harmonic  freciuency  in
question;

The  neutral  is  thus  subjected  to  a  third  harmonic  voltage  some  12
per  cent,  greater  than  if  it  were  isolated,  but  for  the  higher  harmonics
belonging  to  this  series  (of  the  third  and  its  odd  multiples),  the  differ-
ence is  inappreciable.

From  the  standpoint  of  noise  interference  in  telephone  circuits,
residuals  of  the  series  consisting  of  the  third  harmonic  and  its  odd
multiples  are  frequently  troublesome  where  the  neutral  of  a  three-
phase  system  is  grounded  directly  or  through  a  low  resistance.  These
residuals,  of  course,  are  not  affected  by  power  circuit  transpositions,
either  as  to  their  magnitudes  or  as  to  their  inductive  effects  upon
exposed  telephone  circuits.  It  is  therefore  of  interest  to  examine  xhe
expressions  just  obtained  for  the  case  in  which  the  neutral  is  grounded
through  the  coil.     While  the  neutral  current  will  not  be  the  same  as

the  residual  current  except  when  only  one  line  is  supplied  from  the
transformer  bank,  the  effect  upon  the  former  should  in  general  be  at
least  approximately  proportional  to  the  effect  upon  the  residual  cur-
rent in  any  line  supplied  from  the  bank.

In  writing  equation  (7),  any  difference  between  the  induced  voltage
jEoi  and  the  voltage  appearing  between  line  and  neutral  has  been
ignored.  To  the  extent  that  this  is  justifiable,  the  expressions  for  the
case  of  the  solidly  grounded  neutral  may  be  obtained  by  making  the
denominators  of  the  right  hand  sides  of  (8)  and  (9)  each  unity.  If
the  transformer  bank  is  provided  with  a  delta  winding  of  low  im-
pedance, in  particular  if  it  is  connected  delta  on  one  side,  this  pro-
cedure gives  a  fair  approximation  to  the  correct  expressions,  since
the  impedance  through  which  the  voltage  £oi  regulates  is  in  this
case  merely  the  transformer  leakage  impedance.  The  resulting
conclusions  with  respect  to  the  advantage  of  the  reactor — for  ex-
ample, that  the  third  harmonic  residual  voltage  or  neutral  current  is
1/8  as  large,  the  ninth  1/80  as  large,  etc.,  with  the  reactor  as  with
solidly  grounded  neutral — should  not,  in  any  event,  be  unfavorable  to
the  latter  method  of  grounding  unless  the  electrical  length  of  the  line
approaches  the  point  at  which  its  reactance  to  ground  becomes
positive.

If  the  transformers  are  so  connected  as  to  provide  no  path  for  triple
harmonic  magnetizing  currents  other  than  through  line  admittance
to  ground  and  the  impedance  between  neutral  and  ground,  the  in-
duced voltage  jEoi  is  not  the  same  for  the  two  methods  of  grounding
under  consideration,  because  the  impedance  to  the  triple  harmonic
magnetizing  currents  is  appreciably  different  in  two  cases.  A  con-
venient method  of  taking  this  effect  into  account  is  to  regard  the  in-
duced voltage  as  due  to  a  fictitious  impedanceless  generator  of  de-
terminate voltage  regulating  through  the  mutual  impedance  of  the
transformer  windings  for  the  frequency  in  question.''  If  Z'^  is  one-
third  of  this  mutual  impedance  and  Vo\^  is  the  voltage  of  the  fictitious
generator,  the  expression  for  the  neutral  current  with  ground  con-
nection through  the  reactor  becomes

'The  voltage  thus  assumed  is,  of  course,  not  identical  with  the  induced  voltage
for  which  the  symbol  Eoi  has  hitherto  been  used,  and  for  this  reason  the  new  symbol
Foi  is  used  for  it.  The  corresponding  7?oi  would  be  Foi  diminished  by  the  drop  through
the  mutual  impedance.

The  corresponding  expressions  for  solidly  grounded  neutral  are  ob-
tained by  omitting  m-  in  the  denominator  for  each  of  the  equations
just  derived.  Thus  the  advantage  of  grounding  through  the  reactor
relative  to  grounding  directly  depends  on  the  magnitude  of  F'Z'^  as
compared  to  the  square  of  the  order  of  the  harmonic.  Z'„  depends
upon  the  voltage  and  the  kva.  capacity  of  the  transformers  and  is
mostly  inductive  reactance.  For  high  voltage  transformer  banks
of  small  capacity  feeding  very  extensive  networks,  the  gain  indicated
by  equations  (10)  and  (11)  from  the  use  of"  the  reactor  would  prob-
ably not  be  large.  It  would  be  important,  however,  where  the  aggre-
gate capacity  of  the  supply  transformers  is  moderate  or  large  and  the
connected  network  is  of  moderate  extent  and  voltage.  For  instance,
using  the  data  of  the  example  considered  in  an  earlier  part  of  this

for  a  total  transformer  capacity  of  7,000  to  8,000  kva.,  with  line  voltage
from  20,000  to  30,000,  we  should  have  L'^Coi'^  equal  to  about  4  at
180  cycles/sec.  In  other  words,  in  this  case,  the  employment  of  the
reactor  would  reduce  the  residual  voltage  and  the  neutral  current  of
the  third  harmonic  frequency  due  to  a  star-star  solidly  grounded
transformer  bank  by  about  75  per  cent.,  and  residuals  of  other  fre-
quencies belonging  to  the  same  series  probably  by  larger  amounts.

In  the  earlier  discussion  relating  to  harmonics  not  belonging  to  the
triple  series,  comparison  was  made  between  a  system  grounded  through
a  Petersen  reactor  and  the  isolated  system.  In  a  similar  comparison
with  respect  to  the  triple  harmonic  series,  the  isolated  system  has  the
advantage,  since  residuals  of  this  series  theoretically  do  not  appear
in  such  a  system,  as  the  voltages  are  not  impressed  between  wires.
As  a  practical  matter,  an  isolated  system  would  probably  not  be
entirely  free  of  triple  harmonic  residuals,  owing  to  dissimilarities  in
transformers  or  elsewhere.  Such  accidental  effects  can  hardly  be
taken  into  account  in  a  theoretical  discussion.  However,  in  setting
up  a  comparison  between  the  isolated  system  and  that  grounded
through  the  reactor,  an  idea  of  the  relative  importance  of  the  triple
harmonic  residual  voltages  existing  in  the  latter  case  can  perhaps  be
obtained  by  comparing  their  theoretical  magnitudes  with  the  theoreti-

cal  magnitudes  of  residual  voltages  in  the  isolated  system  of  non-
triple  frequencies.

The  residual  voltage  due  to  one  of  these  non-triple  frequencies,
which  is  three  times  the  neutral  voltage,  is  ^y'  E'oi,  according  to
equation  (6).  Here  y'  is  the  fractional  residual  admittance  and  E'oi
may  be  taken  as  the  induced  voltage  in  the  transformer  for  the  fre-
quency in  question.  For  a  harmonic  belonging  to  the  triple  series,
with  neutral  grounded  through  the  reactor,  the  absolute  value  of  the

the  harmonic  and  Eqi  the  induced  voltage,  if  we  assume  the  trans-
former bank  provided  with  a  low  impedance  path  for  triple  harmonics,
and  therefore  neglect  the  difference  between  the  induced  and  the
terminal  voltages.     The  ratio  of  the  triple-series  residual  voltage  to

If  we  take  the  ninth  as  the  harmonic  of  the  triple  series  and  assume
equal  values  of  the  induced  voltages  £01  and  Fq'i  it  will  be  seen  that
I  y'  I  must  be  of  the  order  of  0;01  if  the  residual  voltage  of  the  triple
harmonic  series  is  to  be  as  large  as  the  other.  This  amount  of  un-
balance is  somewhat  larger  than  has  been  found  at  this  frequency
(540  cycles/sec.)  in  an  actual  transposed  line.^  If  we  consider  the
higher  harmonics  of  the  triple  series,  |  y'  \  would  have  to  be  made
progressively  smaller  in  order  that  the  ratio  might  remain  unity.
Thus,  for  the  21st  harmonic,  |  y'  \  would  have  to  be  of  the  order  of
0.002.  While,  of  course,  |  y'  \  may  be  made  as  small  as  desired  by
sufficiently  close  power  circuit  transpositions,  it  appears  that  in  prac-
tical cases  where  transformer  banks  have  delta  windings,  one  may
expect  the  residual  voltages  of  the  triple  series,  introduced  by  changing
from  an  isolated  system  to  one  grounded  through  the  reactor,  to  be
relatively  unimportant  except  in  the  case  of  the  third  harmonic  and
perhaps  in  that  of  the  ninth.  This  statement  would  not  be  true  if,
as  with  star-star  transformers  under  some  circumstances,  no  low
impedance  path  is  provided  for  magnetizing  currents  of  the
triple  harmonic  series.  Such  cases  are  not  common  in  operating
practice.

The  method  of  estimating  comparative  effects  here  applied  to  the
case  of  triple  harmonic  residual  voltages  is  not  available  for  residual
currents.     To  take  account  of  the  latter  in  comparing  the  isolated

•  Inductive  Interference  between  Power  and  Communication  Circuits,  California
Railroad  Commission,  Technical  Report  No.  51.

system  and  the  system  with  neutral  ^rouncled  through  the  reactor,
recourse  may  be  had  to  the  indirect  method  of  reference  to  the  solidly
grounded  neutral  system,  as  in  the  discussion  of  residual  currents  of
the  non-triple  series  on  page  52.  Such  a  procedure,  of  course,  in-
volves a  reference  to  general  experience  also.  It  has  been  shown  in
the  earlier  discussion  that  for  a  triple  series  harmonic  of  order  m
the  neutral  current  wMth  the  reactor  is  approximately  1/  {m^  —  1)
as  large  as  with  the  dead-grounded  neutral  if  a  low  impedance  path
for  triple  frequency  magnetizing  currents  is  provided,  as  by  a  delta
winding.  The  establishment  of  this  system  of  neutral  currents,  even
though  they  are  small,  when  a  previously  isolated  system  is  grounded
through  a  Petersen  reactor,  constitutes  an  addition  to  the  residuals
which  produce  induction  in  neighboring  circuits.  However,  it  is  not
to  be  expected  that  the  added  inductive  effects  would  be  important.
Where  no  low  impedance  path  for  the  triple  series  magnetizing  cur-
rents exists,  the  reactor  is  relatively  less  effective  in  suppressing
residual  currents  of  this  series.  The  triple  harmonic  neutral  currents
of  a  power  system  connected  in  this  manner  and  grounded  through  a
Petersen  coil  might  in  some  cases  lead  to  inductive  effects  of  some
significance.

In  general,  for  harmonics  of  orders  not  divisible  by  three,  grounding
through  a  moderate  resistance  (large,  however,  compared  to  other
impedances  involved  in  a  short  circuit  to  ground)  will  be  more  ad-
vantageous as  regards  residual  voltages,  and  less  advantageous  as
regards  residual  currents,  than  grounding  through  the  reactor.
Grounding  through  zero  impedance  would,  of  course,  generally  lead
to  the  smallest  residual  voltages  and  the  largest  residual  currents  of
these  frequencies.  For  frequencies  belonging  to  the  tr-iple  series,
grounding  through  the  reactor  will  be  considerably  more  advantageous
than  grounding  through  a  moderate  resistance  as  regards  both  residual
voltages  and  residual  currents.  It  may  be  expected  that  with  moder-
ate neutral  resistance,  residual  currents  and  voltages  of  the  triple
series  will  both  be  nearer  in  magnitude  to  those  obtaining  with  zero
neutral  impedance  than  to  those  obtaining  with  the  Petersen  coil.
The  moderate  neutral  resistance  is  relatively  more  effective  at  the
higher  frequencies  in  reducing  residual  currents  of  all  harmonics
and  residual  voltages  of  the  triple  series;  for  harmonic  residual
voltages  not  belonging  to  the  triple  series,  it  is  relatively  more  effective
at  the  lower  frequencies.

I  wish  to  express  my  gratitude  for  helpful  suggestions  and  criticism
received  in  the  preparation  of  this  paper  from  Messrs.  L.  P.  Ferris
and  R.  G.  McCurdy,  and  also  from  Mr.  R.  K.  Honaman.

1.  At  times  of  a  fault  to  ground  on  a  power  system  with  neutral
grounded  through  a  Petersen  reactor,  the  action  of  the  latter  tends  to
extinguish  the  arc  and  to  prevent  its  restriking.  Theoretical  con-
siderations, applied  to  a  practical  case,  indicate  that  the  transient
over-voltage  on  a  sound  phase  at  the  instant  of  occurrence  of  the
fault  is  substantially  the  same  as  in  a  system  with  isolated  neutral.

2.  Grounding  the  neutral  through  a  Petersen  earth  coil  instead  of
directly  or  through  a  low  resistance  would  largely  prevent  the  electro-
magnetic inductive  effects  to  which  exposed  communication  circuits
are  liable  at  times  of  faults  to  ground  in  systems  grounded  in  the
latter  manner.  (Extensive  high  voltage  networks  are  perhaps  an
exception  to  this  statement.  But  even  here,  the  electromagnetic
inductive  effects  would  in  general  not  be  greater  with  the  reactor
than  with  isolated  neutral.)  However,  effects  due  to  electric  induc-
tion similar  to  those  from  an  isolated  system  may  be  expected  to
appear.  Except  for  long,  close  parallels  involving  open-wire  com-
munication circuits  these  effects  should  in  general  be  much  less  severe
than  the  electromagnetic  inductive  effects  from  a  system  with  dead-
grounded  neutral.  The  extent  and  severity  of  the  inductive  effects
experienced  from  the  system  grounded  through  the  reactor  would
further  tend  to  be  smaller  than  with  the  isolated  system,  because  of
the  effect  of  the  reactor  in  preventing  arcing  grounds.

3.  Grounding  the  neutral  through  a  resistance  large  compared  to
other  impedances  involved  in  a  short  circuit  to  ground  should  have
an  advantage  over  grounding  through  the  Petersen  reactor,  in  that
the  former  method  presents  fewer  difficulties  in  respect  to  power
system  protective  relays,  so  that  it  would  reduce  the  possibility  of  the
continuance  of  inductive  disturbances  over  considerable  periods  of
time,  which  might  be  involved  in  grounding  through  the  reactor,
under  present  relay  practice.  From  an  inductive  interference  stand-
point, a  choice  between  the  two  methods  would  depend  upon  the
circumstances  of  particular  cases.  Advances  in  the  art  of  relay
protection  would  improve  the  position  of  the  reactor  in  such  con-
siderations.

4.  Under  normal  power  system  operating  conditions,  the  use  of  the
reactor  may  lead  to  excessive  residual  voltages  of  fundamental  fre-
quency if  the  admittamces  from  phases  to  ground  are  unbalanced.
Such  unbalance  may  be  reduced  to  the  extent  necessary  from  this
point  of  view  by  power  circuit  transpositions.

5.  Under  normal  operating  conditions,  it  is  to  be  expected  that  the
residual  voltages  and  currents  of  the  triple  harmonic  series  occurring

with  neutral  grounded  through  zero  or  a  low  impedance  would  he
largely  reduced  by  grounding  through  the  Petersen  reactor  instead.
Residuals  of  other  harmonic  frequencies  should  be  substantially  the
same  as  with  isolated  neutral,  and  are  controllable  by  means  of  power
circuit  transpositions.  The  method  of  grounding  the  neutral  through
a  resistance  of  moderate  value  is  favorable  to  the  reduction  of  residual
voltages  of  the  harmonics  whose  orders  are  not  multiples  of  three,
but  is  relatively  unfavorable  to  the  suppression  of  residual  currents
of  these  frequencies.  It  is  also  considerably  less  effective  than  the
reactor  in  preventing  residuals,  either  voltages  or  currents,  belong-
ing to  the  triple  harmonic  series,  which  are  not  amenable  to  treat-
ment by  transpositions.

Synopsis:  Engineering  and  construction  features  involved  in  a  complete
telephone  cable  system  over  300  miles  in  length  and  connecting  Philadelphia
and  Pittsburgh,  Pa.,  are  described  in  the  following  paper.  This  cable  is
designed  to  operate  as  an  extension  of  the  Boston-Washington  under-
ground cable  system  with  which  it  connects  at  Philadelphia.  It  is  also
designed  for  operation  in  connection  with  the  Pittsburgh-Chicago  cable
now  under  construction,  and  other  cable  projects  included  in  a  compre-
hensive fundarnpntal  plan.

Beginning  with  the  fundamental  factor  of  public  requirements  for  com-
munication service  between  cities  separated  by  various  distances,  there  are
next  considered  the  methods  available  to  provide  this  service.  Small-
gage,  quadded,  aerial  cable,  which  was  decided  upon  for  use  in  this  section
after  careful  economic  studies,  is  described  in  a  general  way  and  the  im-
portant advantages  of  the  application  of  loading  and  telephone  repeaters  are
outlined.  The  use,  in  connection  with  this  cable,  of  the  recently  developed
metallic  telegraph  system  for  cables  is  referred  to  and  some  facts  are  given
regarding  power  plants,  test  boards  and  buildings.  A  few  of  the  many
possible  combinations  of  cable  and  equipment  facilities  into  complete
telephone  circuits,  which  will  furnish  the  service  required  as  economically
as  now  possible,  are  illustrated.

The  necessity  of  complete  coordination  of  the  many  factors  involved
in  a  project  of  this  kind  is  emphasized.

THE  placing  in  service  in  the  latter  part  of  1921  of  the  final  section
of  a  continuous  telephone  cable  over  300  miles  in  length  between
Philadelphia  and  Pittsburgh  marked  a  new  point  of  achievement
in  the  steady  development  and  construction  of  facilities  designed
to  render  to  the  public  the  best  possible  long-distance  telephone
service.  Furthermore,  this  cable  forms  an  important  part  of  a  com-
prehensive plan  of  long-distance  cable  construction  throughout  that
section  of  the  United  States  lying  in  general  east  of  the  Mississippi
River  and  north  of  the  Ohio  and  Potomac  Rivers.

In  the  discussion  of  a  project  of  this  kind  which  involves  many  new
practices  and  the  expenditure  of  several  millions  of  dollars  and  which,
with  related  work  already  completed,  forms  the  groundwork  for
large  expenditures  in  the  future,  it  is  usual  to  inquire  first  into  the
underlying  reasons  for  carrying  out  the  project  and  then  into  the
methods  adopted.  In  the  following  discussion  an  endeavor  will
therefore  be  made  to  furnish  some  information  on  these  two  items
in  their  relation  to  the  Philadelphia-Pittsburgh  cable,  although,  as
will  be  obvious,  the  many  different  points  can  be  covered  in  only

'  Presented  at  a  meeting  of  the  Philadelphia  Section  of  the  A.  I.  E.  E.,  January  9,
1922,  presented  at  the  Annual  Convention  of  the  A.  I.  E.  E.,  Niagara  Falls,  Ont.,
June  26-30,  1922,  and  appearing  in  the  Journal  of  the  A.  I.  E.  E.  for  August,  1922.

the  most  general  way  in  the  space  available.  However,  before  going
ahead  with  the  discussion,  I  would  like  to  point  out  that  this  project
is  not  unlike  many  others  in  that,  as  a  whole  and  in  the  component
parts,  there  have  been  required,  first,  the  careful  consideration  and
decisions  of  the  executives,  then  the  underlying  work  of  many  scien-
tists, inventors  and  engineers,  then  the  skilled  work  of  the  manu-
facturers and  construction  forces,  and  finally  the  maintenance  and
operation  by  trained  people  who  are  responsible  for  the  continuous
service  so  vitally  necessary  to  the  industrial  and  social  structure  of
the  country.  The  point  to  be  emphasized  here  is  that  the  coordina-
tion of  all  of  these  factors  and  the  close  cooperation  of  all  of  the  many
hundreds  of  people  concerned  are  the  important  things.

Fig.  1  is  an  outline  map  of  a  section  of  the  United  States  and  shows
the  routes  of  existing  and  proposed  long  telephone  cables  of  the  Bell
system.  It  will  be  noted  that  the  present  and  proposed  routes  follow
in  a  general  way  the  routes  of  trunk-line  railroads.  This  general
section  contains  m.ore  than  50  per  cent  of  the  entire  population  of
the  United  States  but  less  than  15  per  cent  of  the  area,  and  the  in-
dustrial and  telephone  development  is,  of  course,  very  great.  Fur-
thermore, the  nearby  surrounding  states,  supplying  as  they  do  large
quantities  of  food  products  and  raw  materials,  are  commercially
related  to  this  section  in  a  very  peculiar  way  and  this  fact  greatly
influences  the  long-distance  telephone  development  along  the  par-
ticular cable  routes  indicated.  The  routes  through  the  State  of
Pennsylvania  and  the  offices  at  Philadelphia  and  Pittsburgh,  which  are
the  terminals  of  the  cable  that  is  more  particularly  the  subject  of
this  discussion,  occupy  strategic  positions  in  this  system.

Circuits  of  the  American  Telephone  and  Telegraph  Company  and
the  Bell  Telephone  Company  of  Pennsylvania  are  carried  over  these
routes  and  this  cable  was  jointly  planned  and  installed  by  these
companies.

Fig.  2  is  an  outline  map  of  the  State  of  Pennsylvania  and  shows
the  situation  in  this  section  a  little  more  in  detail.  On  this  map  are
shown  some  of  the  larger  cities  and  routes  of  the  longer  and  more
important  toll  and  long-distance  telephone  lines.  As  indicated,
these  lines  are  mainly  of  the  familiar  aerial  wire  type  which  has  been
generally  used  in  the  past  for  this  purpose  and  which  is  today  the
most  efficient  and  economical  type  of  construction  for  many  cases.
In    the    general    section    between    Philadelphia    and    Pittsburgh    the

requirements  for  circuits  are  very  heavy  and  in  addition,  as  is  well-
known,  the  topography  of  the  country  is  such  that  the  through  routes
which  can  economically  be  used  for  pole  lines  are  limited.  At  present,
these  few  routes  are  fully  occupied  by  the  pole  lines  of  the  various
utilities  and  included  in  these  lines  are  three  fully  loaded  telephone
trunk  lines.  Another  item  of  importance  in  the  consideration  of
aerial  wire  construction  is  the  very  severe  damage  frequently  experi-
enced in  many  sections  of  the  country  on  heavy  aerial  wire  lines
from  ice  and  wind  storms.  Even  lines  built  with  exceptional  strength
fail  in  these  storms  and  the  interruptions  to  service  are  serious  mat-
ters to  the  users  as  well  as  to  the  telephone  companies.     The  restora-

Fig.  3 — Damage  to  Section  of  New  York-Boston  Main  Line  Near  Worcester,  Mass.
Storm  of  November  28,  1921

tion  costs  under  the  conditions  that  naturally  exist  at  such  times  are
abnormally  high.

Figs.  3  and  4  show  the  effects  at  one  point  of  the  ice  and  wind  storm
in  New  England  on  November  28,  1921,  and  are  proof  that  this
problem  is  real.  This  particular  spot  is  near  Worcester,  Mass.,  and
the  line  is  a  section  of  one  of  the  principal  aerial  wire  routes  between
New  York  and  Boston.  In  this  storm,  many  thousands  of  poles
were  broken  and  even  where  a  few  poles  remained  standing  due  to
specially  strong  construction,  the  load  of  ice  combined  with  the  wind
was  too  great  for  the  wires  to  withstand.  There  is  therefore  a  prac-
tical limit  to  the  number  of  wires  that  can  be  safely  and  economically
carried  on  a  pole  line.

existing  pole  lines  are  fully  loaded,  and  where  estimated  future  circuit
requirements  are  of  considerable  magnitude,  it  is  obvious  that  different
methods  of  providing  facilities,  if  available,  must  sooner  or  later
be  given  serious  consideration.  The  conditions  between  Phila-
delphia and  Pittsburgh  and  in  general  along  all  of  the  cable  routes
shown  on  Fig.  1  are  now,  or  are  expected  within  a  few  years  to  be,
such  as  to  make  the  use  of  some  type  of  construction  other  than  aerial
wire  desirable  for  most  of  the  circuits.

Fig.  4 — Section  of  New  York-Boston  Main  Line  Showing  Wires  Heavily  Loaded  with

and  of  the  methods  available  for  providing  long-distance  telephone
facilities,  which  in  general  are  aerial  wire  and  cable,  it  has  been  decided
that  for  relief  in  these  sections  the  cable  method  will  give  the  best
and  most  economical  results.  Long  underground  cables,  as  is  well-
known,  have  been  in  operation  for  many  years  between  Boston,  New
York,  Philadelphia,  Baltimore  and  Washington,  Chicago  and  Mil-
waukee and  in  other  sections.  However,  the  type  of  cable  and  asso-
ciated apparatus  which  is  now  being  used  in  the  development  of  the
more  comprehensive  plan  is  quite  different  from  that  originally  used
between  Boston  and  Washington  and  in  the  other  sections,  particu-
larly in  the  use  of  copper  conductors  of  a  smaller  gage  combined
with  improved  loading  coils,   the  vacuum  tube  telephone  repeater

and  other  methods  and  apparatus  which  are  the  result  of  recent
developments.  Lead-covered  aerial  cable  supported  on  wooden  pole
lines  is  to  be  used  in  general  on  all  of  the  routes  except  in  the  two
sections  just  mentioned  and  through  cities  or  where  special  condi-
tions exist  for  short  distances.  The  possibility  of  now  using  con-
ductors of  No.  16  and  No.  19  A.  W.  G.  instead  of  conductors  up  to

No.  10  A.  W.  G.  as  in  the  older  cables,  has  contributed  to  make  aerial
construction  rather  than  underground  conduit  the  more  economical
in  many  sections,  as  one  cable  will  provide  for  a  much  greater  number
of  circuits  and  consequently  fewer  cables  will  be  required.

The  general  type  of  aerial  construction  which  was  used  for  over
250  miles  of  the  total  distance  of  302  miles  from  Philadelphia  to  Pitts-
burgh may  be  seen  from  Figs.  5  and  6  which  illustrate  the  poles,  steel
suspension  strand,  metal  supporting  rings  and  the  cable.  The  poles
are  25-foot  untreated  chestnut  spaced  100  feet  apart  and  designed
to  carry  additional  cables  in  the  future.  While  the  poles  are  new
and  carry  only  one  cable  they  have  a  factor  of  safety  of  about  9  under
the  most  severe  storm  conditions  expected,  but  this  will,  of  course,  be
reduced  as  other  cables  are  placed  and  will  gradually  be  decreased
on  account  of  decay  at  the  ground  line  until  it  becomes  necessary  to
start  replacing  the  poles.  Many  of  these  poles  were  grown  near  the
locations  where  they  now  stand.     In  other  sections,   it  is  planned

to  use  butt-treated  chestnut  or  cedar  poles,  or  creosoted  pine  poles
where  these  prove  to  be  the  more  economical.

The  galvanized  steel  suspension  strand  has  a  breaking  strength
of  about  16,000  pounds  and  the  actual  tension  under  normal  condi-
tions is  about  7,000  pounds.  In  placing  the  strand,  it  is  necessary
to  pull  it  to  just  the  right  tension  in  order  that  when  the  cable  is
hung  it  will  have  the  proper  sag.  The  correct  tension  is  readily
determined  by  what  is  known  as  the  "oscillation"  method.  The
metal  rings  are  spaced  16  inches  apart  and  the  cable  weighs  about
7>^  pounds  per  foot.

The  size  and  make-up.of  the  cable  vary  somewhat  with  the  number  of
circuits  of  the  various  types  that  are  to  be  provided  in  the  different
sections,  but  in  general  it  is  full  size,  that  is,  its  over-all  diameter  is

2^  in.  which  is  about  the  maximum  size  of  telephone  cable.  The
sheath  is  of  lead-antimony  alloy,  one-eighth  of  an  inch  thick,  and
under  normal  conditions  it  is,  of  course,  air-tight  to  keep  moisture
from  entering.  The  cable  for  the  aerial  section  was  received  from  the
factory  in  500-foot  lengths,  this  being  largely  determined  by  the
arrangement  necessary  to  permit  the  proper  installation  tests.

We  might  next  consider  the  route  selected  and  for  this  purpose
Fig.  2  will  again  be  helpful.     It  will  be  noted  that  starting  at  Phila-

delphia,  the  ca]:)le  is  routed  to  Reading  touching  Pottstown,  Phoenix-
ville  and  other  points.  From  Reading  to  Harrisburg  the  cable  follows
closely  the  William  Penn  Highway,  although  in  sections  it  was  neces-
sary to  obtain  private  right-of-way  or  to  use  longer  routes  removed
from  this  highway  on  account  of  the  lines  of  various  kinds  already
in  operation  there.  It  is  very  desirable  for  economic  reasons  to
keep  the  length  of  these  cables  as  short  as  possible  and  in  some  cases
this  is  absolutely  necessary  to  obtain   proper  operating  conditions.

How^ever,  the  most  direct  routes  cannot  always  be  used,  for  many
obvious  reasons,  and  this  problem  required  careful  consideration
in  all  sections  of  the  cable.

Between  Harrisburg  and  Pittsburgh  the  Allegheny  Mountains
had  to  be  crossed  and  for  this  crossing  only  two  general  routes  were
found  practicable,  the  first  following  an  existing  pole  line  which  is
the  New  York-Chicago  telephone  line  through  Lewuston,  Altoona,
etc..  and  which  we  may  call  the  northern  route,  and  second  a  southern
route  through  Shippensburg,  Bedford  and  Ligonier  for  the  most  part
along  the  Philadelphia-Chicago  line  and  also  the  Lincoln  Highway.
A  middle  route  which  is  now  used  for  the  Harrisburg-Pittsburgh  line
was  not  seriously  considered  as  the  country  was  too  rough  for  econom-
ical construction  and  maintenance  and  no  important  advantages
were  to  be  obtained.  After  careful  surveys  and  cost  studies,  taking
into  account  all  existing  and  anticipated  conditions,  such  as  circuit

requirements  and  towns  to  be  reached,  length  of  practicable  routes,
maintenance  conditions,  freedom  from  proiiable  physical  and  electrical
interference,  etc.,  it  was  decided  to  build  on  the  southern  route.

This  route,  while  of  nearly  the  same  length  as  the  northern  one  and
offering  some  important  advantages,  was  not  free  from  difficulties
as  it  crosses  the  Allegheny  Mountains  within  a  few  miles  of  the  highest

point.  Fig.  7  shows  the  cable  line  on  what  is  know  n  as  the  seven-mile
stretch  of  the  Lincoln  Highway  east  of  Ligonier,  and  here  the  going
was  fairly  good.  The  Philadelphia-Chicago  aerial  wire  line  is  also
shown  and  two  of  the  crossarms  carrying  10  wires  each  are  to  be
removed  in  the  near  future  and  the  circuits  operated  in  the  cable.
It  is  planned  to  remove  the  remaining  two  crossarms  later  on.  Fig.  8
shows  the  cable  across  a  valley  and  is  taken  from  the  point  on  the
Lincoln  Highway  called  Grand  View\  Fig.  9  shows  the  crossing
of  the  Juniata  River  east  of  Bedford  where  special  construction  was
used.  Fig.  10  shows  just  one  example  of  the  conditions  encountered
in  crossing  the  many  mountains  and  a  photograph  does  not  do  the
scenery  or  the  construction  difificulties  justice.  On  account  of  the
steep  slopes,  clamps  are  used  at  many  points  to  fasten  the  cable  to
the  strand.

Narrow-gage  timber  railroads  were  used  in  the  mountains  where
possible  to  get  material  to  the  job  and  Fig.  11  shows  one  of  the  regular

flat  cars  adapted  for  our  purpose.  Fig.  12  shows  two  5-ton  tractors
in  action  on  top  of  one  of  the  mountains.  As  many  sections  of  the
country  are  very  rough  and  highways  several  miles  distant  it  seemed
that  no  other  method  of  transporting  the  cable  reels,  wiiich  weigh

nearly  5,000  pounds,  could  possibly  be  used,  and  certainly  no  other
means  would  have  been  as  satisfactory.  Even  with  these  methods
the  cable  reels  could  not  always  be  delivered  where  desired  and  in
some  cases  it  was  necessary  to  pull  the  sections  of  cable  through  the
rings  for  a  distance  of  nearly  a  mile  to  get  them  in  place.

As  stated  before,  the  make-up  of  the  cable  varies  somewhat  with
the  circuit  requirements  in  the  different  sections  but  the  wires  and
arrangement  in  a  typical  section  of  cable  are  roughly  illustrated  in
Fig.  13.

The  cable  is  of  quadded  construction,  that  is,  the  wires  are  first
wrapped  with  dry  paper  for  insulation  and  twisted  into  pairs  and  then
two  pairs  are  twisted  into  what  is  called  a  quad.     These  quads  are

arranged  in  concentric  layers  as  shown  and  great  care  and  skill  are
required  in  the  design  and  manufacture  or  there  is  certain  to  be  serious
cross-talk  between  the  several  hundred  circiiits  when  used  for  long-
distance service.  Even  after  the  application  of  the  best  present  manu-
facturing methods,  tests  are  made  on  all  circuits  at  three  points  in
each  loading  section  of  6000  feet  while  the  cable  is  being  spliced.
These  tests  are  made  in  order  to  determine  the  best  possible  arrange-

Fig.  14 — General  Phantom  Circuit  Arrangement.   Four  wires  providing  three  circuits

ment  of  conductors  for  still  further  reducing  cross-talk  between  circuits,
and  the  splicing  is  done  accordingly.

There  are  19  quads  of  No.  16  A.  W.  G.  and  120  quads  of  No.  19
A.  W.  G.  pure  copper  conductors  in  one  of  the  principal  sections,  and
the  arrangement  of  the  four  wires  in  each  quad  is  such  that  two  physi-
cal circuits  and  one  phantom  circuit  are  made  available.  The  method
of  obtaining  three  telephone  circuits  from  two  pairs  of  wires  is  old  and
extensively  used.  It  is  illustrated  in  Fig.  14.  The  method  results
in  a  50  per  cent  increase  in  the  number  of  available  circuits  and  its
application  to  this  project  is  therefore  of  very  great  economic  impor-
tance. Now  the  total  of  139  quads  multiplied  by  3  gives  417  circuits
or  as  many  as  could  be  carried  on  about  14  heavily  loaded  pole  lines
if  aerial  wire  were  used,  but  as  will  be  described  later,  we  will  have  to
use  two  of  these  circuits  to  make  one  telephone  circuit  in  some  cases
where  the  distances  are  comparatively  great,  so  it  is  expected  that
only  about  300  telephone  circuits  will  be  obtained  for  regular  service.
This  is  as  many  as  could  be  carried  on  10  heavily  loaded  pole  lines  if
aerial  wire  were  used.  It  is  now  thought  that  in  some  sections  this
number  of  circuits  will  take  care  of  future  demands  for  about  10  years
after  allowing  for  the  dismantling  of  some  existing  aerial  wire.

As  these  cables  can  be  obtained  in  any  size  desired  up  to  the  maxi-
mum, the  period  for  which  they  should  be  engineered  can  be  determined
from  studies  of  circuit  requirements  and  costs.  These  studies  are  of
very  great  importance  and  the  cost  considerations  include,  of  course,

annual  costs  of  the  various  plans  over  proper  periods  as  well  as  first
costs.

Loading  coils  are  now  connected  to  many  of  the  circuits  and  all  of
the  circuits  in  this  cable  are  intended  to  be  equipped  with  coils  located
at  6000-foot  intervals.  The  theory  and  practice  of  loading  are  de-
scribed in  papers  previously  presented  before  the  Institute^  and  for
our  purpose  it  will  be  sufficient  to  state  that  these  loading  coils  very
materially  reduce  the  attenuation  losses  and  improve  the  quality  of
transmission  as  compared  to  cable  circuits  not  so  equipped.  The  im-
provement in  so  far  as  the  attenuation  losses  are  concerned,  varies
with  the  type  of  circuit  and  loading  coils,  but  with  one  of  the  No.  19

A.  W.  G.  circuits  in  this  cable  loaded  with  coils  having  an  inductance  of
0.175  henry  located  at  6000-ft.  intervals,  the  losses  are  only  about  one-
third  as  great  as  in  a  similar  circuit  without  the  coils.  The  connections
and  arrangements  of  the  coils  are  shown  in  Fig.  15  and  it  will  be  noted
that  coils  have  been  connected  to  both  the  physical  and  phantom  cir-
cuits. The  arrangement  is  such  that  there  is  no  appreciable  inter-
ference between  circuits  due  to  magnetic  action  in  the  iron  cores  of  the
different  coils  or  to  the  necessarily  close  electrical  relation  in  the
windings.

The  loading  coils  are  potted  and  sealed  in  iron  pots,  two  of  which
are  shown  in  Fig.  16,  and  in  the  country  these  are  mounted  on  pole
fixtures.  Each  pot  contains  36  groups  of  3  coils  each.  The  pots  are
nearly  30  inches  in  diameter  at  the  flange,  52  inches  high  and  weigh
about  2700  pounds.  The  pots  can  be  obtained  in  different  sizes
depending  upon  the  number  of  coils  which  it  is  desired  to  install  at
one   time.     When   the  cable  was  installed,  extra  lead  sleeves  were

placed  at  the  loading  points  and  a  little  slack  left  in  the  wire  to  facili-
tate the  connection  of  four  additional  loading  pots  to  the  cable  at

some  later  date  when  the  circuits  are  needed.  The  loading  points
must  be  uniformly  spaced  in  order  to  obtain  the  proper  impedance
characteristics  in  the  circuits  as  will  be  referred  to  later.  Fig.  17
shows  the  iron  core  of  a  loading  coil  and   Fig.   18  shows  this   core

wound  with  insulated  wire  and   then  wrapped  with   cloth  and   the
terminals  brought  out  nearly  ready  for  potting.     Fig.  19  shows  several

coils  arranged  on  one  of  the  spindles  which  will  be  placed  in  the  iron
pot  also  shown.  This  particular  pot  will  hold  7  spindles  and  when
they  are  in  place,  the  pot  will  be  filled  with  compound  and  thoroughly-
sealed.

Telephone  Repeaters
Even  with   the  improvement  in   the  quality  of  transmission  and
reduced  attenuation  losses  effected  by  the  use  of  loading  coils,  loaded

cable  circuits  alone  of  No.  16  and  No.  19  A.  W.  G.  could  be  satisfac-
torily operated  for  distances  less  than  100  and  60  miles,  respectively,
and  this  is  far  short  of  our  requirements  in  this  case.  In  fact,  we  wish
to  operate  some  telephone  circuits  on  these  conductors  and  through  this
cable  and  future  cables  up  to  at  least  1000  miles  in  length.     This

can  be  accomplished  1)\'  tlie  use  of  telephone  repeaters  connected  to
the  loaded  conductors.

all  the  while  the  original  wave  shape.  Therefore,  if  one  or  more  tele-
phone repeaters  are  properly  inserted  in  circuits  adapted  to  their  use,
the  range  of  satisfactory  transmission  can  be  greatly  extended.  As
many  hundreds  of  vacuum-tube  repeaters  are  in  operation  on  the
Philadelphia-Pittsburgh  cable  and  connected  cables,  and  as  a  great
many  more  are  planned  for  future  installation,  we  will  briefly  consider
the  elementary  features  of  some  of  the  types  of  repeaters  used.

element  of  this  type  of  repeater.  It  is  a  small  glass  bulb  with  a
vacuum  that  is  as  good  as  is  practicable  to  obtain.  In  the  tube
is   a   filament   which   is   heated   to   incandescence   during   operation,

and  a  grid  and  plate.  The  circuits  directly  associated  with  the  tube
are  shown  in  more  detail  in  Fig.  21,  and  this  would  constitute  a  device
for  amplifying  currents  from  one  direction.  As  is  well  understood,
any  change  in  the  potential  impressed  on  the  grid  causes  a  change  in
the  current  flowing  in  the  plate-filament  circuit.  To  obtain  complete
two-way  repeater  action  two  of  these  amplifier  arrangements  are
combined  with  the  circuits  shown  in  Fig.  22.

It  will  be  noted  that  the  line  circuit  from  one  direction,  for  instance,
the  one  designated  "line  west,"  is  connected  through  a  three-winding
transformer  to  a  balancing  network  which  is  so  made  up  as  to  balance

the  line  as  nearly  as  possible  at  telephone  frecjuencies.  This  balance
is  essential  to  proper  repeater  operation.  The  circuit  arrangement  is
such  that  part  of  the  incoming  energy  is  diverted  to  that  part  of  the
circuit  containing  the  input  coil  directly  associated  with  this  three-
winding  transformer.  By  the  action  of  the  vacuum-tube  arrangement
amplified  energy  is  transmitted  to  the  line  east.  That  part  of  the
original  incoming  energy  from  the  line  west  that  goes  through  the
balancing  network  or  the  output  coil  is  not,  of  course,  transmitted
along  into  the  line  east.  The  operation  in  the  case  of  currents  incom-
ing from  the  line  east  is  similar  and  it  w^ill  be  noted  that  the  complete
repeater  circuit  is  made  up  of  two  symmetrical  parts.  This  circuit
arrangement  constitutes  what  is  known  as  a  two-wire  repeater  and  the
apparatus  is,  of  course,  all  closely  associated  in  the  same  office.

Equipped  with  TelepNsne  Repeaters  end
Ai-ranged  for  Connection  to  Wn  Wire  Circyiti  ft  the  Terminil*

Fig.   23 — Four-Wire  Circuit   equipped  with  telephone  repeaters  and  arranged  for
connection  to  two  wire-circuits  at  the  terminals

Several  of  these  repeaters  may  be  inserted  in  tandem  at  appropriate
points  in  a  circuit,  but  there  is  a  limit  to  the  length  of  circuit  that  can
be  satisfactorily  operated  with  this  arrangement,  this  length  depend-
ing upon  the  type  of  the  facilities  used.  When  longer  circuits  are
required,  a  four-wire  arrangement  is  used,  as  shown  in  Fig.  23.  It
will  be  noted  that  in  this  arrangement  the  three-winding  transformers
are  not  located  in  the  same  office  but  may  be  in  offices  several  hundred
miles  apart.  At  each  of  the  intermediate  stations  a  vacuum-tube
amplifier  arranged  for  amplification  in  one  direction  only  is  connected
to  each  of  the  two  branches  of  the  circuit.  Two  circuits  are,  of
course,  required  between  the  terminals  and  these  may  be  either
physical  or  phantom  circuits.

not  required  at  each  repeater  station  and  the  general  matter  of  balance
and  consequently  good  repeater  operation  in  the  circuit  as  a  whole  is
greatly  simplified.  This  arrangement  can,  therefore,  be  satisfactorily
used  for  long  circuits  where  two-wire  operation  might  be  impracticable,

and  examples  would  be  such  circuits  as  New  York-Pittsburgh  or  New
York-Chicago.

Both  of  these  types  of  circuits  may  be  operated  on  No.  19  A.  W.  G.
four-wire  facilities  which  may  be  either  physical  or  phantom  circuits.

Fig.  24  shows  a  group  of  repeaters  installed  in  the  office  at  Reading,
Pa.,  and  Fig.  25  shows  one  of  the  four-wire  repeater  units  in  somewhat
greater  detail.

In  order  that  networks  may  be  used  to  balance  the  lines  for  repeater
operation,  it  is  necessary  as  a  practical  proposition  that  the  impe-
dance characteristics  of  the  lines  be  fairly  uniform  over  the  range  of
telephone  frequencies.  The  solid  line  in  Fig.  26  shows  the  resist-
ance component  of  the  impedance  of  a  No.  19  loaded  cable  circuit
with  all  loading  coils  in  place.     The  solid  line  in  Fig.  27  shcnss  the

resistance  component  found  in  impedance  measurements  on  the  same
circuit  with  one  coil  omitted  at  the  thirteenth  loading  point  from
the  end  at  which  the  tests  were  made.  It  will  be  noted  that  in  the
latter  case  the  characteristics  of  the  circuitsvary  greatly  with  frequency.
It  would  therefore  be  very  difficult  as  a  practical  proposition  to  build
up  a  network  that  would  balance  lines  in  this  condition,  and  such
variations  in  the  electrical  characteristics  of  a  circuit  impair  the
quality  of  telephone  transmission,  as  the  currents  of  different  fre-
quencies are  differently  affected.  The  necessity  for  careful  main-
tenance work  in  promptly  replacing  loading  coils  which  may  become
defective  or  preventing  other  irregularities  from  creeping  into  the  plant
will  therefore  be  clear.

The  resistance  of  small-gage  cable  conductors  is  one  of  the  important
factors  that  determine  the  transmission  losses  of  a  circuit.  The
resistance  of  a  No.  19  A.  W.  G.  pair  is  about  88  ohms  per  mile  so  that

Fig.  27 — Cable  Circuit  with  Loading  Coil  Missing  at  Thirteenth  Loading  Point  from

in  a  long  circuit  this  factor  of  line  resistance  reaches  considerable
proportions.  Now  as  most  of  the  cable  is  aerial,  the  resistance  of
the  conductors  is  of  course  affected  by  changes  in  temperature  both
daily  and  seasonal  and  the  transmission  losses  vary  accordingly.
These  changes  in  transmission  values  are  of  such  magnitude  that
automatic  transmission  regulators  are  being  provided  for  certain
groups  of  longer  circuits.  All  changes  in  the  transmission  equivalents
of  the  circuits  from  whatever  causes  must  be  carefully  watched  and
necessary  adjustments  made  or  the  service  will  be  seriously  affected.

In  the  section  between  Philadelphia  and  Pittsburgh  practically  all
of  the  existing  long  aerial  wire  circuits  are  composited,  that  is,  they
are  arranged  for  simultaneous  telephone  and  telegraph  operation.
The  telegraph  circuits  thus  obtained  are  generally  used  in  furnishing
what  is  sometimes  called  "leased  wire"  service.  The  ground  return
system  providing  either  full  duplex  or  single-line  operation  is  used
and  the  line  currents  average  about  75  milliamperes.  This  grounded
telegraph  system  cannot  be  used  where  simultaneous  telephone  and
telegraph  service  is  desired  on  loaded  cible  circuits  of  the  length
involved  in  this  cable,  and  as  a  part  of  the  work  of  carrying  out  the
comprehensive  toll  cable  plans  of  the  Bell  system,  a  new  telegraph
system  had  to  be  developed.  It  was  found  preferable  to  use  a  metallic
return  circuit  and  to  limit  the  line  current  to  a  value  between  3  and  5
milliamperes  in  order  to  prevent  serious  interference  to  the  telephone
circuits  due  to  the  "flutter  effect, "^  Morse  thump,  and  mutual  inter-
ference between  telegraph  circuits.  Morse  thump  results  when  the
composite  sets,  that  is,  the  apparatus  used  for  separating  the  tele-
phone and  telegraph  currents,  do  not  completely  prevent  the  latter
from  entering  the  telephone  circuit,  thus  causing  interference.  The
telegraph  repeaters  are  located  at  about  100-mile  intervals  on  the
No.  19  circuits  and  at  somewhat  less  frequent  intervals  on  No.  16
circuits.  The  telegraph  apparatus  is  of  course  located  in  the  same
buildings  that  are  used  to  house  the  telephone  repeaters,  and  on  the
Philadelphia-Pittsburgh  cable  telegraph  repeaters  will  be  located
initially  at  Philadelphia,  Harrisburg,  Bedford  and  Pittsburgh.

All  of  the  conductors  in  the  cables  are  carried  into  stations  located
at  about  50-mile  intervals  and  apparatus  is  provided  in  these  stations
for  making  regular  tests  to  ascertain  the  condition  of  the  cable  and  to
locate  trouble  quickly.  At  these  offices  the  different  kinds  of  operat-
ing apparatus  are  also  connected  to  the  cable  conductors;  examples
of  this  apparatus  are  phantom  repeating  coils,  composite  sets  to  per-
mit simultaneous  telephone  and  telegraph  operation,  telegraph
repeaters,  telephone  repeaters  and  associated  balancing  equipment,
signaling  apparatus,  and  where  required,  the  switchboards  necessary
for  making  the  telephone  connections  involved  in  furnishing  service.
It  is  necessary  that  this  apparatus  which  is  installed  in  large  quantities

be  systematically  arranged  and  facilities  provided  for  making  quick
changes  in  the  circuit  arrangement.  The  circuits  are  wired  through
jacks  installed  in  groups  in  test  boards  for  this  purpose  and  to  facilitate
testing.  One  of  these  boards  is  illustrated  in  Fig.  28.  This  particular
board  is  located  in  one  of  the  larger  offices.  The  test  boards  in  one
of  the  repeater  stations,  such  as  Bedford,  would  consist  of  a  smaller

number  of  positions.     A  position  is  three  feet  in  length,
each  position  bears  a  number.

Telephone  repeaters  of  either  the  two-wire  or  four-wire  type  are
connected  to  the  circuits  at  approximate  intervals  of  either  50  or  100
miles,  depending  upon  the  type  of  facilities  which  it  is  economical
to  use  in  the  different  circuits  and  the  kind  of  service  for  which  a  given
circuit  is  intended.  As  mentioned  above,  telegraph  repeaters  are
installed  at  about  100-mile  intervals.  At  some  of  these  points  existing
offices  are  used  while  in  a  number  of  cases  it  was  necessary  to  erect
buildings  for  the  sole  purpose  of  housing  the  repeaters,  testing  appa-
ratus and  other  equipment  associated  with  the  cable.  For  example,
new  buildings  of  fire-proof  construction  were  erected  at  Shippensburg,
Bedford  and  Ligonier.  Fig.  29  is  a  view  of  the  building  at  the  latter
point  and  the  other  two  buildings  are  similar  to  this  one,  the  dimensions
being  about  50  by  80  feet.     Power  plants  are  installed  in  these  build-

ings  to  furnish  current  of  the  proper  characteristics  for  operating  the
apparatus,  and  storage  batteries  are  provided  to  insure  uninter-
rupted service.  As  an  indication  of  the  size  of  these  plants  the  24-
Nolt  storage  batteries  installed  for  the  initial  load  at  Bedford  have
a  capacity  of  2240  ampere-hours  and  this  provides  about  one  day's
reserve.  The  capacity  can,  of  course,  be  increased  as  repeaters  are
added  from  time  to  time  when  additional  circuits  are  needed.  Storage
batteries  of  smaller  sizes  supplying  current  at  potentials  of  30,  120
and  130  volts  are  also  provided.

Fig.  30  shows  two  possible  methods  of  building  up  a  Philadelphia-
Pittsburgh  terminal  circuit  and  Fig.  31,  a  method  of  building  up  a
New  York-Pittsburgh  terminal  circuit.  In  all  three  cases  these
telephone  circuits  are  intended  to  have  a  transmission  equivalent  of
about    12   miles   of   standard   cable.     Some   Philadelphia-Pittsburgh

terminal  circuits  of  the  first  type  have  been  in  everyday  operation
for  several  months,  but  it  is  not  the  most  economical  arrangement
that  it  is  possible  to  obtain  for  general  use  in  providing  this  or  similar
service.  It  will  be  noted  that  No.  19  four-wire  facilities  are  used
between  Philadelphia  and  Harrisburg  and  four-wire  repeaters  are
located  at  these  two  points.     At  Harrisburg  the  four-wire  circuit  is

connected  to  a  No.  16  two-wire  circuit  with  a  two-wire  repeater  at
Bedford.  This  arrangement  was  used  in  order  to  start  service  through
the  cable  with  the  facilities  available,  but  it  is  intended  later  on  to  use
the  arrangement  shown  in  example  No.  2.

In  example  No.  2,  No.  16  heavily  loaded  conductors  are  used  and
two-wire  repeaters  are  located  at  Reading,  Shippensburg  and  Ligonier.
The  total  transmission  equivalent  of  this  circuit  without  repeaters  is

PITTSBUnCH  LICONIER  BCOrORD  SHIPPCNSBURC  HtRRISBURC  READING  PHILIDCLPHI*

about  50  miles  of  standard  cable  so  that  in  order  to  obtain  a  net
equivalent  of  12  miles  for  the  circuit  each  of  the  three  repeaters  must
give  a  transmission  gain  of  nearly  13  miles  of  standard  cable.  This
circuit  could  not  of  course  be  used  for  telephone  purposes  without
repeaters.

The  third  example  shows  how  it  is  expected  to  operate  New  York-
Pittsburgh  circuits  intended  for  business  between  these  two  terminals.

Four-wire  No.  19  loaded  cable  facilities  are  used  with  four-wire  tele-
phone repeaters  located  at  New  York,  Philadelphia,  Harrisburg,
Bedford  and  Pittsburgh.

Even  with  conductors  of  only  two  gages  in  the  cable,  it  is  clear  that
many  different  combinations  of  facilities  can  be  built  up  into  tele-
phone circuits  and  an  endeavor  is  always  made  to  use  the  most  eco-

nomical  arrangement  that  will  furnish  the  service  required  over  each
circuit  group.  The  examples  described  above  are  of  circuits  used  for
business  between  the  terminals  indicated  and  if  these  circuits  were
to  be  connected  to  others  extending  to  points  considerable  distances
beyond  these  terminals  different  arrangements  would  be  required.
The  cable  conductors  used  in  building  up  these  telephone  circuits
can  be  ccmposited  and  telegraph  circuits  are  thus  provided  for  simul-
taneou!^  operation  with  the  telephone  circuits.

In  the  above  discussion,  an  effort  has  been  made  to  furnish  some
descriptive  information  regarding  a  complete  cable  system  recently
completed  and  now  in  successful  operation  between  Philadelphia  and
Pittsburgh  and  designed  for  long-distance  telephone  and  telegraph
service.  In  one  sense  this  discussion  may  be  considered  a  report  of
the  present  status  of  the  toll  cable  plant  intended  to  connect  Atlantic
Seaboard  cities  wdth  Chicago  and  other  cities,  and  extensions  are  now
under  construction.  However,  most  of  the  general  methods  which
it  is  planned  to  use  in  these  extensions  are  not  expected  to  differ
greatly  from  those  described.

An  important  feature  of  this  cable  project  is  the  fact  that  while
many  new  developments  and  practices  are  utilized,  the  design  of  the
system  as  a  whole  is  such  as  to  fit  in  economically  with  existing  wire
and  cable  systems  and  proposed  extensions.

Synopsis:  The  present  paper  presents  an  extensive  theoretical  investiga-
tion of  the  impedance  of  the  "sea  return"  of  various  types  of  submarine
cables.  In  the  case  of  the  cables  used  for  submarine  telegraphy  the  im-
pedance of  the  sea  return  has  been  practically  negligible  because  of  the  low
frequencies  involved.  For  these  low  frequencies  the  cross-section  of  the  re-
turn path  is  very  large  and  its  resistance  low,  even  though  the  specific
resistance  of  sea  water  is  of  the  order  of  ten  million  times  that  of  copper.
As  the  frequency  of  the  cable  current  is  raised,  however,  the  return  cur-
rents crowd  in  nearer  the  cable  and  the  resistance  of  the  return  path  is
increased.  For  frequencies  in  and  above  the  telephone  range,  the  return
currents  are  forced  into  the  steel  armor  wires  around  the  cable  and  into  the
water  just  outside  of  the  insulation.  The  small  cross-section  of  the  water
involved  and  the  loss  in  the  armor  wires  cause  the  resistance  of  the  return
path  to  become  a  very  large  part  of  the  total  resistance  of  the  circuit.

The  present  investigation  led  to  the  conclusion  that  the  resistance  of
the  return  path  could  be  greatly  diminished  by  winding  a  low  resistance
conductor  in  the  form  of  a  copper  tape  immediately  around  the  gutta
percha  insulation  applied  to  the  core  of  the  cable.  The  concentric,  cylin-
drical conductor  thus  formed  lies  within  the  armor  wires  but  is  not  insu-
lated from  them  and  the  sea  water.  Estimates  of  the  sea  return  which
would  have  been  obtained  in  the  Key  West-Havana  cable  if  no  copper
tape  had  been  provided  give  values  of  4,  6.5,  and  8  ohms  per  nautical  mile
at  1,000,  3,000  and  5,000  cycles.  The  resistance  actually  obtained  with
the  copper  tape  does  not  exceed  1.7  ohms  at  5,000  cycles.  The  greater
values  would  have  increased  the  attenuation  by  approximately  30%  at
1,000  cycles  and  by  50%  at  the  two  higher  frequencies.  The  present
cable  permits  of  the  operation  of  a  carrier  telegraph  channel  at  3,800  cycles,
this  lying  above  the  range  of  telephone  frequencies.

The  paper  gives  a  comparison  of  the  theoretical  conclusions  with  ex-
perimental data  and  the  agreement  is  so  satisfactory  as  to  indicate  that
the  theory  is  a  reliable  guide  in  the  design  of  such  a  cable. — Editor.

THE  transmission  characteristics  of  a  conducting  system,  such  as
a  submarine  cable  circuit,  are  determined  by  its  propagation
constant,  F,  and  characteristic  impedance,  K,  which  may  be  calcu-
lated for  the  frequency  p  12-k  from  the  formulas:

where  R,  L,  G  and  C  are  the  four  fundamental  line  parameters,  re-
sistance, inductance,  leakance,  and  capacity,  all  per  unit  length.  These
formulas  are  rigorous  for  all  types  of  transmission  systems;  but  the
determination  of  the  line  parameters  is  not  always  possible  by  ele-
mentary methods,  and  may  indeed  be  a  matter  of  considerable  com-

plexity  and  involve  rather  difficult  analysis.  In  the  case  of  the  sub-
marine cable,  exact  formulas  are  available  for  calculating  the  capacity
and  leakage  and  the  core  impedance.  Considerable  uncertainty  is
introduced  into  the  theory,  however,  on  account  of  the  lack  of  a
method  of  determining  the  "return  impedance,"  that  is,  the  con-
tribution of  the  "sea  return"  (sea  water,  armor  wires,  etc.)  to  the
effective  resistance  and  inductance  of  the  circuit.  An  investigation
of  this  problem  was  undertaken  by  the  writers  in  connection  with  the
research  program  of  the  American  Telephone  and  Telegraph  Company
and  the  Western  Electric  Company.

The  purpose  of  the  present  paper  is  to  discuss  transmission  over
the  submarine  cable,  and,  more  particularly,  to  develop  rigorous
formulas  for  the  calculation  of  the  impedance  of  the  return  con-
ductor of  the  cable.  The  results  of  theoretical  calculations  are  then
compared  with  actual  experimental  data;  and  the  agreement  between
theory  and  experiment  is  so  satisfactory  as  to  indicate  that  the  former
is  a  reliable  guide  in  the  design  and  predetermination  of  the  cable.

Besides  providing  a  method  for  accurately  calculating  the  trans-
mission characteristics  of  a  submarine  cable,  the  present  analysis
leads  to  the  following  general  conclusions:

(1)  Contrary  to  usual  assumption,  the  "sea  return"  impedance
is  by  no  means  negligible.  Even  at  quite  moderate  frequencies  there
is  a  considerable  crowding  of  the  return  current  into  the  immediate
neighborhood  of  the  cable,  with  a  consequent  rapid  increase  of  the
resistance  and  a  corresponding  decrease  of  the  inductance  of  the
circuit.  Except  at  the  lowest  frequencies,  therefore,  the  impedance
of  the  "sea  return"  is  a  very  important  factor.

(2)  The  armor  wires  which  surround  the  cable,  and  which  are
necessary  for  mechanical  protection,  have  a  very  pronounced  effect
on  the  impedance  of  the  sea  return,  and  even  at  moderate  frequencies
may  become  the  controlling  factor.  Their  action  is  to  screen  the
current  from  the  sea  water  itself,  and,  as  the  frequency  increases,
to  carry  more  and  more  of  the  return  current,  until  it  is  almost  en-
tirely confined  to  the  armor  wires  and  excluded  from  the  sea  water.

(3)  The  rapid  increase  in  the  impedance  of  the  armor  wires  with
frequency,  and  their  pronounced  and  even  controlling  effect  on  trans-
mission makes  a  thorough-going  study  of  their  role  in  the  electrical
system  a  matter  of  first-class  importance.  Heretofore  they  appear
to  have  been  regarded  only  as  a  mechanical  protection,  and  their
effect  on  transmission  has  been  ignored.  The  accurate  method  of
calculating  their  impedance  which  is  developed  in  the  following  pages
is  believed  to  have  considerable  value  in  this  connection.

(4)  At  relatively  high  frequencies,  the  return  impedance,  and
hence  the  attenuation  and  the  distortion,  may  be  very  greatly  de-
creased by  a  correctly  designed  thin  metallic  sheath  concentric  with
the  core,  and  in  electrical  contact  with  the  armor  wires.  The  very
important  action  of  such  a  sheath,  even  when  extremely  thin,  does  not
appear  to  have  been  adequately  recognized  or  studied.  It  is  suggested
that  the  introduction  of  such  a  sheath  alifords  a  means  of  greatly
increasing   the   range   of   frequencies  which  the  cable   can   transmit.

The  general  problem  of  determining  the  transmission  character-
istics of  a  system  consisting  of  an  insulated  conductor  surrounded  by  a
concentric  ring  of  armor  wires  immersed  in  sea  water  is  of  consider-
able difficulty,  since  in  this  case  the  propagated  wave  must  be  repre-
sented as  a  set  of  component  waves  centered  upon  or  diverging  from
the  axes  of  the  core  and  of  the  individual  armor  wires.  The  problem
was  first  simplified  by  replacing  the  ring  of  armor  wires  by  a  cylindrical
sheath,  thus  giving  circular  symmetry  to  the  structure.  The  analysis
of  this  case,  however,  showed  that  the  effect  of  the  iron  sheath  re-
placing the  armor  wires  was  so  pronounced  as  to  make  this  simplifying
assumption  of  doubtful  validity.  The  general  problem  was  there-
fore attacked,  and  rigorous  methods  developed  for  calculating  the
effect  of  the  armor  wires  upon  transmission.  The  results  in  this
case  differ  markedly  from  those  obtained  for  the  case  of  a  continuous
iron  sheath,  which  indicates  that  great  caution  must  be  used  in  making
assumptions  regarding  the  physical  structure  of  the  armoring.

The  present  paper  follows  rather  closely  the  course  of  the  writers'
investigation.  In  Section  II  is  analyzed  the  problem  of  transmission
over  a  system  consisting  of  n  coaxial  cylindrical  conductors,  which
may  be  either  in  electrical  contact  at  their  adjacent  surfaces  or  sepa-
rated from  each  other  by  dielectric  spaces.  The  outermost  con-
ductor, consisting  of  the  sea  water,  is  assumed  to  extend  to  infinity.
This  analysis  is  then  applied,  in  Section  III,  to  the  case  of  a  sub-
marine cable  which  is  armored  with  a  continuous  iron  sheath.  This
problem  is  not  only  of  interest  in  itself,  but  serves  as  a  first  approxi-
mation to  the  case  of  an  actual  cable,  and  gives  a  clear  qualitative
idea  of  the  effect  of  the  various  factors  on  transmission.  In  Section
IV  the  problem  of  the  submarine  cable  armored  with  a  ring  of  iron
wires  is  attacked  and  solved  by  rigorous  methods,  and  the  theoretical
results  are  then  compared  with  experimental  data.

The  solution  of  the  problem  of  transmission  of  periodic  currents
over  a  system  comprising  n  coaxial  cylindrical  conductors  consists

in  finding  the  particular  solution  of  Maxwell's  equations  which  satis-
fies the  boundary  conditions — continuity  of  tangential  electric  and
magnetic  forces  at  the  surfaces  of  the  conductors.  Let  the  common
axis  of  the  conductors  coincide  with  the  Z  axis  of  a  system  of  polar
coordinates,  R,  <I>,  Z,  and  let  the  electric  and  inagnetic  variables  in-
volve the  common  factor  exp  (  — F  2  +  ipt),  T  is  therefore  the  propa-
gation factor  characterizing  transmission,  and  p  is  2ir  times  the  fre-
quency. This  factor  will  not  be  explicitly  written  in  any  of  the  work
that  follows,  but  it  will  be  assumed  to  be  incorporated  in  each  of  the
electric  variables  so  that

From  symmetry,  it  is  evident  that  the  component  of  electric  field
intensity  in  the  direction  of  <^  vanishes,  and  that  the  magnetic  lines
of  force  are  circles  lying  in  planes  perpendicular  to  the  axis  of  the
system,  and  centered  on  that  axis.  Also,  the  axial  and  radial  electric
forces  are  independent  of  0.  It  can  be  shown  that  the  radial  compo-
nent of  electric  field  intensity  in  the  conductors  is  negligibly  small  com-
pared with  the  axial  component.  The  latter,  for  a  given  conductor,
is  of  the  form  E  exp{  —  Tz  -\-  ift),  where  £  is  a  solution  of  the  differen-
tial equation

Here  X  and  m  are  the  electrical  conductivity  and  the  magnetic  perme-
ability of  the  particular  conductor,  measured  in  absolute  electro-
magnetic units,  and  £  is  a  function  of  r  alone.

For  the  frequencies  in  which  we  are  interested  it  may  be  shown
that  T-/4Tr\ijLp  is  exceedingly  small,  so  that  (2)  may  be  written

We  will  designate  by  the  subscript  j  all  quantities  pertaining  to  the
j'^  conductor,  counting  from  the  axis.  The  solution  of  (3)  for  this
conductor  may  then  be  written

where  /<,  and  K^  are  Bessel  functions  of  zero  order,  Aj  and  Bj  are
arbitrary  constants  and

where  the  prime  indicates  differentiation  with  respect  to  pj.  Taking
the  line  integral  of  both  sides  of  (5)  around  circular  paths  in  con-
ductor j  lying  close  to  the  inner  and  outer  surfaces  of  the  cylinder  we
obtain

The  values  of  the  electric  field  intensity  at  the  inner  and  outer  sur-
faces of  the/''  conductor  can  be  written,  from  (4)

We  liave  now  succcecled  in  cxpressin;j;  tlu'  electric  forces  in  the
conductors  as  linear  functions  of  the  currents  /i  .  .  .  /„,  the  coeffi-
cients being  of  the  nature  of  inipxxlances,  by  a  method  which  is  simply
an  application  of  the  principle  of  continuity  of  magnetic  field  intensity.
The  remaining  boundar\-  condition,  continuity  of  the  tangential
component  of  electrical  field  intensit\-  gives,  where  two  consecutive
cylinders  are  in  electrical   contact,

This  gives  m  relations  between  the  n  currents  of  the  system,  m
being  the  number  of  contacts  between  successive  cylinders.  In  the
case  where  the  j  and  (_;  +  l)st  conductors  are  separated  by  a  layer
of  dielectric  material,  a  relation  between  the  boundary  values  of
electric  field  intensity  may  be  obtained  as  follows:

is  the  potential  difference  between  the  j  and  {j  +  l)st  conductors,
in  the  sense  employed  in  ordinary  circuit  theory.  If  we  now  apply  the
law

where  Qj  is  the  charge  on  the  f^  conductor  and  kj  is  the  dielectric
constant  of  the  medium,  whence,

where   the   last   term   represents   the   leakage   current,   gj   being   the
specific  conductivity  of  the  dielectric.
From  (13)  we  have

An  equation  of  this  sort  may  be  obtained  for  each  layer  of  dielectric
and  these  combined  with  equations  (9)  and  the  condition  that  the
electric  field  intensity  in  the  sea  water  must  vanish  at  infinity,

give  n  relations  between  /i  .  .  .  /„.     In  order  that  these  shall   be  con-
sistent, the  determinant  of  the  coef^cients  must  vanish.

This  is  an  equation  in  F^  of  degree  equal  to  the  number  of  dielectric
layers;  consequently,  there  are  as  many  independent  modes  of  propaga-
tion in  the  system  as  there  are  branches  in  the  network  of  conductors.
From  this  point  the  method  of  determining  the  behavior  of  the
system  depends  upon  conditions  in  the  particular  problem.  For  the
case  where  there  are  k  dielectric  layers  separating  the  conductors
into  ^  +  1  groups  the  current  on  the  j'^  group  may  be  written  in  the
form

where   T^  .  .  .  T^k  are  the  k  roots  of  the  determinant   (17)   and    Aji
,  .  .  A^',,  Bji  .  .  .  Bp  are   constants.     These  constants  are  not  all  in-

dependent,  however,  since,  for  each  value  of  F,  Fi  for  instance,  there
exist  k  relations  of  the  form  (16)  which  the  corresponding  set  of
constants  Aw,  A21,  ■  ■  ■  Aki  must  satisfy.  The  remaining  2k  inde-
pendent constants  can  then  be  determined  from  a  knowledge  of  the
conditions  at  the  terminals  of  the  conductors.

It  is  important  to  observe  that  the  transmission  characteristics  of
a  system  of  coaxial  conductors  are  influenced  to  a  great  extent  by
the  manner  of  connecting  the  various  members  of  the  system.
Anomalies  in  the  impedance  of  a  complicated  network  such  as  a
submarine  cable  with  several  conducting  sheaths  in  the  return  path,
may  often  be  traced  to  lack  of  proper  connections  between  the  sheaths,
or  to  faulty  joints.

The  submarine  cable  armored  with  a  continuous  coaxial  sheath,
as  shown  in  Fig.  2,  is  a  particular  case  of  the  foregoing,  and  one  which
presents  a  clearer  idea  of  the  physical  significance  of  the  various  steps
in  the  general  theory.     There  are  only  two  groups  of  conductors,  the

first  consisting  of  the  core  conductor,  and  the  second  comprising  the
iron  sheath  and  the  sea  water,  the  two  groups  being  separated  by  the
insulating  material  and  the  layer  of  jute.  Consequently,  there  is
only  one  mode  of  propagation,  and  the  analysis  is  considerably  sim-
plified.

The  jute  is  assumed  to  contain  sufficient  sea  water  so  that  although
it  conducts  practically  no  current  axially,  it  maintains  equality  of
potential  between  the  outer  surface  of  the  gutta  percha  and  the  inner

where  £"i  and  E'-i  are  the  values  of  electric  field  intensity  at  the
outer  surface  of  the  core  conductor  and  the  inner  surface  of  the  iron,
respectively,  V  is  the  potential  difTerence  between  these  two  surfaces,
and  $  is  the  magnetic  flux  threading  unit  length  of  the  gutta  percha
and  jute.     Also,  from  (14)

where  gu  and  ki2  are  the  electrical  constants  of  the  gutta  percha,
and  b  is  the  external  radius  of  the  core.  It  is  evident,  that  G  and  C
are  respectively  the  leakage  and  capacity  of  unit  length  of  the  cable.
Therefore,  from  (1),

where  R  and  L  are  the  resistance  and  inductance  of  unit  length  of  the
cable,  including  the  sea  return.     Equation  (18)  may  then  be  written

where  Zi  may  be  termed  the  "  internal  impedance  "  per  unit  length
of  this  conductor.     In  fact,  when  we  place  Vi  =  0  in  (8)  we  obtain

which  is  the  usual  formula  for  the  internal  impedance  of  a  c\lindrical
conductor.
Similarly

minus  sign  being  due  to  the  fact  that  the  current  in  the  return  is
in  the  negative  direction  of  z.

where  I2  is  the  current  in  the  iron  sheath.  The  value  of  this  current
can  be  found  by  applying  the  condition  of  continuity  of  electric
field  intensity  at  the  common  surface  of  the  iron  and  the  sea  water,
as  in  equation  (9).     This  gives

in  which  I3  is  the  current  in  the  sea  water.  From  (8)  it  can  be  seen
that  Z33  =  0,  since  X3  =  00 ,  therefore

as  the  internal  impedance  of  the  return  conductor.     The  resistance
and  reactance  per  unit  length  of  this  portion  of  the  circuit  are  then
represented  by  the  real  and  imaginary  parts  of  (28)  respectively.
We  may  then  determine  R  and  L  from  the  formula

62  and  ai  being  the  inner  radius  of  the  iron  and  the  outer  radius  of
the  core  conductor,  respectively.

For  purposes  of  comparison,   the  return   impedance  is  calculated
for  the  case  where  the  iron  armoring  is  absent,  the  return  current

TVie   expression    for   Z2   simplifies   considerably.     The   electric   field
intensity  in  the  sea  water  may  be  written,  from  (4),

the  term  in  J^  being  absent  in  order  to  permit  £2  to  vanish  at  infinity.
Also,  from  (6),

The  resistance  and  inductance  of  the  sea  return  of  a  submarine
cable  were  calculated  from  formula  (28).  employing  the  following
values  for  the  constants:

The  armoring  was  then  assumed  to  be  replaced  by  sea  water,  and
the  resistance  and  inductance  of  the  cable  were  calculated  from  (33).

It  is  evident  from  these  curves  that  the  effect  of  the  iron  armoring
is  to  increase  considerably  the  impedance  of  the  return  path.     The

/4  -  Resistance  ~  Iron  Sheet
8  -  Inductance  -  Iron  Sheat
C  -  Resistance  -  No  Armor
D  ~  Inductance   ~  No  Armor

physical  explanation  of  this  fact  is  that  the  iron  acts  as  a  shield  to
screen  from  the  sea  water  the  electromagnetic  effects  of  the  current
flowing  in  the  cable  conductor.  Energy  is  dissipated  in  the  armoring
and  is  prevented  from  spreading  out  through  the  surrounding  medium.
The  assumption  that  the  armor  wires  could  be  replaced  by  a  solid
cylinder  of  iron  is,  therefore,  subject  to  question,  since  it  is  possible
that  the  larger  surface  area  of  the  assemblage  of  armor  wires,  and
the  gaps  between  these  wires  may  be  effective  in  diminishing  the
energy  dissipated  in  the  armoring  and  consequently  diminishing  the
screening  effect.     This  problem  is  investigated  in  the  following  section.

The  physical  system  under  consideration  is  shown  schematically
in  cross-section  in  Fig.  4,  and  consists  of  an  insulated  conductor  and

protective  covering  of  jute,  surrouiuied  !)>•  a  riiij^  of  N  armor  wires
immersed  in  sea  water.  The  method  of  solution  is  essentially  similar
to  that  given  in  the  preceding  pages,  and  consists  in  determining  the
values  of  electric  field  intensity  at  the  outer  surface  of  the  core  con-
ductor and  the  inner  surface  of  the  return  conductor,  from  which  the
internal  impedances  of  the  two  conductors  can  be  found.

The  main  dif^culty  in  the  analysis  is  caused  by  the  lack  of  uniaxial
symmetry  in  the  return  conductor.  This  was  overcome  by  employ-
ing a  method  developed  by  one  of  the  authors^  in  a  study  of  trans-
mission in  parallel  wires.

The  electric  field  intensity  in  the  sea  w^ater  satisfies  the  differential
equation

Assuming  that  the  current  distribution  in  the  core  conductor  is
independent  of  the  angle  0,  that  is,  neglecting  the  individual  char-
acter of  the  armor  wires  only  in  their  efifect  on  the  current  distribu-
tion in  the  core,  the  effect  due  to  the  current  in  the  core  is  represented

'"Wave  Propagation  over  Parallel  Wires;  The  Proximity  Effect."  John  R.
Carson,  PJiil.  Mag.,  vol.  xli,  p.  607  (1921).

by  the  first  term  of  such  a  series,  and  the  total  field  intensity  may  be
written

Pj  and  4:j  being  referred  to  the  axis  of  wire  j,  as  shown  in  Fig.  5.  That
is,  the  resultant  field  is  expressible  as  a  set  of  waves  centered  on  the
axis  of  the  cable  and  the  axes  of  the  N  armor  wires.

In  the  neighborhood  of  the  armor  wires  the  arguments  of  the  Bessel
functions  are  sufficiently  small  ^  to  permit  of  the  approximations

magnetic  intensity  in  the  sea  water  can  be  obtained  by  differentiation.

X  and  y.  being  the  electrical  conductivity  and  the  magnetic  perme-
ability, respectively,  of  the  material  of  the  armor  wire.  The  quan-
tities a  and  4>  are  centered  on  the  axis  of  the  wire.

In  order  to  determine  the  coefficients  A,  B^,  Bi,  —  ,  Co,  Ci,  —  we
make  use  of  the  fact  that  the  electric  and  the  magnetic  field  intensi-
ties are  continuous  at  the  surface  of  the  wire.  It  is  obvious,  however,
that  nothing  can  be  learned  by  equating  (35)  and  (36)  since  they
are  formally  dissimilar.  We  therefore  transform  ■*  the  various  terms
of  (35)  to  a  common  axis  which  coincides  with  the  axis  of  one  of  the
armor  wires,  hereafter  called  wire  "  zero,"  and  the  electric  field
intensity  in  the  sea  water,  close  to  the  surface  of  the  armor  wire,  is

The  tangential   magnetic  field  intensity  in   the  sea  water  at  the
surface  of  wire  "  zero  "  is,  therefore,

To  satisfy  the  condition  of  continuity  of  electric  and  magnetic
field  intensities  at  the  surface  of  the  armor  wire  it  is  necessary  that
the  coefftcients  of  the  corresponding  terms  of  (36)  and  (38)  and  of
(37)  and  (41)  be  equal.     This  gives

From  these  expressions  the  quantities  Bi  .  .  .  Ci  .  .  .  can  be  de-
termined.    Multiplying  (43)  by  tui  and  subtracting  (45)  gives

which  expresses  C„  in  terms  of  </„.     Multiplying  (43)  by  f/„'  (f)  and
(45)  by  /„  (f),  and  subtracting  gives

From  the  infinite  set  of  simultaneous  equations   (47)   the  infinitely
many  variables  q„  may  be  determined  in  terms  of  A  and  B^.^

We  have  thus  determined  the  arbitrary  constants  C^  ■  .  .  C„  and
qi  .  .  .  g„  (or  Bi  .  .  .  B„)  as  functions  of  A  and  Bg.  It  remains  to
express  the  latter  quantities  in  terms  of  physical  quantities.     If  /i

We  can,  therefore,  express  all  the  arbitrary  constants  as  linear,  homo-
geneous functions  of  !„  and  Zi.

Having  shown  that  the  constants  A,  B^  .  .  .  of  the  series  (35)  are
proportional  to  I^,  we  can  express  the  electric  field  intensity  at  the
inner  surface  of  the  return  conductor  in  the  form

The  computation  of  Z2  is  facilitated  by  transforming  the  terms  of
(35)  to  the  axis  of  the  core  conductor  ^  and  placing  r  =  c  —  a.  We
thus  obtain

E2=-Z2lo={A+NBo)K-A\og{c-a)-NBo\ogc-N{qi-q2  +  qz...)
+  (terms  containing  cos  d,  cos  26,  etc.,  as  factors).     (53)

We  have,  by  applying  the  curl  law  to  an  elementary  contour  which
links  the  core  conductor  and  the  return.

>o  and  Ho  being  the  electrical  constants  of  the  core  conductor  and
Oo  its  radius.  The  value  given  above  for  $12  holds  only  for  the  con-
tour on  which  £2  is  independent  of  the  angle  d,  that  is,  when  the  terms
of  (53)  that  contain  cos  6,  cos  26,  etc.,  vanish.  The  value  of  Z2  to
be  used  in  (54)  is  therefore  determined  from

where  R  and  L  are  the  resistance  and  inductance  per  unit  length  of
the  cable,  including  the  sea  return.
We  have  then  from  (54),

(1)  Determine  from  (47)  the  quantities  qi  .  .  .  q„  in  terms  of  A  and
Bo,  and  then  in  terms  of  /i  and  /„  by  (49)  and  (50).

(4)  Eliminate  /i  from  these  two  relations,  thus  obtaining  £2  in
terms  of  I^-     Then  Zo  =  —  E2/ 1^.

(5)  Substitute  this  value  of  Z2  and  the  value  of  Zi  calculated
from  (55)  in  equation  (58).

(6)  The  resistance  and  the  inductance  per  unit  length  of  the  cable
may  then  be  determined  from  the  real  and  imaginary  parts  of  the
latter  equation.

effect  of  the  presence  of  the  iron  upon  the  resistance  of  the  return
conductor  is  still  noticeable,  although  it  is  much  less  than  in  the  case
of  the  continuous  iron  sheath.  The  reason  for  this  is  evident  after
inspection  of  the  curves  of  Fig.  6,  which  show  the  percentage  of  return
current  carried  by  the  armor  in  the  two  cases.  Especially  at  the
lower  frequencies,  the  return  current  is  much  more  confined  by  the
continuous  sheath  than  it  is  by  the  wires.

As  a  check  of  the  method,  the  resistance  and  inductance  of  the
Seattle-Sitka  cable  of  the  United  States  Signal  Corps  were  calcu-
lated for  frequencies  in  the  range  50  to  600  cycles  per  second,  and

A- Resistance' Small   Diameter  Armor  Ring.
B- Resistance 'Large  Diameter  Armor   Ring
C  -  Inductance  ~  Small  Diameter  Armor  Ring.
D- Inductance -Large  Diameter  Armor   Ring.
O'Experimental  Values

the  values  so  obtained  were  then  compared  with  the  results  of  meas-
urements recently  made  upon  this  cable. ^  The  constants  used  in
the  calculations  were  as  follows:

'  "The  Use  of  Alternating  Currents  for  Submarine  Cable  Transmission,"  Frederick
E.  Pernot,  Jour,  of  the  Franklin  Instilute,  vol.  190,  p.  323,  1920.

Owing  to  lack  of  information  concerning  the  mean  radius  of  the
ring  of  armor  wires,  two  sets  of  data  were  computed  employing  the
values  c  =  0.6148  and  c  =  0.920,  which  correspond,  respectively,  to
zero  and  maximum  separation  of  the  armor  wires.

The  results  of  the  calculations  are  shown  in  Fig.  7.  The  experi-
mental values  are  indicated  by  small  circles,  and  agree  well  with  the
theoretical    values    throughout    the    range    of    frequencies.     The    re-

sistance  of  the  sea  return  increases  most  rapidly  in  the  region  of
frequencies  used  in  ordinary  telegraphy,  0  to  100  cycles  per  second.
In  this  range  the  inductance  of  the  cable  also  has  its  greatest  values,
and  these  two  effects  have  considerable  influence  in  determining  the
transmission  characteristics  of  the  cable.

The  percentage  of  the  return  current  that  is  carried  by  the  armor
wires  is  shown  in   Fig.  8.

As  was  previously  pointed  out,  the  effect  of  the  shielding  action
of  the  iron  armor  of  a  submarine  cable  is  to  diminish  the  electro-
magnetic field  which  is  propagated  through  the  sea  water,  and  which
gives  rise  to  the  return  current.  Combined  with  this  effect  is  the
shielding  action  of  the  sea  water  adjacent  to  the  cable,  upon  the  dis-
tant portions.  The  total  shielding  effect  increases  with  the  fre-
quency until  a  point  is  reached  where  practically  the  whole  of  the
return  current  is  carried  by  the  armor  wires.

Several  remedies  have  been  suggested  for  diminishing  the  damping
effect  of  the  armor  wires.  It  can  be  proved,  for  example,  that  for  a
given  size  of  core  and  .weight  of  armor,  the  number  and  size  of  armor
wires  can  be  chosen  so  as  to  give  a  minimum  value  of  return  im-
pedance. A  proper  choice  of  the  electrical  constants  of  the  ma-
terial of  which  the  armor  is  constructed  would  also  be  of  advantage,
since  the  return  impedance  is  somewhat  larger  for  iron  than  it  is  for
material  of  higher  or  lower  conductivity.

Another  method  of  diminishing  the  return  impedance,  which  has
been  used  in  practice,  is  to  wrap  the  cable  core  with  a  number  of  con-
centric layers  of  conducting  tape  before  it  is  covered  with  jute.  The
return  current,  as  it  crowds  in  toward  the  core  with  increasing  fre-
quency, will  then  have  a  path  of  comparatively  low  impedance,  and
at  the  higher  frequencies  only  a  small  portion  of  the  current  will  be
carried  by  the  armor  wires  and  the  sea  water.  The  impedance  of
the  return  path  can  be  calculated  for  this  case  by  the  methods  given
in  the  preceding  pages.  The  following  table  compares  the  values
of  the  resistance  of  the  return  conductor  calculated  by  three  different
methods,  and  determined  experimentally,  for  a  cable  provided  with
a  brass  tape  5  mils  in  thickness.

The  experimental  values  are  the  results  of  a  series  of  measure-
ments made  by  the  Department  of  Development  and   Research  of

*  This  is  an  empirical  formula  which  has  been  found  to  be  fairly  close  in  most
cases.  The  correction  factor  suggested  itself  in  that  it  takes  care  of  the  increased
surface  of  the  armor  wires,  as  compared  with  the  corresponding  continuous  sheath.

the  American  Telephone  and  Telegraph  Company  upon  the  Victoria-
Vancouver  submarine  cable.  The  calculated  values  were  obtained
by  both  the  approximate  and  the  exact  methods,  discussed  in  the
preceding  pages,  in  which  the  armor  of  the  cable  is  treated,  respec-
tively, as  a  continuous  sheath  and  as  a  ring  of  wires.  The  modifica-
tions which  must  be  introduced  to  include  the  effect  of  the  conduct-
ing tape  are  outlined  in  the  discussion  of  the  general  theory.  The
agreement  between  the  calculated  and  the  measured  values  of  return
resistance  proves  that  the  method  developed  in  the  present  paper
is  accurate  even  at  the  highest  frequencies  employed  in  telephony.

The  Bessel  Functions  of  zero  order  of  the  first  and  second  kinds,
Jo  (p)  and  Ko  (p),  used  in  the  preceding  work  are  all  to  a  complex
argument  p  =  ^'gvTwhere  5  is  a  real  number  and  i  =  V-  1.  The
following  formulas^  may  be  used  for  determining  the  values  of  these
functions:

The  reports  of  the  British  Association  for  1912  and  1915  give  the
values  in  this  range  of  the  functions  ber  q,  ber'  q,  bei  q,  bei'  q,  ker  g,
ker'q,  kei  q,  kei'q  which  are  defined  by  the  relations

»  It  is  to  be  noted  that  this  approximation  for  Ko  (p)  differs  from  the  expression
used  by  J.  J.  Thomson,  "Recent  Researches  in  Electricity  and  Magnetism,"  p.  263.
Thomson's  formula  (2)  from  which  his  approximation  was  derived,  contains  a
number  of  errors  and  should  read

In   problems  involving  Fourier-Bessel  expansions  it  is  sometimes
necessary  to  transform  quantities  of  the  form

from  the  system  of  coordinates  pj,  (pj  to  the  systems  p,  4>  or  r,  d  which
are  related  as  shown  in  Fig.  5.

The  vectors  Zj,  Z  and  C,  as  may  be  seen  from  Fig.  5,  have  the
lengths  Pj,  p  and  c,  respectively,  and  the  directions  indicated  by  the
arrows.

The  values  qi,  52  •  •  •  may  be  determined  by  a  method  of  approxi-
mations, g„  being  the  limit  of  the  sequence

This  method,  however,  while  formally  simple  and  direct  is  not
usually  well  adapted  for  numerical  solution.  For  all  sizes  of  armor
wire  and  for  frequencies  of  practical  importance  the  argument  f  in
the  expression  (48)  is  small  compared  with  /i  and  the  quantities,

are  all  nearly  unity.     This  suggests  the  use  of  the  following  method
of  solution  of  equations  (47).

in  which  Cu,  etc.,  are  numerics.  This  solution  is  effected  by  retain-
ing a  finite  number  of  equations  and  an  equal  number  of  variables
and  solving  by  the  usual  methods.  It  will  be  found  that  except  in
extreme  cases,  a  very  good  approximation  can  be  gotten  by  ignoring
all  the  p's  except  the  first  four.  The  qs  may  then  be  obtained  by
the  relation

This    system    is    easily    adapted    to    solution    by    successive    ap-
proximations,

C„i,  etc.,  being  the  numerical  coefficients  which  appear  in  the  ex-
pressions for  pi,  p2  .  .  .  .

Synopsis:  The  frequency  distribution  of  energy  in  speech  has  been  de-
termined for  six  speakers,  four  men  and  two  women,  for  a  50-syllable
sentence  of  connected  speech,  and  also  for  a  list  of  50  disconnected  syllables.
The  speech  was  received  by  a  condenser  transmitter  whose  voltage  output,
amplified  3,000  fold,  was  impressed  on  the  grids  of  twin  single  stage  amplifi-
ers. The  unmodified  output  of  one  of  these  amplifiers  was  measured  by  a
thermocouple  and  was  a  known  function  of  the  total  energy  received  by  the
transmitter,  corrections  being  made  for  the  slight  variation  with  frequency
of  the  response  of  the  circuit.  The  output  of  the  other  amplifier  was  limited
by  a  series  resonant  circuit  to  a  narrow  band  of  frequencies,  the  energy  in
this  band  being  measured  by  a  second  thermocouple.  The  damping  of  the
resonant  circuit  was  so  chosen  that  sufficient  resolving  power  and  suiificient
energy,  sensitiveness  were  obtained  over  the  range  from  75  to  5,000  cycles
per  second;  and  23  frequency  settings  were  made  to  cover  this  range.  For
each  syllable  simultaneous  readings  were  recorded  on  the  two  thermocouples
at  each  frequency  setting.  The  consecutive  syllables  were  pronounced  de-
liberately by  each  speaker,  maintaining  as  nearly  as  possible  the  normal
modulation  of  the  voice.  Corrections  were  applied  to  offset  the  unavoidable
variations  in  total  energy  incidental  to  repetition  of  a  given  syllable.
13,800  observations  were  made  for  all  speakers.  The  energy  distribution
curves  obtained  are  essentially  the  same  for  connected  as  for  disconnected
speech,  and  indicate  that  differences  between  individuals  are  more  important
than  variations  due  to  the  particular  test  material  chosen.  A  composite
curve  drawn  from  the  individual  curves  shows  a  great  concentration  of
speech  energy  in  the  low  frequencies,  a  result  which  would  not  be  expected
from  data  previously  published  by  others.  The  actual  results  contain
a  factor  due  to  standing  waves  between  the  speaker's  mouth  and  the
transmitter,  a  complication  always  present  in  telephoning;  this  could  not
be  eliminated.

The  rate  of  energy  output  in  speech  for  the  normally  modulated  voice,  was
determined  from  the  readings  for  total  energy  and  was  found  to  be  about
125  ergs  per  second.

IN  the  study  of  speech  and  its  reproduction  by  mechanical  apparatus
it  is  necessary  to  consider  its  composition  from  several  different
points  of  view.  We  desire  first  of  all  to  know  the  actual  frequency
distribution  of  the  total  energy  in  speech,  as  well  as  the  separate  dis-
tributions for  each  individual  sound.  We  also  desire  to  know  the
apparent  distribution  of  energy,  that  is,  the  distribution  as  perceived
by  the  ear.  Finally,  we  wish  to  know  the  importance  of  each  fre-
quency, that  is,  the  contribution  to  "articulation"  or  "quality"
in  the  exact  reproduction  of  speech  which  can  be  traced  to  the  energy
of  each  elementary  band  of  frequencies  in  the  speech  range.  In  all
three  cases  certain  frequency  functions  are  used  to  represent  these
distributions.  The  advantage  of  considering  these  difTerent  frequency
distribution  functions  separately  has  already  been  indicated  by  one
of  the  present  writers.^

1  Reprinted  from  The  Physical  Review,  N.S.,  Vol.  XIX.  No.  3,  March,  1922.
»"The  Composition  of  Speech,"  Phys.  Rev.,  X,  p.  74,  1917.

In  our  judgment  the  most  important  of  these  data  of  speech  study  is
the  actual  energy  distribution,  considering  speech  as  "a  continuous  Mow
of  distributed  energy, "  in  accorchmce  with  the  ideas  expressed  in  the
earlier  paper.  The  present  paper  offers  a  determination  of  this
fundamental  factor.

To  determine  the  energy  distribution  in  speech  to  a  high  degree  of
accuracy  it  would  be  desirable  to  analyze  a  certain  amount  of  con-
nected speech  and  take  a  time  average  of  the  energy  distribution  of
the  whole.  This  is  not  feasible  at  the  present  time,  but  a  very  close
approach  to  this  result  has  been  made.  The  method  consists  in
analyzing  the  speech  waves  as  impressed  on  a  condense  transmitter,
using  a  tuned  circuit  to  transmit  narrow  frequency  bands  of  energy  and
pronouncing  the  separate  syllables  of  the  connected  speech  so  slowly
that  the  kick  of  a  direct  current  galvanometer  connected  to  an  A.  C.
thermocouple  can  be  separately  read  for  each  syllable.  Using  a  suit-
able calibration  for  the  whole  apparatus,  the  magnitude  of  this  kick
can  be  interpreted  in  terms  of  the  time  integral  of  the  energy  at  a
particular  frequency  setting  for  each  syllable.  A  mean  of  the  read-
ings for  all  the  syllables  in  the  "speech"  at  any  frequency  setting
gives  the  relative  energy  at  that  frequency.

The  present  method  is  a  modification  of  an  earlier  method  in  which
approximate  analyses  of  speech  sounds  were  made,  using  a  condenser
transmitter,  tuned  circuit,  an  amplifying-rectifying  circuit,  and  ballis-
tic -galvanometer.  The  method  is,  however,  much  improved  as  we
now  have  very  accurately  calibrated  condenser  transmitters  of  better
design,^  and  a  great  deal  of  care  has  been  taken  to  calibrate  the  suc-
cessive elements  of  the  train  of  apparatus,  and  increase  the  resolving
power.

Sound  waves  emitted  from  the  mouth  of  the  speaker  are  allowed  to
fall  upon  the  diaphragm  of  a  condenser  transmitter,  connected  in  the
conventional  manner  to  the  input  of  a  three-stage  amplifier.  The
output  of  this  is  impressed  upon  the  input  circuits  of  twin  single
stage  amplifiers,  potentiometers  being  interposed  to  permit  regula-
tion of  the  grid  voltages  of  the  twin  amplifier  tubes.

The  output  circuits  of  the  fourth  stage  consist  of  the  high  windings
of  two  step  down  ironclad  transformers.  These  step  down  trans-
formers have  a  voltage  ratio  of  1 1 :  1  and  are  designed  to  work  between
impedances  of  6,000  and  50  ohms.  The  low^  impedance  winding  of
one  of  these  transformers  operates  into  a  thermocouple  heater  of,

'  The  present  design  of  the  condenser  transmitter  and  its  calibration  are  fully
treated  in  a  paper  by  Dr.  E.  C.  Wente  which  will  appear  shortly  in  this  Journal.

roughly,  40  ohms  resistance.     The  low  side  of  the  other  transformer
operates  through  a  tuned  circuit  into  a  similar  thermocouple  heater.

-Circuit  Used  for  the  Analysis  of  Speech.     (The  Usual  Details  of  the  Three-
Stage  Amplifier  Are  Not  Shown)

When  the  diaphragm  of  the  condenser  transmitter  is  set  in  vibration
by  speech  a  current  made  up  of  a  range  of  frequencies  flows  in  the
heater  of  thermocouple  I.,  while  the  heater  of  thermocouple  II  is
traversed  only  by  such  a  band  of  frequencies  as  the  resonant  circuit
allows.     Fig.  2  shows  a  number  of  typical  resonance  curves  obtained

in  the  course  of  calibrating  this  apparatus.  These  curves  are  such
that  the  tuned  circuit  functions  as  a  filter  transmitter  only  a  narrow
region  of  frequencies.     One  side  of  the  twin  amplifier  transmits  the

entire  electrical  response  of  tl.c  system;  the  other  side  suppresses
all  save  a  band  of  frequencies,  the  center  of  this  hand  being  shifted
by  resetting  the  condenser  and  inductometer.

Having  chosen  for  analysis  a  piece  of  connected  discourse,  the
speaker  utters  the  successive  syllables  separately  but  as  nearly  as
may  be  with  the  same  inflection  and  volume  as  if  the  syllables  were
continuously  spoken.  Two  observers  record  the  readings  of  microam-
meters  in  the  couple  circuits  of  the  thermocouples.  One  of  these
instruments  gives  a  deflection  corresponding  to  the  total  energy  of
the  syllable  uttered;  the  deflection  of  the  other  instrument  corre-
sponds to  the  energy  of  the  syllable  lying  within  the  limits  of  trans-
mission of  the  tuned  circuit.

Preliminary  experiments  were  carried  out  to  determine  the  relation
between  momentary  deflection  read  on  the  microammeter,  and  the
current  momentarily  flowing  in  the  thermocouple  heater.  Currents  of
different  values  were  caused  to  flow  for  intervals  of  time  varying
from  0.2  second  to  1.2  seconds,  and  the  deflections  were  found  nearly
proportional  to  the  product  of  current  squared  and  time  interval;
this  proportionality  was  most  nearly  exact  when  the  current  was
weak  and  the  time  intervals  short.  For  all  cases  likely  to  be  dupli-
cated in  the  speech  analysis  work  the  error  might  be  taken  as  about
5  per  cent,  a  quantity  small  in  comparison  with  the  inevitable  un-
certainties due  to  other  causes.

Quite  low  damping  is  attained  in  the  resonant  circuit.  The  values
of  inductance  used  ranged  from  0.20  to  0.66  henry  and  the  total  re-
sistance of  the  circuit— transformer  winding,  inductometer  coil,
thermocouple  heater— is  of  the  order  of  100  ohms.  The  damping
thus  ranges  from  75  to  250.

A  switch  is  so  introduced  that  it  is  possible  to  include  in  series  with
the  thermocouple  the  resonant  circuit,  or  replace  it  by  a  non-in-
ductive resistance  whose  value  is  approximately  that  of  the  A.  C.
resistance  of  the  inductometer  winding.  With  the  tuned  circuit
excluded,  an  alternating  current  of  suitable  magnitude  is  caused  to
flow  in  the  thermocouple  heater;  the  tuned  circuit  is  then  substituted
and  the  new  value  of  the  current  observed,  the  input  voltage  remaining
constant.  The  ratio  of  current  squared  "tuned  circuit  in"  to  current
squared  "tuned  circuit  out"  is  plotted  against  frequency,  yielding  a
curve  for  energy  transmission.

Twenty-three  bands  in  all  were  considered  adequate  for  the  analysis
of  energy  distribution  in  speech;  the  centers  of  these  were  at  75,  100,
200,  300  cycles,  400  to  3,200  cycles  by  steps  of  200;  3,500,  4,000,  4,500,

5,000  cycles  per  second.  Beyond  5,000  cycles  per  second,  the  energy
is  so  low  as  to  be  impossible  of  measurement  with  the  apparatus  used.
A  Weston  Type  322  microammeter  recorded  the  couple  current  for  the
tuned  circuit  side  of  the  twin  single  stage  amplifier.  With  this  instru-
ment and  the  thermocouple  used,  0.2  microampere  in  the  couple  circuit
corresponds  to  one-quarter  of  a  milliampere  in  the  heater,  and  this  is
the  lowest  readable  deflection  of  the  Weston  instrument.

Three  corrections  have  to  be  made,  the  first  being  the  correction
for  varying  volume.

Simultaneous  observations  are  made,  at  each  setting  of  the  tuned
circuit,  of  the  filtered  and  the  unfiltered  energy  of  each  syllable.  It
is  not  possible  to  utter  a  given  syllable  with  the  same  intensity  and
at  the  same  distance  from  the  transmitter  for  every  one  of  twenty-

Fig.  3 — Illustrating  Correction  of  ObservaLions,  Necessary  Because  of  Variation  in
Resolving  Power  with  Frequency  Setting

three  times.  Accordingly,  the  "unfiltered"  readings  are  averaged  and
each  of  the  filtered  readings  for  each  syllable  reduced  from  the  value
actually  observed  to  the  value  that  would  have  been  read  had  the
volume  and  distance  been  such  as  to  give  the  average  "unfiltered"
reading.  This  procedure  is  quite  legitimate  if  it  be  granted  possible
to  maintain  a  definite  composition  of  the  syllable  in  question  through-
out the  changes  of  the  tuned  circuit  setting.

A  second  correction  was  made  for  the  varying  area  of  tuned  circuit
curves.

In  Fig.  3  let  S{j)  be  the  speech  spectrum  determined  by  'deal
methods;  "i?"  the  transmission  curve  of  the  tuned  circuit,  set  for  a
resonant  frequency/.  An  ideal  transmission  curve  would  be  a  rectangle
when  plotted  in  this  figure,  of  height  "/^"  and  transmission  range  A/.

The  true  amount  of  energy  5(0  associated  with  frequency/,  and  the
experimentally  determined  value  which  we  may  call  (5/)  are  con-
nected by  the  relation

we  may  take  for  all  practical  purposes  S{J)  =  Sif),  considering  the
narrowness  of  the  transmission  range.  We  must  therefore  find  the
factor  h^f,  proportional  to  the  area  of  each  tuned  circuit  curve  and
divide  the  energy  received  through  the  filtered  side  by  /?A/,  in  order  to
obtain  S{f).  This  treatment  may  be  gone  through  for  each  syllable
individually,  but  it  is  more  convenient  to  sum  the  tuned  circuit  read-
ings for  all  the  syllables  used,  corrected  one  at  a  time  for  varying
volume,  and  then  apply  the  curve  area  correction  to  this  sum.

A  third  correction  was  made  for  the  varying  frequency-sensitivity  of
the  whole  apparatus.  Thus  far  we  have  discussed  only  the  electrical
energy  in  the  output  circuit  of  the  fourth  stage.  It  remains  to  show  in
what  way  this  is  related  to  the  mechanical  energy  of  the  diaphragm,
and  this  in  turn  to  the  incident  sound  energy.

The  calibration  of  the  circuit  as  a  whole  was  made  by  introducing  a
small  resistance  carrying  alternating  current  in  series  with  the  con-
denser transmitter,  thus  introducing  a  known  potential  drop  in  the
undisturbed  input  mesh  of  the  circuit.

An  amplification  curve  is  appended  {A,  Fig.  4)  which  gives  to  an
arbitrary  scale  the  ratio  of  volts  output  to  volts  input  as  a  function  of
frequency,  for  the  system  as  actually  operated.  The  calibration  of  the
condenser  transmitter,  shown  in  Fig.  4,  Curve  C,  gives  the  open
circuit  voltage  of  the  transmitter  per  unit  pressure  on  the  diaphragm
as  a  function  of  frequency.  The  product  of  these  curves  is  the  volts
output  per  unit  alternating  pressure  on  the  diaphragm,  and  the  square
of  this  product,  curve  E  is  proportional  to  the  electrical  energy  output
per  unit  sound  energy  incident  on  the  diaphragm,  if  we  assume  that
the  sound  energy  is  proportional  to  the  square  of  the  alternating
pressure.  This  point,  however,  requires  some  further  discussion,
which  will  be  given  later  on.

It  is  plain  from  curve  E  that  the  response  of  the  system  is  a  maxi-
mum of  frequencies  in  the  neighborhood  of  2,250  cycles.  If,  now,  the
observations  already  corrected  for  varying  volume  and  for  area  of
resonance  curves,  are  subjected  to  further  correction  for  the  exaggera-
tion of  these  frequencies,  it  is  possible  to  draw  a  curve  which  shall

exhibit  the  mean  square  of  the  excess  pressure  on  the  diaphragm,  as  a
function  of  frequency  in  the  voice  exciting  the  vibration.  We  obtain
this  corrected  curve  by  dividing  the  results,  after  the  first  and  second
corrections  above  have  been  made,  by  the  ordiiiates  of  curve  R.

In  order  to  investigate  the  possibilities  of  this  method  it  was  decided
to  work  with  a  rather  short  piece  of  connected  speech,  and  to  use  a
limited  number  of  observers,  on  account  of  the  large  number  of  ob-
servations which  are  required  for  each  separate  syllable.  With  six
speakers  (four  men  and  two  women)  each  pronouncing  the  test  sentence
of  fifty  syllables  for  each  of  the  twenty-three  frequency  settings,  6,900
separate  observations  were  required.  It  is  believed  that  representa-
tive results  have  been  obtained  from  these  observations,  but  if  this
is  not  the  case  then  some  method  of  graphical  registration  of  the  energy-
time  curve  of  speech  for  the  different  frequency  settings  must  be
applied  in  order  to  handle  the  vast  amount  of  data  involved  in  work
on  an  appreciably  larger  scale.

"Quite  four  score  and  seven  years  ago  our  father  brought  forth  on  this  continent,
a  nice  new  nation,  conceived  in  liberty,  and  dedicated  to  the  proposition  that  all
men  are  created  equal."

The  two  italicized  words  were  added  to  the  first  sentence  of  the
"Gettysburg  Address"  in  order  to  bring  the  total  up  to  fifty  syllables,
and  improve  the  balance  between  the  vowel  sounds.

plotted  so  that  J^  5  (/)  df—  1  in  each  case.  In  Fig.  5  the  individual
curves  for  each  of  the  six  speakers  are  shown  on  a  small  scale ;  in  Fig.  6
the  composite  curve  for  the  men  and  the  composite  curve  for  the
women,  drawn  separately,  and  in  Fig.  7  the  composite  curve  for  all
six  speakers,  giving  the  data  of  curves  QA  and  65  equal  weight.

These  curves  are  very  similar  to  a  curve  obtained  by  Dr.  Fletcher  of
this  laboratory,  using  block  filters  and  based  on  the  simple  calling
sentence  "Now  we're  off  on  one."  A  general  consideration  of  this  fact
and  of  the  data  shown  leads  us  to  believe  that  the  differences  between
curves  of  this  sort,  made  by  the  method  described  are  due  rather
more  to  differences  between  the  voices  of  the  individual  speakers
than  to  the  particular  piece  of  connected  speech  which  is  chosen,  pro-
vided the  speech  is  of  reasonable  length.  The  differences  between
the  different  voices  are  so  marked  that  we  should  expect  them  to  remain
even  though  we  used  as  test  material  a  connected  speech  ten  or  fifty
times  as  long  as  the  sentence  used.

An  interesting  comparison  may  be  made  between  the  curves  shown
for  the  energy  distribution  of  "continuous  speech"  and  certain  specu-
lative curves  previously  constructed  to  indicate  the  energy  distribu-

tion.  One  of  these  curves  is  shown  in  Fig.  8.  Curve  A  was  constructed
by  one  of  the  writers  in  1916  in  an  attempt  to  synthesize  the  energy
curve  from  the  energy  distributions  of  the  vowel  sounds,  using  the
vowel  analyses  of  Dr.  Dayton  C.  Miller.  Curve  C  is  the  composite
"continuous  speech"  curve  of  Fig.  7.    The  vowel  sounds  analyzed  by

Miller  were  intoned  and  the  vowel  sounds  analyzed  by  us  were  spoken,
but  Miller's  work  seemed  to  show  that  there  was  no  essential  differ-
ence between  intoned  and  spoken  vowel  sounds.  There  is,  however,  a
very  noticeable  difference  between  Curve  A  and  Curve  C,  the  energy
in  the  fundamental  tone  of  the  speaker's  voice  coming  out  much
more  strongly  in  Curve  C.  We  should  expect  that  our  improved  ap-
paratus would  record  the  energy  in  the  lower  frequencies  more  cor-
rectly than  the  apparatus  heretofore  used  but  as  we  used  different
test  material  (connected  speech  instead  of  disconnected  syllables  or
vowel  sounds)  it  is  not  immediately  evident  which  of  these  two  factors
is  responsible  for  the  differences  between  the  A  and  the  C  curves.

In  order  to  investigate  this  point  more  fully  the  testing  routine  for
all  six  speakers  was  repeated,  using  instead  of  the  fifty-syllable  sen-
tence, the  fifty  disconnected  syllables  of  one  of  the  standard  articula-
tion testing  lists,  as  used  by  Dr.  Fletcher  ii  this  laboratory.  The
results  for  energy  distribution  are  shown  in  Fig.  9,  Curve  A  being

the  mean  energy  distribution  for  the  four  male  speakers,  using  the
syllables,  while  Curve  B  is  the  mean  energy  distribution  of  the  two
female  speakers.  Curves  ^A  and  95  may  be  compared  with  Curves
6-4  and  65  which  represent  the  sentence  of  continuous  speech.  The
two  sets  of  curves  are  essentially  the  same  as  shown  in  Fig.  8,  C  and  B

being  respectively  the  composite  curves  for  all  speakers,  using  con-
nected and  disconnected  speech.

Such  small  differences  as  exist  between  Curves  C  and  B  of  Fig.  8
may  probably  be  due  to  differences  in  the  distribution  of  the  vowel
sounds  in  the  connected  and  disconnected  test  material.  This  dis-
tribution is  given  in  the  following  table:

The  similarity  between  Curves  C  and  B  of  Fig.  8  is  evidence  of  the
general  reliability  of  the  method,  and  leads  to  two  rather  important
conclusions.

In  the  first  place,  characteristic  results  have  been  obtained  for  a
given  set  of  speakers,  using  two  different  types  of  test  materials.    This

seems  to  show  that  the  choice  of  test  material  does  not  require  especial
consideration,  provided  it  is  of  sufficient  length.  It  seems  to  be  a
matter  of  rather  greater  importance  to  increase  the  number  of
observers.

In  the  second  place,  it  seems  that  for  the  actual  energy  distribution,
the  results  previously  obtained  from  the  vowel  analyses  are  definitely
in  error,  in  that  they  show  relatively  little  energy  associated  with  the
lower  voice  frequencies.

The  foregoing  treatment  provides  a  curve  showing  the  frequency
distribution  of  the  square  of  the  excess  pressure  on  the  diaphragm.
In  an  undisturbed  field  of  sound  energy  we  have  for  the  intensity

in  which  p  is  the  mean  density  of  the  medium,  a  the  velocity  of  sound
in  the  medium  and  P  the  maximum  excess  pressure.

It  remains  for  us  to  consider  in  how  far  the  results  obtained  represent
the  frequency  distribution  of  sound  energy  in  speech.

Due  to  the  fact  that  at  frequencies  where  the  sound  wave-length  is
short  and  comparable  with  the  diameter  of  the  transmitter,  consid-
erable reflection  takes  place,  and  the  pressure  on  the  diaphragm  is
proportionately  greater  for  these  frequencies  than  for  those  which  are
not  accompanied  by  strong  reflection.  In  this  respect  again  the
higher  frequencies  provoke  the  greater  response  in  the  system.

The  following  experiment  was  tried  to  investigate  this  variation.  A
wall  six  feet  square,  with  a  central  hole  to  fit  over  the  condenser  trans-
mitter, was  brought  up  to  make  the  transmitter  a  part  of  a  plane  wall.
The  clearance  around  the  periphery  of  the  transmitter  was  tightly
closed,  and  reflection  was  to  be  expected  at  all  frequencies.  Where
total  reflection  takes  place,  a  given  quantity  of  sound  energy  result?
in  twice  the  alternating  pressure  on  the  diaphragm  as  when  no  reflection
occurs.  That  is,  the  resulting  electrical  energy  observed  should  be  four
times  as  great  for  total  reflection  as  for  no  reflection.  The  wall  was
expected  to  cause  reflection  at  all  frequencies,  and  the  experiment
consisted  in  reading  the  electrical  response,  with  and  without  the  wall,
the  condenser  transmitter  being -exposed  to  tones  of  frequencies  from
200  to  10,000  cycles  per  second  under  definite  adjustments  of  the
supply  circuit  of  a  receiver  producing  this  tone.  When  the  frequency
is  low,  little  reflection  takes  place  from  the  transmitter  standing  alone,
and  bringing  up  the  wall  should  cause  a  great  increase  in  the  response

of  the  system.  At  high  frequencies  the  transmitter  should  reflect
nearly  as  much  alone  as  when  part  of  a  large  wall,  and  the  readings
with  and  without  the  wall  should  be  nearly  equal.  Plotting  ratio  of
response  without,  to  response  wuth  the  wall  was  expected  to  yield  a
curve  which  could  be  used  to  make  the  final  reduction  of  electrical
output  to  incident  sound  energy,  and  so  permit  a  more  accurate  de-
termination of  the  spectrum  of  sound  energy  of  the  voice.

Thus,  the  curves  finally  obtained  show  no  more  than  the  frequency
distribution  of  energy  in  speech  in  terms  of  the  mechanical  energy  of  a
more  or  less  ideal  transmitter  diaphragm.  However,  this  information
has  its  value  because  in  any  given  configuration  of  transmitter,
speaker,  and  room,  there  is  a  definite  correspondence  between  the  sound
energy  of  the  voice  and  the  force  acting  on  the  diaphragm  on  which  it
falls,  and  in  telephony  at  any  rate  it  is  this  action  on  the  diaphragm
with  which  we  are  immediately  concerned.

In  conclusion  we  may  give  a  determination  of  the  total  energy  rate
of  speech,  obtained  as  a  by-product  of  the  preceding  investigation.
Knowing  the  calibration  of  the  system  in  absolute  units,  it  is  possible
to  determine  the  alternating  pressure  on  the  condenser  transmitter
diaphragm  exposed  to  continuous  speech  from  the  normally  modulated
voice  under  the  conditions  of  the  experiment.  Using  the  mean  of  the
values  obtained  with  9  observers  we  find  for  the  alternating  pressure
11.3  dynes  per  sq.  cm.  (r.m.s.)  for  a  distance  of  2.5  cm.  from  mouth  to
diaphragm.  This  corresponds  to  an  energy  flow  of  3.2  ergs  per  sq.
cm.  per  second.  Assuming  that  this  energy  flow  is  distributed  uni-
formly over  a  hemisphere  of  2.5  cm.  radius,  we  may  take  125  ergs
per  second  as  the  total  sound  energy  flow  from  the  lips  with  the
normally  modulated  voice.

VARIOUS  phases  of  this  subject  have  received  serious  study  by
phoneticians,  otologists,  and  physicists.  On  account  of  its  universal
interest,  it  has  received  attention  from  men  in  many  branches  of
science.  In  spite  of  the  large  amount  of  time  devoted  to  the  sub-
ject, the  progress  in  understanding  its  fundamental  aspects  has  been
rather  slow.  At  the  present  time  the  physical  properties  which
differentiate  the  various  fundamental  speech  sounds  are  understood
in  only  a  very  fragmentary  way.  Some  very  interesting  and  pains-
taking work  has  been  done  on  the  physical  analysis  of  vowel  sounds,
but  the  results  to  date  are  far  from  conclusive.  Although  several
theories  have  been  advanced  to  explain  the  way  in  which  the  ear
interprets  sound  waves,  they  are  still  in  the  controversial  stage.

The  material  which  is  presented  here  is  the  result  of  an  investi-
gation which  has  been  carried  on  in  the  Research  Laboratories  of
the  American  Telephone  and  Telegraph  Company  and  Western
Electric  Company  during  the  past  few  years.

To  make  a  quantitative  study  of  speech  and  hearing  it  is  necessary
to  obtain  the  speech  sounds  at  varying  degrees  of  loudness  and  with
definitely  known  amounts  of  distortion.  The  main  reason  why  so
few  real  results  have  been  obtained  in  the  investigation  of  speech
sounds  is  due  to  the  fact  that  it  is  extremely  difficult  to  change  the
volume  and  distortion  of  these  sounds  by  acoustic  means.  Due  to
recent  developments  in  the  electrical  transmission  of  speech  it  is
possible  to  produce  the  equivalent  of  these  changes  by  electrical  means.
For  this  purpose  a  telephone  system  was  constructed  which  repro-
duced speech  with  practically  no  distortion.  It  was  arranged  so  that
by  means  of  distortionless  attenuators  the  volume  of  reproduced
speech  could  be  varied  through  a  very  wide  range,  and  so  that  by
introducing  various  kinds  of  electrical  apparatus  the  transmitted
speech  wave  could  be  distorted  in  definitely  known  ways.

A  method  was  developed  for  measuring  quantitatively  the  ability
of  the  ear  to  interpret  the  transmitted  speech  sounds  under  different
conditions  of  distortion  and  loudness.  By  choosing  these  conditions
properly,  considerable  information  was  gained  concerning  both  speech
and  hearing.     This  indirect  method  of  attack  has  a  distinct  advantage

*  Presented  at  a  meeting  of  the  Electrical  Section  of  the  Franklin  Institute  held
Thursday,  March  30,  1922.  Reprinted  from  the  Journal  of  the  Franklin  Institute
for  June  1922.

for  engineering  purposes,  in  that  it  measures  directly  the  thing  of
most  interest,  namely,  the  degrading  effect  upon  telephone  conversa-
tion of  introducing  electrical  distortion  into  the  transmission  circuit.
However,  the  application  of  the  results  is  not  limited  to  this  particular
field.

Briefly  stated  the  method  consists  in  pronouncing  detached  speech
sounds  into  the  transmitting  end  of  the  system  and  having  observers
write  the  sounds  which  they  hear  at  the  receiving  end.  The  com-
parison of  the  called  sounds  with  those  observed  shows  the  number
and  kinds  of  errors  which  are  made.  The  per  cent  of  the  total  sounds
spoken  which  are  correctly  received  is  called  the  articulation  of  the
system.

lip  against  lip
tongue  against  teeth
tongue  against  hard  palate
tongue  against  soft  palate

In  order  to  understand  the  construction  of  the  articulation  lists
and  also  to  interj^ret  the  results  of  this  investij^ation,  I  desire  to
give  here  a  brief  classification  of  the  speech  sounds,  which  is  based
upon  tiie  position  of  the  various  speech  organs  when  the  sounds  are
being  produced.     It  is  shown  in  the  accompanying  table  (Table  I).

The  pure  vowels  are  arranged  in  the  vowel  triangle,  which  is  familiar
to  phoneticians.  Starting  with  the  sound  u  the  lips  are  rounded
and  there  is  formed  a  single  resonant  cavity  in  the  front  part  of  the
mouth.  Passing  along  the  left  side  of  the  triangle  from  u  to  a  the
mouth  is  gradually  opened  with  the  tongue  lowered  to  form  the  suc-
cessive vowels.  Going  along  the  right  side  of  the  triangle  from  a  to
e,  the  tongue  is  gradually  raised  to  the  front  part  of  the  mouth  form-
ing two  resonant  chambers  in  the  mouth  cavity.  An  infinite  number
of  different  shadings  of  these  vowels  may  be  produced  by  placing
the  mouth  in  the  various  intermediate  positions,  but  the  ones  which
are  shown  were  chosen  as  being  the  most  distinct.

The  sounds  w,  y,  ou,  I  and  h  are  classed  as  combinational  and
transitional  vowels.  As  the  mouth  is  placed  in  the  position  to  say  u
and  then  suddenly  changed  so  as  to  form  any  other  vowel  in  the
triangle,  the  result  obtained  is  signified  in  writing  by  placing  the
ktter  w  before  the  vowel.  In  a  similar  way  we  get  the  effect  usually
designated  by  y  if  the  position  of  the  vowel  suddenly  changes  from
e  to  any  other  vowel.  An  infinite  variety  of  dipthongs  can  be  formed
by  changing  the  position  of  the  mouth  necessary  to  form  one  vowel
to  that  to  form  another  without  interrupting  the  voice.  The  most
distinct  and  principal  ones  used  in  our  language  are  formed  by  passing
from  the  sound  a  to  either  extreme  corner  of  the  triangle  and  are
known  as  ou  and  I.  When  a  vowel  commences  a  syllable  it  is  formed
by  suddenly  opening  the  glottis,  permitting  the  air,  which  has  been
held  in  the  lungs,  to  escape  into  the  mouth,  which  is  formed  for  the
proper  vowel.  If  the  glottis  remains  open  and  the  vowel  is  started
by  the  sudden  contraction  of  the  lungs,  we  have  the  effect  which  is
represented  in  writing  by  placing  an  h  before  the  vowel.  The  sounds
1  and  r  are  called  semi-vowels  because  the  voice  train  is  partially
interrupted,  although  the  sound  can  be  continued.  The  stop  and
fricative  consonants  are  classified  in  a  manner  which  is  familiar  to
phoneticians.

It  will  be  noticed  that  the  markings  are  not  those  used  in  the  inter-
national phonetic  alphabet  which  were  entirely  too  complicated  for
practical  use.  Only  the  bar  and  accent  stroke  are  used.  These
can  be  written  quickly  and  with  little  chance  of  error.

be  combined  into  syllables.  For  the  purpose  of  this  investigation
they  were  combined  into  mono-syllables  of  the  simple  types  con-
sonant-vowel,  vowel-consonant,   and   consonant-vowel-consonant.

To  eliminate  memory  efTects  every  possible  combination  of  the
sounds  into  these  types  of  syllables  was  used  unless  there  was  a  good
reason  for  excluding  it.  The  complete  list  contained  8700  syllables.
For  convenience  of  testing  these  syllables  were  divided  into  groups
of  fifty.  Each  group  contained  the  same  kind  and  number  of  syllable
forms  and  an  equal  number  of  each  of  the  fundamental  vowel  and
consonant  sounds.

To  illustrate  the  technique  of  articulation  testing  a  sample  list
is  given  in  Table  II.  fn  the  first  column  the  syllable  is  given  in  its
phonetic  form.  A  key-word  showing  how  each  syllable  is  pro-
nounced is  given  in  the  second  column.  These  syllables  were  written
on  cards  which  were  shuffled  each  time  before  they  were  used,  so
that  the  order  in  which  they  were  pronounced  was  entirely  hap-
hazard. One  hundred  and  seventy-four  similar  lists  were  used  in
this    work.     In    order    to    eliminate    personal    peculiarities,    several

callers  and  observers  were  used.  In  Table  III  are  shown  the  results
obtained  by  an  observer  when  this  list  was  transmitted  over  a  system
which  eliminated  all  frequencies  above  1250  cycles  per  second.

The  correct  word  is  written  opposite  all  of  the  syllables  which
were  recorded  incorrectly.  The  errors  for  each  of  the  fundamental
sounds  were  taken  from  this  original  sheet  and  recorded  on  an  analysis

sheet  as  shown  in  Table  IV.  for  example  it  will  he  noticed  that  p
was  recorded  as  k  24.4  per  cent,  as  p  45  per  cent,  and  as  t  22.2  per  cent
of  the  times  called.  On  the  other  hand  the  sound  w  was  only  recorded
incorrectly  1  per  cent  of  the  times  called.

For  this  system  the  consonant  articulation  was  65.8  and  the  vowel
articulation  83.4.

The  telephone  system  used  in  this  investigation  is  probably  more
nearly  perfect  than  any  other  which  has  yet  been  built.  Its  essential
elements  are  a  condenser  transmitter  to  receive  the  speech  waves
and  transform  them  into  the  electrical  form,  an  amplifier  for  magni-
fying the  intensity  of  the  electrical  speech  currents,  an  attenuator
for  controlling  the  intensity,  an  equalizing  network,  and  a  receiver
for  delivering  the  speech  to  the  ear.  A  schematic  arrangement  of
the  circuit  is  shown  in  Fig.  1.

A  detailed  description  of  the  construction  and  operation  of  the
condenser  transmitter  has  been  given  by  Crandall  and  Wente  and
published  in  the  Physical  Review}  It  is  simply  an  air  condenser,
one  of  its  plates  being  a  flexible  metal  diaphragm.

A  five-stage  vacuum  tube  amplifier  was  used.  Particular  care
was  taken  in  coupling  the  stages  together,  so  that  the  amplifier  was
practically  free  from  frequency  distortion.

The  attenuator  consisted  of  a  potentiometer  arrangement  which
could  reduce  the  amplitude  of  the  speech  waves  to  approximately
one-millionth  of  their  maximum  values.

densers  and  inductance  coils  having  a  frequency  selectivity  which
was  the  complement  of  that  of  the  rest  of  the  system.

The  telephone  receiver  was  a  bipolar  type  having  a  special  con-
struction which  was  designed  to  broaden  the  range  of  frequency
response.

The  reproducing  efficiency  of  the  system  from  the  mouth  of  the
speaker  to  the  ear  of  the  listener  for  each  frequency  is  shown  in  Fig.  2.

The  pitch  or  frequency  of  the  tone  is  given  on  the  X  axis.  The
ordinates  represent  amplitude  ratios  or  the  number  of  times  the
amplitude  of  the  tone  reaching  the  ear  was  greater  than  that  which
entered  the  transmitter.  It  will  be  seen  that  this  high  quality  system
has  practically  a  uniform  response  for  all  frequencies  throughout  the
speech  range.

In  order  that  its  uniformity  may  be  appreciated,  a  comparison
curve  is  given.  This  curve  shows  the  deviation  in  the  sensitivity
of  a  typical  individual  ear  from  the  average  sensitivity  of  a  large
number  of  ears.  The  ordinates  represent  the  ratio  of  amplitudes
at  the  various  pitches  which  was  necessary  to  bring  the  tone  to  the
threshold  of  audibility.  It  is  evident  that  this  deviation  is  much
larger  than  the  departure  of  the  high  quality  circuit  from  uniformity.

To  show  that  this  particular  individual's  curve  is  typical,  the
curves  for  both  ears  of  20  women  are  given  in  Fig  3.  For  convenience
these  curves,  are   plotted   on   logarithmic   paper.     If   an   arithmetic

scale  is  used,  all  of  the  eur\es  below  the  mean  are  crowded  together
in  the  small  space  between  zero  and  one,  and  all  those  above  the
mean  are  stretched  out  from  one  to  infinity.  By  using  a  logarithmic
plot  a  symmetrical  distribution  is  obtained.     The  method  of  obtain-

It  is  interesting  to  note  that  they  indicate  that  each  individual
has  a  hearing  characteristic  which  is  quite  difTerent  from  other  in-
dividuals. Consequently  speech  sounds  differently  to  difTerent
persons.  Any  distortions  of  the  speech  sounds  will  necessarily
affect  some  persons  differently  from  others.  It  is  evident  then  that
in  discussing  speech  and  hearing  we  must  deal  w^ith  statistical  averages.

Experimental  articulation  tests  showed  that  the  ear  interpreted
the  speech  which  was  transmitted  over  this  high  quality  system
practically  as  well  as  that  transmitted  through  the  air.  Some  may
wonder  why  such  good  quality  is  not  furnished  telephone  users  in
commercial  practice:  Scientifically  speaking,  it  is  possible  to  furnish
such  quality,  but  it  is  evident  that  the  equipment  involved  is  so  com-

plicated  that  such  service  would  be  altogether  too  costly  for  com-
mercial use;   people  could  not  afford  to  pay  for  it.

The  Relation  Between  the  Volume  and  Articulation  of
Undistorted  Speech

in  Fig.  4.  The  abscissas  in  this  curve  represent  loudness  and  are
expressed  as  the  natural  logarithm  of  the  number  of  times  the  speech
wave  amplitude  has  been  decreased  from  the  initial  intensity  at
]/^  inch  in  front  of  the  mouth  of  the  callers.  This  unit  of  loudness
has  never  been  given  a  name,  and  as  a  matter  of  convenience  in
this  work  it  is  called  a  napier.  It  will  be  noticed  that  when  the
volume  is  reduced  11}/^  napiers  below  the  initial  speech  intensity
the  articulation  becomes  zero.  This  point  also  represents  the  value
at  which  the  speech  becomes  inaudible  and  corresponds  to  approxi-
mately 1/1000  dynes  per  square  centimetre  pressure  variation  against
the  ear  drum.  In  energy  units  it  is  a  reduction  of  ten  billion  times
below  the  initial  speech  intensity.  For  very  loud  initial  speech
this  point  is  shifted  about  1  napier.  For  purposes  of  comparison
the  intensity  reductions  are  also  indicated  on  the  loudness  axis.

At  3  napiers  below  or  at  about  1/1000  of  the  initial  speech  in-
tensity the  articulation  becomes  a  maximum.  Louder  speech  than
this  seems  to  deaden  the  nerves  so  that  a  person  makes  a  less  accurate

interpretation  of  the  received  speech.  These  results  were  obtained
in  a  room  which  was  especially  constructed  to  exclude  outside  noise.
When  noise  is  present  at  the  receiving  station  the  optimum  loudness
increases  as  the   noise  increases.

The  articulation  data  were  analyzed  so  as  to  show  the  errors  of
each  of  the  fundamental  sounds.  The  curves  given  in  big.  5  show
the  results  of  this  analysis.  It  will  be  noticed  that  the  \olume  at
which  errors  begin  to  be  appreciable  is  different  for  the  different
sounds  and  is  usualK'  higher  for  the  consonants  than  for  the  vowels.

Within  the  precision  of  the  test  the  intersection  point  on  the  X  axis
was  the  same  for  all  the  sounds,  namely  at  11.5  napiers.

It  will  be  noticed  that  the  consonants  are  usually  harder  to  hear
than  the  vowels.  However,  the  speech  sounds  e  and  I,  r,  ng  form
notable  exceptions  to  this  general  rule,  since  the  former  is  among
the  most  difficult,  while  the  latter  are  among  the  very  easiest  speech
sounds.  The  order  in  which  the  speech  sounds  are  given  here  rep-
resents their  relative  difficulty  of  interpretation  when  received  at
average  intensities.  At  all  intensities,  the  sounds  th,  f  and  v  are
the  most  difficult.  Z,  h  and  s  become  very  difficult  at  weak  volumes.
The  sounds  i,  ou,  er  and  6  are  missed  less  than  10  per  cent  of  the
time,  even  with  "very  weak"  intensity.  At  "average"  volumes
there  are  only  three  sounds  more  difficult  than  e  while  at  "very
weak"  volumes  there  are  23  sounds  more  difficult.  At  very  weak
volumes  1,  which  is  the  easiest  sound  at  "average"  volumes  is  missed
three  times  as  often  as  e.

We  will   now  pass  to  a  consideration  of  the  effect  of  distortion
upon  the  articulation  of  the  sounds.

In  order  to  investigate  distortion  we  would  like  to  be  able  to  take
the  train  of  speech  waves  going  from  the  mouth  to  the  ear  and  oper-
ate upon  it  in  various  ways  such  as  eliminating  frequencies  in  certain
regions  without   marring  or  disturbing  other  frequencies.      For  ex-

ample,  if  all  frequencies  above  1000  were  eliminated,  it  would  be
possible  to  determine  what  intelligibility  is  carried  by  this  range  of
frequencies.

Fortunately  one  of  the  recent  electrical  inventions  is  admirably
adapted  for  this  purpose,  namely,  the  electrical  wave  filter  invented
by  Dr.  G.  A.  Campbell.  This  device  was  used  extensively  in  this
investigation.

The  schematic  circuit  diagrams  of  the  two  types  of  filters  which
were  used  are  given  in  Fig.  6.

This  arrangement  of  coils  and  condensers  produces  an  electrical
conductor  with  the  unusual  properties  that  it  transmits  without
appreciable  diminution  in  amplitude  any  frequency  between  certain
limits  and  reduces  the  amplitude  of  all  frequencies  outside  these
limits  to  less  than  1/1000  of  their  original  value.  By  varying  the
numerical  values  of  the  inductances  and  capacities  this  transmitted
range  can  be  placed  at  any  desired  position.  In  the  arrangement
which  was  used  in  the  investigation  these  coils  and  condensers  were

housed  in  two  boxes.  The  switching  mechanism  was  arranged  so
that  by  turning  a  dial  the  condensers  and  coils  were  connected  in
such  a  way  that  the  filter  transmitted  different  frequency  bands.

In  Fig.  7  are  shown  the  transmission  properties  of  the  low  pass
filter  when  the  dial  is  set  to  transmit  frcciuencics  from  0  to  1500.
It  is  seen  that  for  frequencies  below  1400  the  amplitudes  of  the  trans-
mitted tones  are  always  greater  than  .8  of  their  initial  values,  while
for  frequencies  above  1500  the  amplitudes  are  decreased  to  less  than
.001  of  their  initial  values.  These  electrical  filters  were  connected
into   the  high   quality  circuit  between   the   third  and   fourth   stages

of  the  amplifier  as  indicated  in  Fig.  1.  This  combination  formed  a
system  which  would  pick  up  a  complex  sound  wave  and  transmit
faithfully  to  the  ear  those  component  frequencies  in  any  desired
region  and  eliminate  all  other  frequencies.

Articulation  tests  were  made  with  these  filter  systems  and  the
results  analyzed  as  described  above.  In  Fig.  8  the  syllable  articu-
lation results  are  shown  in  graphical  form.  The  ordinates  for  the
solid  curves  represent  the  per  cent  of  the  articulation  syllables  called
into  the  system  which  were  correctly  recorded  at  the  observing  end.
The  abscissas  represent  the  so-called  "cut  off"  frequency  of  the
filter.  For  example  on  the  curve  labelled  "Articulation  L"  the
point  (1000,  40)  means  that  a  system  w^hich  transmits  only  frequencies

below  1000  cycles  per  second  has  a  syllable  articulation  of  40  per
cent.  Similarly  on  the  curve  labelled  "Articulation  H"  the  point
(1000,  86)  means  that  a  system  which  transmits  only  frequencies
above  1000  cycles  per  second  has  a  syllable  articulation  of  86  per
cent.  The  dotted  curves  show  the  per  cent  of  the  total  speech  energy
which  is  transmitted  through  the  filter  systems  used  in  the  articula-
tion tests.  These  curves  are  derived  from  the  results  of  Crandall
and  MacKenzie  which  were  recently  published.^

It  will   be  seen   that  although   the   fundamental   cord   tones  with
their  f^.rst  few  harmonies  carry  a  large  portion  of  the  speech  energy,

Effect  upon  the  Articulation   and  the  Energy  of  Speech
of  Eliminating  Certain  Frequency  Regions

they  carry  practically  none  of  the  speech  articulation.  A  filter
system  which  eliminates  all  frequencies  below  500  cycles  per  second
eliminates  60  per  cent  of  the  energy  in  speech,  but  only  reduces  the
articulation  2  per  cent.  A  system  which  eliminates  frequencies
above  1500  cycles  per  second  eliminates  only  10  per  cent  of  the  speech
energy,  but  reduces  the  articulation  35  per  cent.  A  system  which
eliminates  all  frequencies  above  3000  cycles  per  second  has  as  low  a
value  for  the  articulation  as  one  which  eliminates  all  frequencies
below  1000  cycles  per  second.  This  last  statement  may  appear
rather  astonishing  since  it  is  contrary  to  the  popular  notion  of  the
relative  importance  of  various  voice  frequencies  from  an  interpre-
tation standpoint.

The  two  solid  curves  intersect  on  the  1550  cycle  abscissa  and  at
65   per  cent  articulation,  which  shows  that  using  only  frequencies

above  or  frequencies  below  1550  cycles  an  articulation  of  65  per
cent  will  be  obtained.  The  two  dotted  curves  necessarily  intersect
at  50  per  cent.

The  cur\es  in  Fig.  9  show  how  the  articulation  of  some  of  the
fundamental  speech  sounds  was  affected  by  eliminating  certain
frequency  regions.  The  ordinate  gives  the  number  of  times  the
sound  was  written  correctly  per  100  times  called.     As  in  Fig.  8  the

left  hand  curve  shows  the  effect  of  eliminating  all  frequencies  below
and  the  right  hand  curve  the  effect  of  eliminating  all  frequencies
above  the  frequency  specified  by  the  abscissa.

These  nine  speech  sounds  were  chosen  as  representing  three  im-
portant classes.  It  is  seen  that  the  long  vowels  e,  1  and  i  can  be  trans-
mitted with  an  error  of  less  than  3  per  cent  when  using  either  half
of  the  range  of  frequencies.  When  using  either  frequencies  from
0  to  1700  or  from  1700  to  infinity  e  was  interpreted  correctly  98  per
cent  of  the  time.  Similarly  1  was  interpreted  correctly  97  per  cent
of  the  time  when  using  either  the  range  from  0  to  1000  or  1000  to
infinity,  and  i  96  per  cent  of  the  time  when  using  either  the  range
from  0  to  1350  or  from  1350  to  infinity.  The  short  vowels,  u,  o  and
e  are  seen  to  have  important  characteristics  carried  by  frequencies
below  1000.     More  than  a  20  per  cent  error  is  made  on  any  of  these

three  sounds  when  frequencies  below  1000  are  eliminated.  The
elimination  of  frequencies  above  2000  produces  almost  no  effect.

The  fricative  consonants  s,  z  and  th  are  seen  to  be  affected  very
differently  from  those  in  the  other  two  classes.  These  sounds  are
very  definitely  affected  when  frequencies  above  5000  are  eliminated.
The  sounds  s  and  z  are  not  affected  by  the  elimination  frequencies
below  1500.  It  is  principally  due  to  these  three  sounds  that  the
syllable  articulation  is  reduced  from  98  per  cent  to  82  per  cent  when
frequencies  above  2500  cycles  are  eliminated.

A  more  detailed  analysis  of  the  articulation  results  on  all  the  speech
sounds  showing  the  kind  as  well  as  the  number  of  errors  will  be  given
in   a   future   paper.

In  conclusion  then  we  see  that  the  intensity  of  undistorted  speech
which  is  received  by  the  ear  can  be  varied  from  100  times  greater
to  one-millionth  less  than  the  initial  speech  intensity  without  notice-
ably affecting  its  interpretation.  The  intensity  must  be  reduced
to  one-ten-billionth  of  that  initial  speech  intensity  to  reach  the  thres-
hold of  audibility  for  the  average  ear.  Also  it  is  seen  that  any  ap-
paratus designed  to  reproduce  speech  and  preserve  all  of  its  char-
acteristic qualities  must  transmit  frequencies  from  100  to  above
5000  cycles  with  approximately  the  same  efficiency.  Although  most
of  the  energy  in  speech  is  carried  by  frequencies  below  1000,  the
essential  characteristics  which  determine  its  interpretation  are  carried
mostly  by  frequencies  above  1000  cycles.  In  ordinary  conversation
the  sounds  th,  f  and  v  are  the  most  difficult  to  hear  and  are  responsi-
ble for  50  per  cent  of  the  mistakes  of  interpretation.  The  character-
istics of  these  sounds  are  carried  principally  by  the  very  high
frequencies.

It  is  evident  that  progress  in  the  knowledge  of  speech  and  hearing
has  a  great  human  interest.  It  will  greatly  aid  the  linguists,  the
actors,  and  the  medical  specialists.  It  may  lead  to  improved  devices
which  will  alleviate  the  handicaps  of  deaf  and  dumb  persons.  Fur-
thermore this  knowledge  will  be  of  great  importance  to  the  telephone
engineer,  and  since  the  telephone  is  so  universally  used,  any  improve-
ment in  its  quality  will  be  for  the  public  good.

These  humanitarian  and  utilitarian  motives  as  well  as  the  pure
scientific  interest  have  already  attracted  a  number  of  scientists  to
this  field.  Now  that  new  and  powerful  tools  are  available,  it  is
expected  that  in  the  near  future  more  will  be  led  to  pursue  research
along  those  lines.

William  Wilson,  Victoria  University  of  Manchester,  1904-10;
M.Sc,  1908;  Cavendish  Laboratory,  Cambridge  University,  1910-12,
B.A.,1912;  Lecturer  in  Physics,  Toronto  University,  1912-14;  D.Sc
Manchester,  1913.  Engineering  Department  W'estern  Electric  Com-
pany, 1914-  .  Dr.  Wilson  has  pubHshed  numerous  papers  on  radio
activity  and  thermionics  and  since  1917  has  been  in  direct  charge  of
vacuum  tube  design.

George  A.  Campbell,  B.S.,  Massachusetts  Institute  of  Technology,
1891;  A.B.,  Harvard,  1892;  Ph.D.,  1901;  Gottingen,  Vienna  and
Paris,  1893-96.  Mechanical  Department,  American  Bell  Telephone
Company,  1897;  Engineering  Department,  American  Telephone  and
Telegraph  Company,  1903-1919;  Department  of  Development  and
Research,  1919 — ;  Research  Engineer,  1908 — .  Dr.  Campbell  has
published  papers  on  loading  and  the  theory  of  electric  circuits  and  is
also  well-known  to  telephone  engineers  for  his  contributions  to  re-
peater and  substation  circuits.  The  electric  filter  which  is  one  of  his
inventions  plays  a  fundamental  role  in  telephone  repeater,  carrier
current  and  radio  systems.

H.  M.  Trueblood,  B.S.,  Earlham,  1902;  Haverford,  1903;  Massa-
chusetts Institute  of  Technology,  1908-09;  Ph.D.,  Harvard,  1913;
aid  and  assistant  United  States  Coast  and  Geodetic  Survey,  1903-08;
assistant  in  physics,  Harvard^  1912-14;  Joule-Thomson  effect  in
super-heated  steam;  instructor  and  assistant  professor  electrical
engineering,  University  of  Pennsylvania,  1914-17;  Department  of
Development  and  Research,  American  Telephone  and  Telegraph  Corn-
company,  1917 — ;  work  on  inductive  interference.

J.  J.  PiLLiOD,  E.E.,  Ohio  Northern  University,  1908;  American
Telephone  and  Telegraph  Company,  Toledo  Home  Telephone  Com-
pany, and  Union  Switch  and  Signal  Company,  short  periods,  1904-08;
American  Telephone  and  Telegraph  Company,  Long  Lines  Depart-
ment, 1908-11;  Engineering  Department,  1912-13;  Division  Plant
Engineer,  Long  Lines  Department,  1914-17 ;  Engineer  of  Transmission,
1918-19;  Engineer,  1920-.  As  Engineer  of  the  Long  Lines  Depart-
ment, Mr.  Pilliod  has  been  in  general  charge  of  engineering  work  in-
volved in  the  planning  and  installation  of  the  newer  sections  of  the
cable  project  described.

JoHX  R.  Carson,  B.S.,  Princeton,  1907;  E.E.,  1909;  M.S.,  1912;
Research    Department,  Westinghouse    Electric    and    Manufacturing

Company,  1910-12;  instructor  of  physics  and  electrical  engineering,
Princeton,  1912-14;  American  Telephone  and  Telegraph  Company,
Engeneering  Department,  1914-15;  Patent  Department,  1916-17;
Engineering  Department,  1918;  Department  of  Development  and
Research,  1919-.  Mr.  Carson's  work  has  been  along  theoretical  lines
and  he  has  published  several  papers  on  theory  of  electric  circuits  and
electric  wave  propagation.

J.  J.  Gilbert,  A.B.,  University  of  Pennsylvania,  1909;  Harvard,
1910-11;  Chicago,  1911-12;  E.E.,  Armour  Institute,  1915;  in-
structor of  electrical  engineering,  Armour,  1912-17;  Captain  Signal
Corps,  1917-19;  Engineering  Department,  Western  Electric  Com-
pany, 1919,  since  when  he  has  worked  on  submarine  cable  problems.

I.  B.  Crandall,  A.B.,  Wisconsin,  1909;  A.M.,  Princeton,  1910;
Ph.D.,  1916;  Professor  of  Physics  and  Chemistry,  Chekiang  Pro-
vincial College,  1911-12;  Engineering  Department,  Western  Electric
Company,  1913-.  Dr.  Crandall  has  published  papers  on  infra-red
optical  properties,  condenser  transmitter,  thermophone,  etc.  More
recently  he  has  been  associated  with  studies  on  the  nature  and  analysis
of  speech  which  have  been  in  progress  in  the  Laboratory.

Donald  MacKenzie,  A.B.,  Johns  Hopkins,  1908,  A.M.,  1911;
Ph.D.,  1914;  assistant  astronomy,  1914-17;  associate  physicist.
Bureau  of  Standards,  1918-20;  Engineering  Department,  Western
Electric  Company,  1920-.

Harvey  Fletcher,  B.S.,  Brigham  Young,  1907;  Ph.D.,  Chicago,
1911;  instructor  of  physics,  Brigham  Young,  1907-08;  Chicago,
1909-10;  Professor,  Brigham  Young,  1911-16;  Engineering  Depart-
ment, Western  Electric  Company,  1916-.  The  present  paper  by  Dr.
Fletcher  gives  some  of  the  results  of  an  investigation  which  is  being
made  of  the  relation  between  the  frequency  characteristics  of  tele-
phone circuits  and  the  intelligibility  of  transmitted  speech.  Dr.
Fletcher  has  also  published  on  Brownian  movements,  ionization  and
electronics.

Note  :  The  electric  wave-filter,  an  invention  of  Dr.  Campbell,  is  one  of  the
most  important  of  present  day  circuit  developments,  being  indispensable
in  many  branches  of  electrical  communication.  It  makes  possible  the
separation  of  a  broad  band  of  frequencies  into  narrow  bands  in  any  desired
manner,  and  as  will  be  gathered  from  the  present  article,  it  effects  the
separation  much  more  sharply  than  do  tuned  circuits.  As  the  communica-
tion art  develops,  the  need  will  arise  to  transmit  a  growing  number  of  tele-
phone and  telegraph  messages  on  a  given  pair  of  line  wires  and  a  grow-
ing number  of  radio  messages  through  the  ether,  and  the  filter  will  prove
increasingly  useful  in  coping  with  this  situation.  The  filter  stands  beside
the  vacuum  tube  as  one  of  the  two  devices  making  carrier  telegraphy  and
telephony  practicable,  being  used  in  standard  carrier  equipment  to  separate
the  various  carrier  frequencies.  It  is  a  part  of  every  telephone  repeater
set,  cutting  out  and  preventing  the  amplification  of  extreme  line  frequencies
for  which  the  line  is  not  accurately  balanced  by  its  balancing  network.
It  is  being  applied  to  certain  types  of  composited  lines  for  the  separation
of  the  d.c.  Morse  channels  from  the  telephone  channel.  It  is  finding  many
applications  to  radio  of  which  multiplex  radio  is  an  illustration.  The  filter
is  also  being  put  to  numerous  uses  in  the  research  laboratory.

The  present  paper  is  the  first  of  a  series  on  the  electric  wave-filter  to
be  contributed  to  the  Technical  Journal  by  various  authors.  Being  an
introductory  paper  the  author  has  chosen  to  discuss  his  subject  from  a
physical  rather  than  mathematical  point  of  view,  the  fundamental  char-
acteristics of  filters  being  deduced  by  purely  physical  reasoning  and  the
derivation  of  formulas  being  left  to  a  mathematical  appendix. — Editor.

THE  purpose  of  this  paper  is  to  present  an  elementary,  physical
explanation   of  the  wave-filter  as  a  device   for  separating  sin-
usoidal  electrical   currents  of  different   frequencies.     The  discussion

will  be  general,  and  will  not  Involve  assumptions  as  to  the  detailed
construction  of  the  wave-filter;  but  in  order  to  secure  a  certain  nu-
merical concreteness,  curves  for  some  simple  wave-filters  will  be  in-
cluded. The  formulas  employed  in  calculating  these  curves  are
special  cases  of  the  general  formulas  for  the  wave-filters  which  are,
in  conclusion,  deduced  by  the  method  employed  in  the  physical
theory.

All  the  physical  facts  which  are  to  be  presented  in  this  paper,
together  with  many  others,  are  implicitly  contained  in  the  compact
formulas  of  the  appendix.  Although  only  comparatively  few  words
of  explanation  are  required  to  derive  these  formulas,  they  will  not  be
presented  at  the  start,  since  the  path  of  least  resistance  is  to  rely
implicitly  upon  formulas  for  results,  and  ignore  the  troublesome  ques-
tion as  to  the  physical  explanation  of  the  wave-filter.  In  order  to
examine  directly  the  nature  of  the  wave-filter  in  itself,  as  a  physical
structure,  we  proceed  as  though  these  formulas  did  not  exist.

It  is  intended  that  the  present  paper  shall  serve  as  an  introduction
to  important  papers  by  others  in  which  such  subjects  as  transients  on
wave-filters,  specialized  types  of  wave-filters,  and  the  practical  design
of  the  most  efificient  types  of  wave-filters  will  be  discussed.^

A  wave-filter  is  a  device  for  separating  waves  characterized  by  a  dif-
ference in  frequency.  Thus,  the  wave-filter  differentiates  between
certain  states  of  motion  and  not  between  certain  kinds  of  matter,
as  does  the  ordinary  filter.  One  form  of  wave-filter  which  is  well
known  is  the  color  screen  which  passes  only  certain  bands  of  light
frequencies;  diffraction  gratings  and  Lippmann  color  photographs
also  filter  light.  Wave-filters  might  be  constructed  and  employed
for  separating  air  waves,  water  waves,  or  waves  in  solids.  This
paper  will  consider  only  the  filtering  of  electric  waves;  the  same
principles  apply  in  every  case,  however.

^  I  take  pleasure  in  acknowledging  my  indebtedness  to  Mr.  O.  J.  Zobel  for  specific
suggestions,  and  for  the  light  thrown  on  the  whole  subject  of  wave-filters  by  his
introduction  of  substitutions  which  change  the  propagation  constant  without  chang-
ing the  iterative  impedance.

plied  with  its  assigned  narrower  range  of  frequencies.  Thus,  for
instance,  with  three  wa\e-tilters  the  band  of  frequencies  necessary
for  ordinary  telephony  might  ^be  transmitted  to  one  receiving  device,
all  lower  frequencies  transmit^jted  to  a  second  device,  and  all  higher
frequencies  transmitted  to  a"  third  de\'ice — separation  being  made
without  serious  loss  of  energy  in  any  one  of  the  three  bands.

By  means  of  wave-filters  ii^terference  between  difYerent  circuits  or
channels  of  communication  irv  telephony  and  telegraphy,  both  wire  and
radio,  can  be  reduced  provided  they  operate  at  difTerent  frequencies.
The  method  is  furthermore  applicable,  at  least  theoretically,  to  the
reduction  of  interference  between  powder  and  communication  circuits.
The  same  is  true  of  the  simultaneous  use  of  the  ether,  the  earth  return,
and  of  expensive  pieces  of  apparatus  employed  for  several  power  or
communication  purposes.  In  all  cases  the  principle  involved  is  the
same  as  that  of  confining  the  transmission  in  each  circuit  or  channel
to  those  frequencies  which  serve  a  useful  purpose  therein  and  exclud-
ing or  suppressing  the  transmission  of  all  other  frequencies.  In  the
future,  as  the  utility  of  electrical  applications  becomes  more  widely
and  completely  appreciated,  there  will  be  an  imperative  necessity
for  more  and  more  completely  superposing  the  varied  applications  of
electricity;  it  will  then  be  necessary,  to  avoid  interference,  to  make
the  utmost  use  of  every  method  of  separating  frequencies  including
balancing,  tuning,  and  the  use  of  wave-filters.

The  w^ave-filter  problem  in  this  paper  is  discussed  as  a  phase  of
the  artificial  line  problem,  and  it  is  desirable  to  start  with  a  some-
what generalized  definition  of  the  artificial  line.  The  definition
will,  however,  not  include  all  wave-filters  or  all  artificial  lines,  since
a  perfectly  general  definition  is  not  called  for  here.  Even  if  an  ar-
tificial line  is  to  be,  under  certain  wave  conditions,  an  imitation  of,
or  a  substitute  for,  an  actual  line  connecting  distant  points,  hardly
any  limitation  is  thereby  imposed  upon  the  structure  of  the  device;
an  actual  line  need  not  be  uniform  but  may  vary  abruptly  or  gradually
along  its  length  and  may  include  two,  three,  four  or  more  transmis-
sion conductors  of  which  one  may  be  the  earth.  Having  indicated
that  w^ave-filters  partake  of  somewhat  this  same  generality  of  struc-
ture, the  present  paper  is  restricted  to  wave-filters  coming  under
the  somewhat  generalized  artificial  line  specified  by  the  following
definition  :

An  artificial  line  is  a  chain  of  networks  connected  together  in  sequence
through  two  pairs  of  terminals,  the  networks  being  identical  hut  other-

wise  unrestricted.  This  generalized  artificial  line  possesses  the  well-
known  sectional  artificial  line  structure  but  it  need  not  be  an  imita-
tion of,  or  a  substitute  for,  any  known,  real,  transmission  line  con-
necting together  distant  points.  The  general  artificial  line  is  shown
by  Fig.  1  where  N,  N,.  .  .  . are  the  identical  unrestricted  networks
which  may  contain  resistance,  self-inductance,  mutual  inductance,
and  capacity.

In  discussing  this  type  of  structure  as  a  wave-filter,  the  point  of
view  of  an  artificial  line  is  adopted  for  the  reason  that  it  is  advan-
tageous to  regard  the  distribution  of  alternating  currents  as  being
dependent  upon  both  propagation  and  terminal  conditions,  which
are  to  be  separately  considered.     In   this  way   the  attenuation,   or

Fig.    1 — Generalized  Artificial   Line    as    Considered   in   the   Present   Paper,   where
N,  N,  .  .  .  are  Identical  Arbitrary  Electrical  Networks

falling  off,  of  the  current  from  section  to  section  may  be  most  directly
studied.  Terminal  effects  are  not  to  be  ignored,  but  are  allowed
for,  after  the  desired  attenuation  effects  have  been  secured,  possibly
by  an  increase  in  the  number  of  sections  to  be  employed.

The  fundamental  property  of  this  generalized  artificial  line,  which
includes  uniform  lines  as  a  special  case,  is  the  mode  in  which  the
wave  motion  changes  from  one  section  to  the  next,  and  may  be  stated
as  follows:

Upon  an  infinite  artificial  line  a  steady  forced  sinusoidal  disturbance
falls  off  exponentially  j ram  one  section  to  the  next,  while  the  phase  changes
by  a  constant  amount.  Reversing  the  direction  of  propagation  does
not  alter  either  the  attenuation  or  phase  change.  When  complex  quan-
tities are  employed  the  exponential  includes  the  phase  change."^  This
theorem  is  proved,  without  mathematical  equations,   by  observing

^  This  theorem  is  not  new,  but  it  is  ordinarily  derived  by  means  of  differential  or
difference  equations  whereas  it  may  be  derived  from  the  most  elementary  general
considerations,  thus  avoiding  all  necessity  of  using  differential  or  difference  equa-
tions, as  illustrated  in  my  paper  "On  Loaded  Lines  in  Telephonic  Transmission"
{Phil.  Mag.,  vol.  5,  pp.  313-331,  1903).  In  that  discission,  as  well  as  in  this  present
one,  it  is  tacitly  assumed  that  the  line  is  either  an  actual  line  with  resistance,  or  the
limit  of  such  a  line  as  the  resistance  vanishes,  so  that  the  amplitude  of  the  wave
never  increases  towards  the  far  end  of  an  infinite  line.

that  the  percentage  reduction  in  amplitude  and  the  change  in  phase,
in  passing  from  the  end  of  one  section  to  the  corresponding  point  of
the  next  section,  do  not  depend  upon  either  the  absolute  amplitude
or  phase;  they  depend,  instead,  only  upon  the  magnitudes,  angles
and  interconnections  of  the  impedances  between  the  two  points  and
of  the  impedances  beyond  the  second  point.  These  impedances
are,  since  the  line  is  assumed  to  be  periodic  and  infinite,  identically
the  same  for  corresponding  points  between  all  sections  of  the  line,
and,  therefore,  the  relative  changes  in  the  wave  will  be  identical  at
corresponding  points  in  all  sections.  This  proves  the  exponential
falling  off  of  the  disturbance  and  the  constancy  of  phase  change;  the
ordinary  reciprocal  property  shows  that  the  wave  will  fall  off  identic-
ally whichever  be  the  direction  of  propagation.  By  the  superposition
property  it  follows  that  the  steady  state  on  any  finite  portion  of  a
periodic  recurrent  structure  must  be  the  sum  of  two  equally  attenuated
disturbances,  one  propagated  in  each  direction.

The  fundamental  w^ave  propagation  theorem  may  be  generalized
for  any  periodic  recurrent  structure  irrespective  of  the  number  and
kind  of  connections  between  periodic  sections,  provided  the  dis-
turbance is  such  as  to  remain  similar  to  itself  at  corresponding  points
of  each  of  these  connections.

Since,  at  a  given  frequency,  any  network  employed  solely  to  con-
nect a  pair  of  input  terminals  with  a  pair  of  output  terminals  may  be
replaced  by  either  three  star-connected  impedances  or  three  delta-
connected  impedances,  the  general  artificial  line  of  Fig.    1   may  be

Fig.   2 — Equivalent   Artificial   Line  Obtained   by  Substituting  Star   Impedances

Fig.    3 — Equivalent   Artificial    Line   Obtained    by   Substituting   Delta    Impedances

replaced  by  the  equivalent  artificial  line  of  either  Fig.  2  or  Fig.  3.
By  combining  the  series  impedances  in  Fig.  2  and  the  parallel  im-
pedances in  Fig.  3,  the  equivalent  line  in  Fig.  4  is  obtainable.  The
two  ways  of  arriving  at  Fig.  4  give  different  values  for  the  series  and
shunt  impedances  Zi,  Z2,  and  different  terminations  for  the  line,  but
the  propagation  of  the  wave  is  the  same  in  both  cases,  since  the  assumed
substitutions  are  rigorously  exact.  While  Fig.  4  may  be  considered
as  the  generalized  artificial  line  equivalent  to  Fig.  1,  this  requires
including  in  Zi  and  Z2  impedances  which  cannot  always  be  physically
realized  by  means  of  two  entirely  independent  networks,  one  of
which  gives  Zi  and  the  other  Z2.  This  restriction  is  of  no  importance
when  we  are  discussing  the  behavior  of  the  generalized  artificial  line
at  a  single  frequency;  accordingly,  the  ladder  artificial  line  is  suitable
for  this  part  of  the  discussion.  When  we  come  to  the  more  specific
correlation  of  the  behavior  of  the  generalized  artificial  line  at  different
frequencies,  it  will  be  found  more  convenient  to  replace  the  ladder
artificial  line  by  the  lattice  artificial  line,  which  avoids  the  necessity
of  considering  any  impedances  which  are  not  individually  physically
realizable.

The  equivalence  between  Figs.  1  and  4  is  implicitly  based  upon
the  assumption  that  it  is  immaterial,  for  artificial  line  iises,  what
absolute  potentials  the  terminals  1,  2;  3,  4;  5,  6;  etc.  have — this  leaves
us  at  liberty  to  connect  2,  4,  6,  etc.,  together,  so  long  as  we  main-
tain unchanged  the  differences  in  potential  between  1  and  2,  3  and  4,
etc.  Instead  of  connecting  2  and  4  we  might  equally  well  connect
2  and  3,  and  then  Zi  would  connect  1  and  4    as  in  Fig.  5;  with  these

cross-connections  the  propagation  still  remains  unchanged.  We  have
again  obtained  Fig.  4  with  no  circuit  difference  except  the  inter-
change of  terminals  8  and  7  with  terminals  4  and  8;  or,  if  this  is  ignored,
a  reversal  in  the  sign  of  the  current  at  alternate  pairs  of  terminals.
This  shows  that  the  reveisal  of  the  current  in  alternate  sections  of
Fig.  4  may  not  be  of  primary  significance,  since  networks  which  are
essentially  equivalent  have  reversed  currents.

In  order  to  deal,  at  the  start,  with  only  the  simpler  terminal  con-
ditions, we  may  consider  the  line  to  begin  with  only  one-half  of  the
series  impedance  Zi,  or  only  one-half  of  the  bridged  admittance
1  'Zo.  These  mid-points  are  called  the  mid-series  and  mid-shunt
points;  knowing  the  results  of  termination  at  either  of  these  points,
the  effect  of  termination  at  any  other  point  may  be  readily  deter-
mined. For  Fig.  4  termination  at  mid-shunt  has  been  chosen  so
that  each  section  of  the  line  adds  a  complete  symmetrical  mesh  to
the  network.

An  alternator,  introducing  an  impedance  Z^,  is  shown  as  the  source
of  the  steady-state  sinusoidal  current  in  Fig.  4.  Assume  that  the
impedance  Z^  is  variable  at  pleasure,  and  that  it  is  gradually  adjusted
to  make  the  total  impedance  in  the  generator  circuit  vanish, — in  this
case  no  e.m.f.  will  be  required  to  maintain  the  forced  steady-state
which  becomes  a  free  oscillation.  If,  in  addition,  it  is  assumed  that
the  line  has  an  infinite  number  of  sections,  this  required  value  of  Z^
will  be  the  negative  of  the  mid-shunt  iterative  impedance^  of  the  ar-
tificial line,  which  will  be  designated  as  K^.  The  first  shunt  on  the
line  now  includes  — X2  in  parallel  with  2Z2  so  that  its  total  impedance
is,  say,  Z'=  —2ZiK-i.l(^Zi  —  K'^.  The  infinite  line  with  its  first
shunt  given  the  special  value  Z'  is  thus  capable  of  free  oscillation.

It  is  possible  to  simplify  this  infinite  oscillating  circuit  by  cutting

^  The  "iterative  impedance"  of  an  artificial  line  is  the  impedance  which  repeats
itself  when  one  or  more  sections  of  the  artificial  line  are  inserted  between  this  im-
pedance and  the  point  ot  measurement.  It  is  thus  the  impedance  of  an  infinite
length  of  any  actual  artificial" line,  regardless  of  the  termination  of  the  remote  end
of  the  line.  In  general,  its  value  is  different  for  the  two  directions  of  propagation,
but  not  when  the  line  is  symmetrical,  as  at  mid-series  and  mid-shunt.  The  values
at  these  points  are  denoted  by  Kx  and  Ki.  "Iterative  impedance"  is  employed
because  it  is  a  convenient  term  which  is  distinctive  and  describes  the  most  essential
property  of  this  impedance;  it  seems  to  be  more  appropriate  than  "characteristic
impedance,"  "surge  impedance"  and  the  other  synonyms  in  use.

-\-Ki  in  parallel,  which  have  the  impedance  Z"  =  +2Z2i^2/(2Z2+A'2)-
Removing  Z'  together  with  the  infinite  line  on  the  right  there  remains
on  the  left  a  closed  circuit  made  up  of  the  three  impedances  Zi,  Z'
and  Z"  in  series.

After  the  division,  the  infinite  line  on  the  right  will  continue,  with-
out modification,  to  oscillate  freely,  since  it  is  an  exact  duplicate  of
the  original  oscillating  line,  and  so  must  maintain  the  free  oscillation
already  started.  Since  it  oscillates  freely  by  itself,  it  had  originally
no  reaction  upon  the  simple  circuit  from  which  it  was  separated;
this  simple  circuit  on  the  left  must  thus  also  continue  its  own  free
oscillations  without  change  in  period  or  phase.

We  might  continue  and  subdivide  the  entire  infinite  line  into
identical  simple  circuits  but  it  is  sufficient  to  consider  this  one  detached
circuit,  which  is  shown  separately  in  two  ways  by  Fig.  6,  since  from

its  free  oscillations  the  mathematical  formulas  for  the  steady-state
propagation  in  the  artificial  line  may  be  derived.  This  is  deferred,
however,  until  after  the  physical  discussion  is  completed,  so  as  to
leave  no  room  for  doubt  that  the  essentials  of  the  physical  theory
are  really  deduced  without  the  aid  of  mathematical  formulas.

The  generalized  artificial  line,  if  made  up  entirely  of  pure  resist-
ances, will  attenuate  all  frequencies  alike,  and  the  entire  wave  will
be  in  the  same  phase;  this  remains  true,  whatever  be  the  impedance
of  the  individual  branch  of  the  network,  provided  the  ratio  of  the
impedances  of  all  branches  is  a  constant  independent  of  the  frequency.
This  is  precisely  the  condition  to  be  avoided  in  a  wave-filter;  branches
must  not  be  similar  but  dissimilar  as  regards  the  variation  of  impedance
with  frequency.  This  calls  for  inductance  and  capacity  with  neg-
ligible resistance,  so  that  there  is  an  opportunity  for  the  positive
reactance  of  one  branch  to  react  upon  the  negative  reactance  of
another  branch,  in  different  proportions  at  diff^erent  frequencies.
Assuming  the  unit  network  A^^  of  Fig.  1  to  be  made  up  of  a  finite
number  of  pure  reactances,  the  equivalent  impedances  Zi  and  Z2  of
Figs.  4  and  5  must  also  be  pure  reactances.     Under  this  assumption

let  us  consiticr  tlic  free  oscillations  of  I^'ig.  0;  first,  with  A'o  assumed
to  be  a  pure  reactance;  second,  with  A'2  assumed  to  be  a  pure  resist-
ance; and  third,  in  order  to  show  that  this  third  assumption  is  con-
trary to  fact,  with  A'o  assumed  to  be  an  impedance  with  both  resist-
ance and  reactance.

With  Ao  a  reactance,  the  circuit  contains  nothing  but  reactances,
and  free  oscillations  are  possible  if,  and  only  if,  the  total  impedance
of  the  circuit  is  zero.  The  end  impedances  Z'  and  Z"  being  different,
the  potentials  at  the  ends  of  the  mesh  will  be  dilTerent,  and  this  means
that  the  corresponding  wave  on  the  infinite  line  will  be  attenuated,
since  the  ratio  between  these  potentials  is  the  rate  at  which  the  am-
plitudes fall  ofY  per  section.

With  Ao  a  pure  resistance,  a  free  oscillation  is  possible  only  if  the
dissipation  in  the  positive  resistance  at  the  right  end  of  the  circuit
is  exactly  made  up  by  the  hypothetical  source  of  energ\'  existing  in
the  negative  resistance  —  A2  at  the  left  end  of  the  circuit.  An  exact
balance  between  the  energy  supplied  at  one  end  and  that  lost  at  the
other  end  is  possible,  since  the  equal  positive  and  negative  resistances
A2,  —  Ao  carry  equal  currents.  This  continuous  transfer  of  energy
from  the  left  of  the  oscillating  circuit  of  Fig.  6  to  the  right  end  is  the
action  which  goes  on  in  every  section  of  the  infinite  artificial  line,  and
serves  to  pass  forward  the  energy  along  the  infinite  line.

If  Ao  were  complex,  — Ao  on  the  left  of  Fig.  6  and  +A2  on  the
right  would  not  carry  the  same  fraction  of  the  circulating  current  /,
since  they  are  each  shunted  by  a  reactance  2Z2  which  would  allow
less  of  the  current  to  flow  through  +A2  than  through  —  Ao,  if  2Z2
makes  the  smaller  angle  with  +A2,  and  vice  versa.  No  balance
between  absorbed  and  dissipated  energy  is  possible  under  these  con-
ditions when  the  equal  and  opposite  resistance  components  carry
unequal  currents.  A  complex  A2,  therefore,  gives  no  free  oscilla-
tion, and  cannot  occur  with  a  resistanceless  artificial  line.

It  is  perhaps  more  instructive  to  consider  the  transmission  on  the
line  as  a  whole,  rather  than  to  confine  attention  exclusively  to  the
oscillations  of  the  simple  circuit  of  Fig.  6  and  so,  at  this  point,  w^ith-
out  following  further  the  conclusions  to  be  drawn  directly  from  this
oscillating  circuit,  the  fundamental  energy  theorem  of  resistanceless
artificial  lines  will  be  stated,  and  then  proved  as  a  property  of  an
infinite  artificial  line.

Upon  an  infinite  line  of  periodic  recurrent  structure,  and  devoid  of
resistance,  a  sinusoidal  e.m.f.  produces  one  of  two  steady  states,  viz.:

1.  A  to-and-jro  surging  of  energy  without  any  resultant  transfer
of  energy;  currents  and  potential  differences  each  attenuated  from
section  to  section,  but  everywhere  in  the  same  or  opposite  phase  and
mutually  in  quadrature,  or,

2.  A  continuous,  non- attenuated  flow  of  energy  along  the  line
to  infinity  with  no  energy  surging  between  symmetrical  sections;
current  and  potential  non-attenuated,  but  retarded  or  advanced  in
phase  from  section  to  section,  and  mutually  in  phase  at  mid-shunt
and  mid-series  points.

The  critical  frequencies  separating  the  two  states  of  motion  are  the
totality  of  the  resonant  frequencies  of  the  series  impedance,  the  anti-
resonant  frequencies  of  the  shunt  impedance,  and  the  resonant  frequencies
of  a  single  mid-shunt  section  of  the  line.

To  prove  the  several  statements  of  this  theorem  let  us  consider
first  the  consequences  of  assuming  that  the  wave  motion,  in  progress-
ing along  the  line,  is  attenuated,  and  next  the  consequences  of  assum-
ing that  the  wave  motion  changes  its  phase.  If  the  wave  is  atten-
uated, however  little,  at  a  sufficient  distance  it  becomes  negligible,
and  the  more  remote  portions  of  the  line  may  be  completely  removed
without  appreciable  effect  upon  the  disturbance  in  the  nearer  portion
of  the  line.  That  part  of  the  line  which  then  remains  is  a  finite  net-
work of  pure  reactances,  and  in  any  such  network  all  currents  are
always  in  the  same,  or  opposite,  phase;  so,  also,  are  the  potential
differences;  moreover,  the  two  are  mutually  in  quadrature;  there  is
no  continuous  accumulation  of  energy  anywhere,  but  only  an  ex-
change of  energy  back  and  forth  between  the  inductances,  the  ca-
pacities and  the  generator.  Continuously  varying  the  amount  of
the  assumed  attenuation  will  cause  a  continuous  variation  in  the
corresponding  frequency.  The  motion  of  the  assumed  character
may,  therefore,  be  expected  to  occur  throughout  continuous  ranges
or  bands  of  frequencies  and  not  merely  at  isolated  frequencies.

The  question  may  be  asked — How  far  does  the  energy  surge?  Is
the  surge  localized  in  the  individual  section,  or  does  the  surge  carry
the  energy  back  and  forth  over  more  than  one  section,  or  even  in  and
out  of  the  line  as  a  whole?  To  answer  this  question,  it  would  be
necessary,  as  we  will  now  proceed  to  prove,  to  know  something  about
the  actual  construction  of  the  individual  section.  If  each  section  is
actually  made  up  as  shown  in  Fig.  6,  and  this  is  entirely  possible  in
the  present  case  (since  only  positive  and  negative  reactances  would
be  called  for) ,  then  the  section  is  capable  of  free  oscillation,  as  explained

above,  and  the  surging  is  localized  within  the  section;  twice  during
each  cycle  the  amount  of  energy  increases  on  the  right  and  decreases
on  the  left.  But  we  do  not  know  that  the  section  is  made  up  like
Fig.  G;  we  only  know  that  it  is  ecjuivalent  to  Fig.  6  as  regards  input
and  output  relations.  As  far  as  these  external  relations  go,  the  actual
network  may  be  made  exclusively  of  either  inductances  or  capacities
with  the  connections  shown  in  Fig.  4  or  with  the  cross-connections
of  Fig.  5,  according  as  the  current  is  to  have  the  same  or  opposite
signs  in  consecutive  sections.  In  any  network  made  up  exclusively
of  inductances  or  of  capacities,  the  total  energy  falls  to  zero  when
the  current  or  the  potential  falls  to  zero,  respectively.  Twice,  there-
fore, in  every  cycle  the  total  energy  surges  into  this  line  and  then  it
all  returns  to  the  generator.  With  other  networks,  surgings  inter-
mediate betw'een  these  two  extremes  will  occur.  The  theorem,
therefore,  does  not  limit  the  extent  of  the  surging.

Under  the  second  assumption,  the  phase  difference  between  the
currents  at  two  given  points,  separated  by  a  periodic  interval,  is  to
be  an  angle  which  is  neither  zero  nor  a  multiple  of  ±x.  The  assumed
difference  in  phase  can  only  be  due  to  the  infinite  extension  of  the
artificial  line  since,  as  previously  noted,  no  finite  sequence  of  induct-
ances and  capacities  can  produce  any  difference  in  phase.  That
infinite  lines  do  produce  phase  differences  is  well-known;  in  particular,
an  infinite,  uniform,  perfectly  conducting,  metallic  pair  shows  a
continuous  retardation  in  phase.  If  the  infinitely  remote  sections
of  the  artificial  line  are  to  have  this  controlling  effect  oti  the  wave
motion,  the  wave  motion  must  actually  extend  to  infinity,  that  is,
there  can  be  no  attenuation.  The  wave  progressing  indefinitely  to
infinity  without  attenuation  must  be  supplied  continuously  with
energ\';  this  energy  must  flow  along  the  entire  line  with  neither  loss
nor  gain  in  the  reactances  it  encounters  on  the  way.  This  continuous
flow  of  energ>'  can  take  place  only  provided  the  currents  and  poten-
tials are  not  in  quadrature;  they  may  be  in  phase.  In  considering
the  free  oscillations  of  Fig.  6  it  was  shown  that  K2  is  real  if  it  is  not
pure  reactance.  That  is,  for  the  mid-shunt  section  the  current  and
potential  are  in  phase.  It  is  easy  to  show  that  they  are  also  in  phase
at  the  mid-series  point  which  is  also  a  point  of  symmetry.

This  flow-of-energy  state  of  motion  thus  necessarily  characterizes
a  phase-retarded  wave  on  a  resistanceless  artificial  line,  regardless
of  the  amount  of  the  assumed  positive  or  negative  retardation,  which
may  be  taken  to  have  any  value  betw'een  zero  and  exact  opposition
of  phase.  Continuously  varying  the  retardation  throughout  the  180
degrees  will,  in  general,  call  for  a  continuous  change  in  the  frequency

of  the  wave  motion.  The  second  state  of  motion  occurs,  therefore,
throrghout  continuous  ranges  or  bands  of  frequencies.

No  other  state  of  motion  is  possible.  With  given  initial  amplitude
and  pha^e  any  possible  wave  motion  is  completely  defined  by  its
attenuation  and  phase  change.  All  possible  combinations  of  these
two  elements  have  been  included  in  the  two  states,  since  the  excluded
conditions  on  each  assumption  have  been  included  as  a  consequence
of  the  other  assumption.  Thus,  the  exclusion  of  no  attenuation  in
the  first  assumption  was  found  necessarily  to  accompany  the  phase
change  of  the  second  assumption;  currents  in  phase  or  opposed,
which  were  excluded  from  the  second  assumption,  were  found  to  be
necessary  features  accompanying  the  first  assumption.  There  remains
only  to  consider  the  critical  frequencies  separating  the  two  states  of
motion.  At  these  frequencies  there  can  be  no  attenuation  and  lag
angles  of  multiples  of  ^tt,  including  zero,  only.  At  symmetrical
points  the  iterative  impedance  of  the  line  must  be  a  pure  reactance
to  satisfy  the  first  state  of  motion,  and  a  pure  resistance  to  satisfy
the  second  state  of  motion.  The  only  iterative  impedances  which
satisfy  these  conditions  are  zero  and  infinity.

Some  details  relating  to  the  pass  and  stop  bands  and  the  criti-
cal frequencies  are  brought  together  in  the  following  table,  where
■"  stop  (  ±  )"  refers  to  stop  bands,  the  current  being  in  phase  or  op-
posed in  successive  sections,  and  where  7  and  k  refer  to  the  line  obtained
by  uniformly  distributing  I/Z2  with  respect  to  Zi.

It  is  not  necessary  to  check  the  table  item  by  item,  many  of  which
have  already  been  proven,  but  it  will  be  instructive  to  check  some  of
the  items  by  assuming  that  Z1/4Z2,  called  the  ratio  for  brevity,  is
positive  to  begin  with,  and  that  a  continuous  increase  in  frequency
reduces  the  ratio  to  zero  and  back  through  =f  00  to  its  original  posi-
ti\e  value.  This  cycle  starts  with  a  stop  (  +  )  band  since  the  artificial
line  is  in  effect  a  network  of  reactances,  all  of  which  have  the  same
sign ;  there  is  attenuation  and  the  iterative  impedances  are  imaginary.
When  the  ratio  decreases  to  zero,  there  must  be  either  resonance
which  makes  Z\  =  0,  or  anti-resonance  which  makes  Z2  =  00  ;  in
either  case  the  artificial  line  has  degenerated  into  a  much  simpler  cir-
cuit; it  is  a  shunt  made  up  of  all  Z2's  combined  in  parallel,  or  a  simple
series  circuit  made  up  of  all  Zi's,  respectively;  the  iterative  imped-
ances are  0  and  ^  ,  respectively ;  there  is  no  attenuation  in  either  case.

With  a  somewhat  further  increase  of  the  frequency  the  ratio  will
assume  a  small  negative  value  with  the  result  that  the  artificial  line
will  have  both  kinetic  and  potential  energy.  An  analogy  now  exists
between  the  artificial  line  and  an  ordinary  uniform  transmission  line,
which  possesses  both  kinetic  and  potential  energy,  and  is  ordinarily
visualized  as  being  equivalent  to  many  small  positive  reactances,  in
series,  bridged,  to  the  return  conductor,  by  large  negative  reactances.
The  fact  that  uniform  lines  do  freely  transmit  waves  is  a  well-known
physical  principle,  and  it  is  not  necessary  to  repeat  here  the  physical
theory  of  such  transmission  merely  to  show  that  the  same  phenomenon
occurs  with  the  identical  structure  when  it  is  called  an  artificial  line
or  wave-filter.

In  order  to  determine  just  how  far  the  ratio  may  depart  from  zero,
on  the  negative  side,  without  losing  the  property  of  free  transmission,
we  look  for  any  change  in  the  action  of  the  individual  section  of  the
artificial  line  which  is  fundamental ;  nothing  less  than  a  fundamental
change  in  the  behavior  of  the  individual  section  can  produce  such  a
radical  change  in  the  line  as  an  abrupt  transition  from  the  free  trans-
mission of  a  pass  band  to  the  to-and-fro  surging  of  energy  in  a  stop
band.  Now  as  the  ratio  is  made  more  and  more  negative  by  the
assumed  increase  of  frequency,  the  value  —1  is  reached,  at  which
frequency  the  symmetrical  section  (Fig.  6)  of  the  artificial  line  is
capable  of  free  oscillation  by  itself.  This  is  well  recognized  as  a
most  fundamental  change  in  the  properties  of  any  network,  and  it
afifords  grounds  for  expecting  a  complete  change  in  the  character  of
the  propagation  over  the  artificial  line.  The  change  must  be  to  a
stop  band  with  currents  in  opposite  phase,  since  at  resonance  the
potentials  at  the  two  ends  of  a  section  are  in  opposite  phase.

Further  increase  in  the  frequency  cannot  make  any  change  in  the
absolute  difference  in  phase  between  the  two  ends  of  the  other  section,
since  opposition  is  the  greatest  possible  difiference  in  phase;  the  wave
now  adapts  itself  to  increasing  frequency  by  altering  its  attenuation.

Upon  continuing  the  increase  of  frequency,  so  as  to  reduce  the
ratio  to  —  00  ,  we  arrive  at  either  anti-resonance  corresponding  to
Zi  =  00  or  resonance  corresponding  to  Z2  =  0;  the  artificial  line  has
now  degenerated  into  a  row  of  isolated  impedances  Z2,  or  into  a  series
of  impedances  Zi  short-circuited  to  the  return  wire;  in  either  case
the  attenuation  is  infinite  since  no  wave  is  transmitted.  Passing
beyond  this  critical  frequency  the  ratio  becomes  positive,  according
to  our  assumption,  and  we  are  again  in  a  stop  (-f )  band.

While  in  this  rapid  survey  of  what  happens  during  this  frequency
cycle  little  has  been  actually  proven,  it  should  have  been  made
physically  clear  why  abrupt  changes  in  the  character  of  the  trans-
mission occur  at  the  frequencies  making  the  ratio  equal  to  0,  —  1  or
00 ,  since  the  line  degenerates  into  a  simpler  structure,  or  the  phase
change  reaches  its  absolute  maximum,  on  account  of  resonance,  at
these  particular  frequencies.

Information  as  to  the  location  of  the  bands  is  often  obtained  most
readily  by  plotting  both  Zi  and  —AZ^,  as  illustrated  in  Fig.  7,  and
determining  the  critical  frequencies  by  noting  where  the  curves  cross
each  other  and  the  abscissa  axis,  as  well  as  where  they  become  in-
finite. Any  particular  band  is  then  a  pass  band,  a  stop  (  +  )  band
or  a  stop  (  — )  band,  according  as  Zi,  the  abscissa  axis,  or  —  4Z2  lies
between  the  other  two  of  the  three  lines.  In  Fig.  7  the  pass  bands
are  Pi,  P2,  Pz,  Pi\  the  stop  (  +  )  bands  are  52,  54,  56;  and  the  stop
(  — )  bands  are  5i,  S^,  St,  5?,  and  they  illustrate  quite  a  variety  of
sequences.  By  altering  the  curves  the  bands  may  be  shifted,  may
be  made  to  coalesce,  or  may  be  made  to  vanish.

The  pass  band  and  stop  band  characteristics  of  wave-filters  are
concretely  illustrated  for  a  few  typical  cases  by  the  curves  of  Figs.
8-13,  which  show  the  attenuation  constant  A,  the  phase  constant  B,
and  both  the  resistance  R  and  reactance  X  components  of  the  itera-
tive impedance  for  a  range  of  frequencies  which  include  all  of  the
critical  frequencies,  except  infinity.  The  heavy  curves  apply  to  the
ideal  resistanceless  case,  while  the  dotted  curves  assume  a  power
factor  equal  to  l/(207r)  for  each  inductance  which  is  a  value  readily
obtained  in  practice.  This  value  is,  however,  not  sufficiently  large  to
make  these  small  scale  curves  entirely  clear,  since  considerable  por-
tions of  the  dotted  curves  appear  to  be  coincident  with  the  heavy  line
curves;  but  this,  as  far  as  it  goes,  proves  the  value  of  the  present  dis-
cussion which  rests  upon  a  close  approximation  of  actual  wave-filters
to  the  ideal  resistanceless  case.

The  low  pass  resistanceless  wave-filter,  as  shown  by  Fig.  8,  pre-
sents no  attenuation  below  1,000  cycles;  above  this  frequency  the
attenuation  constant  increases  rapidly,  in  fact,  the  full  line  attenuation
curve  increases  at  the  start  with  maximum  rapidity,  since  it  is  there
at  right  angles  to  the  axis.  The  dotted  attenuation  curve,  which  in-
cludes the  effective  resistance  in  the  inductance  coils,  follows  the
ideal  attenuation  curve  closely,  except  in  the  neighborhood  of  1,000
cycles,  where  resistance  rounds  ofi  the  abrupt  corner  which  is  present
in  the  ideal  A  curve.  The  phase  constant  B  is,  at  the  start,  propor-
tional to  the  frequency,  as  for  an  ordinary  uniform  transmission  line;
its  slope  becomes  steeper  as  the  critical  frequency  1,000  is  approached
where  the  curve  reaches  the  ordinate  tt,  at  which  value  it  remains
constant  for  all  higher  frequencies.  As  shown  by  the  dotted  B
curve,  resistance  rounds  off  the  corner  at  the  critical  frequency,  but

Fig.  8— Low  Pass  Wave-Filter:  L  =  I/tt  Henry,  C'  =  1  V  Microfarad
Fig.  9— Complementary  High  Pass  Wave-Filter:  Z,  =  l/47r,  C  =  IAtt

Otherwise  leaves  the  curve  approximately  uinhaiigcd.  The  full  line
curves  for  R^  and  A'l  show  that  in  the  ideal  case  the  iterative  im-
pedance is  pure  resistance  and  pure  reactance  in  the  pass  and  stop
bands  respectively,  and  that  resistance  smooths  the  abrupt  transition
at  the  critical  frequency.

The  high  pass  wave-filter  shown  by  Fig.  9  passes  the  band  which
is  stopped  by  the  low  pass  wave-filter  of  Fig.  8,  and  vice  versa.  For
this  reason  the  two  wave-filters  are  said  to  be  complementary.

Another  set  of  two  complementary  wave-filters  is  shown  by  Figs.
10  and  11,  one  of  which  passes  only  a  single  band  of  frequencies,
not  extending  to  either  zero  or  infinity,  while  the  other  passes  the
remaining  frequencies  only.  The  single  pass  band  of  Fig.  10,  em-
bracing a  total  phase  change  27r  on  the  B  curve,  is  actually  a  case  of
confluent  pass  bands,  each  of  which  embraces  the  normal  angle  tt.
The  tendency  of  the  two  simple  pass  bands  to  separate,  and  leave  a
stop  band  between  them,  is  shown  by  the  hump  in  the  dotted  at-
tenuation constant  curve  at  1,000  cycles.  If,  instead  of  the  two
simple  bands  having  been  brought  together,  one  of  them  had  been
relegated  to  zero  or  infinity,  the  single  remaining  pass  band  would
have  exhibited  the  normal  angular  range  r  in  the  B  curve,  and  there
would  have  been  no  hump  in  the  dotted  A  curve.  The  stop  band  of
Fig.  11  also  illustrates  peculiarities  which  are  not  necessary  features
of  a  wave-filter  with  a  single  stop  band  in  this  position.  This  wave-
filter  is  obtained  from  Fig.  7  by  making  all  bands  vanish  except
Pi,  Sz,  So  and  P3, — by  extending  P2  to  zero,  P3  to  infinity,  and  making
S3  and  Si  coalesce,  so  that  the  attenuation  becomes  infinite  in  the
stop  band  without  passing  from  a  stop  (  — )  to  a  stop  (-f-)  band.
The  coalescing  stop  bands  are  responsible  for  the  rapid  changes  in
the  B,  Ri,  and  A'l  curves  of  Fig.  11  which  would  not  have  appeared
if,  in  Fig.  7,  the  same  pass  band  had  been  obtained  by  retaining  Pi,
52  and  P2  and  making  all  other  bands  vanish.

An  extreme  case  of  complementary  wave-filters  is  shown  by  Figs.
12  and  13,  where  no  frequencies  and  all  frequencies  are  passed  re-
spectively. The  first  result  is  obtained  by  combining  inductances
alone,  which,  as  has  been  pointed  out  above,  can  give  only  an  at-
tenuated disturbance  devoid  of  wave  characteristics.  The  wave-
filter  shown  for  passing  all  frequencies  has  inductance  coils  in  the
line,  and  capacities  diagonally  bridged  across  the  line.  This  wave-
filter  combines  a  constant  iterative  impedance  with  a  progressive
change  in  phase  which  is  sometimes  useful."*     An  outstanding  char-

*  A  theoretical  use  of  the  phase  shifting  afforded  by  the  lattice  artificial  line  was
made  at  page  253  of  "Maximum  Output  Networks  for  Telephone  Substation  and
Repeater  Circuits,"  Trans.  A.  I.  E.  E.,  vol.  39,  pp.  231-280,  1920.

Fig.  12— No  Pass  Wave-Filter:  L,  =  1/t,  Lj  =  l/4x
Fig.  13 — Complementary  All  Pass  Wave-Filter:  L  =  l/27r,  C  =  l/2j

acteristic  of  this  type  of  artificial  line  is  that  it  has,  for  all  frequencies,
the  same  iterative  impedance  as  a  uniform  line  with  the  same  total
series  and  shunt  impedances.  This  artificial  line  will  be  considered
in  more  detail  in  the  next  section  of  this  paper.

Up  to  this  point  we  have  considered  the  properties  of  artificial  line
networks  which  were  supposed  to  be  given.  In  practice  the  problem
is  ordinarily  reversed,  and  we  ask  the  questions:  May  the  locations
of  the  bands  be  arbitrarily  assigned?  May  additional  conditions  be
imposed?  How  may  the  corresponding  network  be  determined,  and
what  is  its  attenuation  in  terms  of  the  assigned  critical  frequen-
cies?    These  questions  might  be  answered  by  a  study  of  Fig.  7,  in

all  its  generality,  but  it  seems  simpler  to  base  the  discussion  upon
the  artificial  line  shown  in  Fig.  14,  which  is  to  be  a  generalization
of  Fig.  13  to  the  extent  of  making  the  two  impedances  Zi  and  Z2
any  possible  actual  driving-point  impedances.  It  is  sometimes
illuminating  to  regard  this  artificial  line  as  a  nest  of  bridges,  one
within  another,  as  shown  by  Fig.  15.

On  interchanging  terminals  3  with  4  and  7  with  8  in  Fig.  14  the
network  of  lines  remains  unchanged;  thus,  Zi  and  4Z2  may  be  inter-
changed in  the  formulas  for  the  artificial  line  with  no  change  in  the
result,  except,  possibly,  one  corresponding  to  a  reversal  of  the  current
at  alternate  junction  points.  Another  elementary  feature  of  this  arti-
ficial line  is  that  it  degenerates  into  a  simple  shunt  or  a  simple  series
circuit  at  the  resonant  or  anti-resonant  frequencies,  respectively,  of
either  Zx  or  Z2,  and  these  are  the  critical  frequencies,  terminating
the  pass  bands.  At  other  frequencies,  a  positive  ratio  Z1/4Z2  must
give  a  stop  band,  since  the  reactances  are  all  of  one  sign.  If  a  small
negative  value  of  this  ratio  gives  free  transmission,  as  we  naturally
expect,  there  will  be  identical  transmission,  except  for  a  reversal  of

sign,  when  the  ratio  has  the  reciprocal  value,  which  will  be  a  large
negative  quantity,  since  we  may  always  interchange  Zi  and  4Z2.
The  consequences  of  this  and  of  other  elementary  properties  of  this
artificial  line  are  brought  together  in  the  following  table:

The  cycle  of  bands:  stop   (  +  ),  pass,  stop  (  — ),  adopted  for  the
table,  carries   the    attenuation  factor    e~^    around  the  periphery  of

a  unit  semi-circle;  in  the  stop  (  +  )  band  it  traverses  the  radius  from
0  to  1,  in  the  pass  band  it  travels  along  the  unit  circle  through  180
degrees  to  the  value  —1,  completing  the  cycle  from  —1  to  0  in  the
stop  (  — )  band.  In  this  cycle  there  are  four  points  of  special  interest,
corresponding  to  ratio  values  1,  0,  —1  and  oo,  for  which  the  wave  is
infinitely  attenuated,  unattenuated  with  an  angular  change  of  0,
of  90,  and  of  180  degrees,  respectively.  It  is  at  the  90  degree  angle
that  resonance  of  the  individual  section  occurs;  the  iterative  im-
pedance is  then  equal  to  2\Z2\.

If  we  plot  Z\  and  4Z2  the  pass  bands  are  shown  by  the  points  where
the  curves  become  zero  or  infinite,  and  the  intersections  of  the  two

Fig.  16 — Graph  for  Locating  the  Pass  and  Stop  Bands  of  the  Lattice  Artificial  Line,

curves  show  the  frequencies  at  which  the  attenuation  becomes  in-
finite. These  intersections  must  be  at  an  acute  angle  since  each
branch  of  the  two  curves  has  a  positive  slope  throughout  its  entire
length ;  for  this  reason  it  may  be  desirable  to  plot  the  ratio  rather  than
the  individual  curves;  this  is  especially  desirable  in  cases  where  the
two  curves  do  not  intersect,  but  are  tangent.  Fig.  16  is  for  a  lattice
network  equivalent  to  two  sections  of  the  ladder  type  illustrated  by
Fig.  7,  and  so  cannot  include  a  stop  (  — )  band.  Accordingly,  the
ratio  does  not  go  above  unity,  although  it  reaches  unity  at  the  two
frequencies  300  and  400,  corresponding  to  the  infinite  attenuation
where  stop   (  — )    and   stop    (  +  )    bands  meet  in   Fig.  7.     It   is  also

unity  at  the  extreme  frequencies  zero  and  infinity.     The  four  pass
bands  have,  of  course,  the  same  locations  as  in  Fig.  7.

Multiplying  the  ratio  by  a  constant  greater  than  unity  introduces
stop  (  — )  bands  along  with  the  stop  (  +  )  bands;  multiplying  it  by
a  constant  less  than  unity  removes  all  infinite  attenuations;  these
changes  within  the  stop  bands  are  made  without  altering  the  loca-
tions of  the  four  pass  bands.

In  connection  with  practical  applications  we  especially  desire  to
know  what  latitude  is  permitted  in  the  preassignment  of  properties
for  a  wave-filter.  If  we  consider  first  the  ideal  lattice  wave-filter,
its  limitations  are  those  inherent  in  the  form  which  its  two  inde-
pendent resistanceless  one-point  impedances^  Zi  and  Zo  may  assume.
The  mathematical  form  of  this  impedance  is  shown  by  formula  (7)
of  the  appendix,  which  may  be  expressed  in  words  as  follows:

Within  a  constant  factor  the  most  general  one-point  reactance  obtain-
able by  means  of  a  finite,  pure  reactance  network  is  an  odd  rational
function  of  the  frequency  which  is  completely  determined  by  assigning
the  resonant  and  anti-resonant  frequencies,  subject  to  the  condition  that
they  alternate  and  include  both  zero  and  infinity.

The  corresponding  general  expressions  for  the  quotient  and  product
of  the  impedances  Zi  and  Zj  are  shown  by  formulas  (8)  and  (9).
Definite,  realizable  values  for  all  of  the  2n-f2  parameters  and
2n  +  l  optional  signs  occurring  in  these  formulas  may  be  deter-
mined in  the  following  manner:

(a)  Assign  the  location  of  all  n  pass  bands,  which  must  be  treated
as  distinct  bands  even  though  two  or  more  are  confluent;  this
fixes  the  values  of  the  2n  roots  pi  .  .  .  p2n  which  correspond
to  the  successive  frequencies  at  the  two  ends  of  the  bands.

(b)  Assign  to  the  lower  or  upper  end  of  each  pass  band  propagation
without  phase  change  from  section  to  section;  this  fixes  the
corresponding  optional  sign  in  formula  (8)  as  +  or  — ,  respec-
tively.

(c)  Assign  a  value  to  the  propagation  constant  at  any  one  non-
critical  frequency  (that  is,  assign  the  attenuation  constant  in  a

*  A  one-point  impedance  of  a  network  is  the  ratio  of  an  impressed  electromotive
force  at  a  point  to  the  resulting  current  at  the  same  point — in  contradistinction  to
two-point  impedances,  where  the  ratio  applies  to  an  electromotive  force  and  the
resulting  current  at  two  different  points.

stop  band  or  the  phase  constant  in  a  pass  band) ;  this  fixes
the  value  of  the  constant  G  and  thus  completely  determines
formula  (8)  on  which  the  propagation  constant  depends.

(d)  Assign  to  the  lower  or  upper  end  of  each  stop  band  the  iterative
impedance  zero;  this  fixes  the  corresponding  optional  sign  in
formula  (9)  as  +  or  — ,  respectively.

(e)  Assign  the  iterative  impedance  at  any  one  non-critical  fre-
quency (subject  to  the  condition  that  it  must  be  a  positive
resistance  in  a  pass  band  and  a  reactance  in  a  stop  band) ;
this  fixes  the  constant  H  and  thereby  the  entire  expression  (9)
upon  which  the  iterative  impedance  depends.

The  quotient  and  product  of  the  impedances  Zi  and  Z2  are  now
fully  determined;  the  values  of  Zi  and  Zi  are  easily  deduced  and  also
the  propagation  constant  and  iterative  impedance  by  formulas  (11)
and  (12);  Zi  and  Zi  are  physically  realizable  except  for  the  necessary
resistance  in  all  networks.

A  lattice  wave-filter  having  any  assigned  pass  bands  is  physically
realizable;  the  location  of  the  pass  bands  fully  determines  the  propagation
constant  and  iterative  impedance  at  all  frequencies  when  their  values
are  assigned  at  one  non-critical  frequency,  and  zero  phase  constant  and
zero  iterative  impedance  are  assigned  to  the  lower  or  upper  end  gf  each
pass  band  and  stop  band,  respectively.

Lattice  Artificial  Line   Equivalent  to  the   Generalized
Artificial  Line  of  Fig.  1

Since  any  number  of  arbitrarily  preassigned  pass  bands  may  be
realized  by  means  of  the  lattice  network,  it  is  natural  to  inquire
whether  this  network  does  not  present  a  generality  which  is  essen-
tially as  comprehensive  as  that  obtainable  by  means  of  any  network
N  in  Fig.  1,  provided  the  generalized  line  is  so  terminated  as  to  equalize
its  iterative  impedances  in  the  two  directions.  This  proves  to  be
the  case.

If  network  A^  has  identical  iterative  impedances  in  both  directions,
the  lattice  network  equivalent  to  two  sections  of  N  is  shown  by  Fig.
17;  each  lattice  impedance  is  secured  by  using  an  N  network;  the  N's
placed  in  the  two  series  branches  of  the  lattice  have  their  far  terminals
short-circuited  so  that  they  each  give  the  impedance  denoted  by
Zo;  the  N's  in  the  two  diagonal  branches  have  their  far  ends  open
and  they  each  give  the  impedance  denoted  by  Zoo.

The  lattice  network  of  l*'ig.  IS  lias  in  each  branch  a  one-p(jinl  im-
pedance obtained  by  means  of  a  duplicate  of  the  given  network  A^
and  an  ideal  transformer.  The  two  lattice  branch  impedances  are
Zq-\-Zr^2Zqr  whcrc  the  three  impedances  Z,,  Zr,  Z^r  are  the
efTective  self  and  mutual  impedances  of  the  network  N  regarded  as  a
transformer.     This  lattice  network  has  identicalK'  the  same  propaga-

tion  constant  as  the  single  network  N  shown  on  the  left.  Since  the
lattice  cannot  have  difTerent  iterative  impedances  in  the  two  direc-
tions, it  actually  compromises  by  assuming  the  sum  of  the  two  itera-
tive impedances  presented  by  N.     A  physical  theory  of  the  equival-

Fig.   18 — Lattice  Network  Having  the  Same  Propagation  Constant  as  N  and  an
Iterative   Impedance  Equal  to  the  Sum  of   the  Two   Iterative    Impedances   of    A'^

ences  shown  in  Figs.  17  and  18  has  not  been  worked  up;  the  analytical
proofs  were  made  by  applying  the  formulas  given  in  the  appendix
under  lattice  networks.

Without  going  to  more  complex  networks  it  is,  of  course,  not  pos-
sible to  get  a  symmetrical  iterative  impedance,  but  that  is  not  necessary
for  our  present  purposes  where  we  are  concerned  primarily  with  the

propagation  constant.     It  has  now  been  shown  with  complete  gener-
ality that:

The  lattice  artificial  line,  with  physically  realizable  branch  impedances ,
is  identically  equivalent  in  propagation  constant  and  mean  iterative
impedance  to  the  chain  of  identical  physically  realizable  networks  con-
nected, together  in  sequence  through  tivo  pairs  of  terminals.

To  complete  this  simplification  of  the  generalized  artificial  line  it  is
necessary  to  know  the  simplest  possible  form  of  the  one-point  im-
pedances employed  in  the  branches  of  the  lattice  network.  The
discussion  of  the  most  general  one-point  impedance  obtainable  by
means  of  any  network  of  resistances,  self  and  mutual  inductances,
leakages  and  capacities  will  find  its  natural  place,  together  with
allied  theorems,  in  a  paper  on  the  subject  of  impedances.  For  the
present  purpose  it  is  sufficient  to  state:

The  most  general  branch  impedance  of  the  lattice  network  may  he
constructed  by  combining,  in  parallel,  resonant  circuits  having  im-
pedances of  the  form  R-\-iLp-\-{G-{-iCp)~^;  or  they  may  equally
well  be  constructed  by  combining,  in  series,  anti-resonant  circuits  having
impedances  of  the  form  \G-\-iCp-\-{R-^iLp)~^Y~^

The  wave-filter  under  discussion  approximates  to  a  resistanceless
artificial  line,  and  such  an  ideal  artificial  line  is  capable  of  two,  and
only  two,  fundamentally  distinct  states  of  motion.  In  one  state  the
disturbance  is  attenuated  along  the  line,  and  there  is  no  flow  of  energy
other  than  a  back  and  forth  surging  of  energy,  the  intensity  of  which
rapidly  dies  out  along  the  line.  In  the  other  state  there  is  a  free
flow  of  energy,  without  loss,  from  section  to  section  along  the  line,
with  no  surge  of  energy  between  symmetrical  sections.  Each  state
holds  for  one  or  more  continuous  bands  of  frequencies;  these  bands
have  been  distinguished  as  stop  bands  and  pass  bands.

A  high  degree  of  discrimination,  between  different  frequencies,
may  be  obtained,  even  if  each  section,  taken  alone,  gives  only  a
moderate  difference  in  attenuation,  by  the  use  of  a  sufificient  number
of  sections  in  the  wave-filter,  since  the  attenuation  factors  vary  in
geometrical  progression  with  the  number  of  sections.

Any  number  of  arbitrarily  located  pass  bands  may  be  realized  by
means  of  the  lattice  artificial  line;  furthermore,  the  propagation
constant  at  one  frequency,  and  the  iterative  impedance  at  one  fre-
quency may  both  be  assigned,  while  the  location  of  zero  phase  con-

stant  and  zero  iterati\e  impedance  at  the  lower  or  upper  end  of  each
pass  band  and  stop  band,  respectively,  is  also  optional.  This  com-
pletely determines  the  lattice  artificial  line.  No  additional  condition,
other  than  iterati\e  impedance  asymmetry,  can  be  realized  by  re-
placing the  lattice  network  b>-  an\-  four  terminal  network.

Formulas  for  the  propagation  constant  and  iterative  impedance  of
the  generalized  artificial  line,  expressed  in  a  number  of  equivalent
forms,  have  already  been  given  in  my  paper  on  Cisoidal  Oscillations,^
but  it  seems  worth  while  to  deduce  the  formulas  anew  here  from  the
free  oscillations  of  the  detached  unit  circuit  of  Fig.  6,  so  as  to  complete
the  physical  theory  by  deducing  the  comprehensive  mathematical
formulas  by  the  same  method  of  procedure.

Ladder  Network  Formulas
Notation:
Zi,  Z2  =  series  impedance   and   shunt   impedance   of   the   section   of

Fig.  L
V  =  A  -{-  iB  =  propagation  constant  per  section.
K\,  A'o  =  iterative  impedances  at  mid-series  and  mid-shunt.
T  =  «  +  '^  =  V  Zi/  Z2  =  propagation  constant    for    uniform   distri-
bution of  Zi  and  1  Z2,  per  unit  length.
^  ~   V  ZiZo  =  iterative  impedance  of  this  same  uniform  line.

this  condition  it  is  sufficient  to  make  use  of  two  other  simple  relations:

the  proportionality  of  the  potential  drops  in  the  direction  of  the  current

«"Cisodial  Oscillations,"  Trans.  A.  I.  E.  E.,  vol.  30,  pp.  873-90),  1911.  In  the
lowest  row  of  squares  of  Table  I,  the  iterative  impedances  and  propagation  constant
of  any  network  are  given  in  fi\-e  different  wa\s,  involving  one-point  and  two-point
impedances,  equivalent  star  impedances,  equivalent  delta  impedances,  equivalent
transformer  impedances,  or  the  determinant  of  the  network.  The  only  typo-
graphical errors  in  Table  I  appear  to  be  the  four  which  occur  in  the  first,  third  and
fifth  squares  of  this  row:  in  tfie  values  for  K,  replace  {S,  —  S^)  by  (5,  —  Sr)  and
place  a  parenthesis  before  U,  —  Ur)\  in  the  first  value  of  AV  replace  5,^  by  S^-;  in
the  last  value  for  T^  add  a  minus  sign  so  that  it  reads  cosh"'.

Ki,  the  mid-series  iterative  impedance  of  the  artificial  Hne,  to  the
total  impedance  on  the  right  of  the  mid-point  of  the  series  impedance
Zi.     These  three  relations,  which  can  be  written  down  at  once,  are:

and  the  formulas  for  Zi  and  Zo  in  terms  of  F  and  Kx  or  7^2  are  likewise
found  to  be:

Formulas  (3)  and  (4)  are  in  the  nature  of  design  formulas  in  that
they  determine  the  impedance  Zi  and  Z2,  at  assigned  frequencies,
which  will  ensure  the  assigned  values  of  V  and  K  at  these  frequencies.
In  general,  however,  it  Avould  not  be  evident  how  best  to  secure  these
required  values  of  Zi  and  Zo;  complicated  or  even  impossible  net-
works might  be  called  for,  even  to  approximate  values  of  Zi  and  Z2
assigned  in  an  arbitrary  manner.  Fortunately,  practical  require-
ments are  ordinarily  satisfied  by  meeting  maximum  and  minimum
values  for  the  attenuation  constant  throughout  assigned  frequency
bands.  Formulas  (8)  and  (9)  may  be  employed  for  this  purpose  as
explained  below.

It  is  convenient  to  have  formulas  (1)  and  (2)  expressed  in  a  variety
of  ways,  since  no  one  form  is  well  suited  for  calculation  throughout
the  entire  range  of  the  variables.  Accordingly,  the  following  analyti-
cally equivalent  expressions  are  here  collected  together  for  reference:

The  formulas  leave  indeterminate  the  signs  of  7,  k,  F,  and  K,  and
also  a  term  ^i^ttw  in  7  and  T.  The  signs  are  to  be  so  chosen  that
the  real  parts  are  positive,  or  become  positive  when  positive  re-
sistance is  added  to  the  system.  The  indeterminate  =*=  i27rn  can
be  made  determinate  only  after  knowing  something  of  the  internal
structure  of  the  unit  network  of  which  the  artificial  line  is  composed;
the  conditions  to  be  met  are — absence  of  phase  differences  when  all
branches  of  the  unit  network  A'^  of  Fig.   1   are  assumed  to  be  pure

resistances  and  continuity  of  phase  as  reactances  are  gradually  intro-
duced to  give  the  actual  network.

Formula  (5)  is  adapted  for  use  in  the  pass  bands,  since  the  ex-
pressions are  real  when  y^  is  real,  negative  and  not  less  than  —  4;
similarly,  formulas  (5a)  and  (5b)  are  adapted  for  use  in  the  stop  (±)
bands,  that  is,  when  7^  is  positive  and  less  than  —  4  respectively.

From  the  theory  of  impedances  we  know  that  any  resistanceless
one-point  impedance  is  expressible  in  the  form

where  the  factor  D  and  the  roots  px,  pi,  .  .  .  pin  are  arbitrary  positive,
reals  subject  only  to  the  condition  that  each  root  is  at  least  as  large
as  the  preceding  one.  This  enables  us  to  write  down  the  forms  which
the  quotient  and  product  of  two  resistanceless  one-point  impedances
may  assume,  which  are  as  follows:

If  in  formulas  1,  2,  5  and  6  we  substitute  for  Z1/Z2  =  y"^  and
Zi  Zi  =  k"^  the  right-hand  side  of  formulas  (8)  and  (9),  respectively,
we  obtain  formulas  for  the  propagation  constant  and  iterative  im-
pedance of  an  artificial  resistanceless  line  in  terms  of  frequencies  at
which  the  propagation  constant  becomes  zero  or  infinite.  Ordi-
narily, however,  we  are  more  interested  in  having  expressions  in
terms  of  the  frequencies  which  terminate  the  pass  bands.  To  secure
these  the  substitutions  should  be  4[8]/(4  -  [8]  )  and  [9]  (1  -  [8]/4)^S
where  [8]  and  [9]  stand  for  the  entire  right-hand  sides  of  formulas
(8)  and  (9).  This  substitution  amounts  to  obtaining  the  lattice  net-
work giving  the  required  pass  bands,  and  then  transforming  to  the

ladder  network  having  the  same  propagation  constant  and  the  same
iterative  impedance  at  mid-series  or  mid-shunt.

The  impedances  of  a  single  section  between  terminals  1  and  2,  with
the  far  end  of  the  section  3  and  4  either  short-circuited  or  open,  are
readily  seen  to  be

Since  vZoZ 00  and  'V  Zq/Zco  are  the  iterative  impedance  and  the
hyperbolic  tangent  of  the  propagation  constant  for  any  symmetrical
artificial  line,  we  have  the  following  analytically  equivalent  formulas
for  the  lattice  network  where  7  =  v  Z1/Z2,  and  k  =  V  Z1Z2  as  for
the  ladder  type.

In  these  formulas  Z1/Z2  =  7^  and  Zi  Z2  =  k"^  might  be  expressed
in  terms  of  the  resonant  and  anti-resonant  complex  frequencies  of
Zi  and  Z2,  the  frequencies  being  made  complex  quantities  so  as  to
include  the  damping.  Where  there  is  no  damping,  that  is,  where  all
network  impedances  are  devoid  of  resistance,  the  simplified  forms
of  these  expressions  are  given  by  formulas  (8)  and  (9).  The  use  of
these  formulas  for  designing  wave  filters  having  assigned  pass  bands
is  explained  at  page  23.

Note:  Much  has  been  written  on  the  subject  of  the  binaural  location
of  pure  tones  but  the  case  of  complex  sounds  has  received  little  attention
in  recent  literature.  The  purpose  of  the  present  paper  is  to  bring  the  dis-
cussion of  complex  sounds  abreast  of  that  relating  to  pure  tones.  Those
who  wish  to  acquaint  themseUcs  with  the  work  on  pure  tones  will  be  inter-
ested in  reading  the  theoretical  work  of  the  authors  and  the  experimental
studies  carried  out  by  G.  VV.  Stewart  and  students  working  under  his
direction.  This  work  has  been  reported  in  various  papers,  most  of  which
have  appeared  during  recent  years  in  the  Physical  Review  and  the  Physi-
kalische  Zeitschrift.

A  resume  of  the  present  paper  is  given  by  the  authors  in  their  concluding
paragraph. — Editor.

THE  need  of  determining  the  location  of  enemy  submarines  and
aeroplanes  during  the  war  brought  into  use  practical  methods
for  locating  a  sound  source  which  depend  upon  differences  between
the  sound  waves  reaching  the  two  ears.  This  stimulated  a  general
study  of  the  phenomena  involved  in  binaural  sound  location.  The
foundation  for  this  study  had  already  been  laid  in  the  work  of  Lord
Rayleigh  and  others,  who,  following  more  or  less  in  his  footsteps,
had  accumulated  a  considerable  amount  of  information  of  both
theoretical  and  experimental  sorts.  Of  this  information  almost  all
that  was  of  a  theoretical  nature  and  a  considerable  portion  of  the
experimental  kind  dealt  only  with  the  location  of  pure  tones,  the  more
complicated  and  in  some  respects  more  important  problem  of  complex
sounds  being  almost  entirely  neglected.  Such  advances  as  were
made  in  the  theoretical  aspects  of  the  problem  during  the  war  were
subject  to  the  same  restriction  so  that  even  to-day  no  comprehensive
theory  has  been  advanced  which  adequately  covers  the  problem  of
the  location  of  such  sounds  as  occur  in  every-day  life,  and  in  the
practical  applications  of  binaural  methods.  However,  the  results
obtained  with  pure  tones  can  be  made  to  throw  considerable  light
upon  the  problem,  and  it  is  primarily  from  this  standpoint  that  the
following  discussion  is  written.

It  may  be  well  at  the  outset  to  review  some  of  the  outstanding
differences  between  the  observed  phenomena  in  the  two  cases.  The
accuracy  of  location  is  much  less  for  pure  tones,  as  is  also  the  sense
of  definiteness  of  the  sound  image.  The  location  of  pure  tones  is  almost
wholly  binaural  as  is  evidenced  by  the  inability  of  persons  deaf  in  one
ear  to  locate  such  a  tone.  With  complex  sounds  not  only  is  the
location  by  binaural  effects  more  accurate  and  definite,  but  also  the
observer  is  not  dependent  on   these  alone.     Persons  who  are  deaf

in  one  ear  can  locate  familiar  complex  sounds  almost  as  well  as  those
with  normal  hearing.

Practically  all  theories  of  sound  location  start  from  the  assumption
that  the  listener  subconsciously  observes  certain  sound  characteris-
tics which  depend  upon  the  position  of  the  source  and  forms  a  judg-
ment of  where  the  source  must  be  by  comparing  these  characteristics
with  information  which  he  has  stored  up  as  a  result  of  his  past  ex-
perience with  cases  in  which  the  position  of  the  source  was  known.
In  order  to  fix  the  position  of  the  source  he  must  assign  to  it  three
coordinates  such  as  its  distance  and  some  two  angles  which  define
its  direction.  To  do  this  he  must  be  able  to  observe  at  least  three
independent  properties  of  the  sound  which  are  functions  of  the  posi-
tion of  the  source.  If  fewer  than  three  are  available  some  difficulty
in  location  is  certain  to  arise.  If  more  than  three  are  available  there
is  the  possibility  of  a  number  of  simultaneous  independent  determina-
tions of  the  three  coordinates.

If  the  sounds  of  every-day  life  were  never  distorted  in  transmission
all  of  these  determinations  would  yield  the  same  set  of  coordinates
and  the  only  advantage  which  the  listener  would  gain  from  the  addi-
tional information  available  would  lie  in  the  fact  that  some  one  set
might  be  peculiarly  sensitive  to  slight  differences  in  the  position
of  the  source,  and  therefore  might  lead  to  increased  certainty  on  the
part  of  the  observer.  Owing  to  reflection  from  the  walls  of  buildings
and  the  like,  the  sounds  of  every-day  life  seldom  arrive  undistorted,
so  that  the  observer  must  always  be  somewhat  uncertain  as  to  whether
or  not  the  coordinates  of  the  sound  source  are  actually  those  which
he  deduces  from  the  properties  of  the  sound  wave  as  it  reaches  his
ears.  If  enough  properties  are  available  to  permit  him  to  make
two  independent  determinations  he  may  use  one  of  them  to  check  the
other,  and  if  they  agree  he  is  justified  in  a  feeling  of  increased  cer-
tainty as  to  the  accuracy  of  his  judgment.  The  more  independent
determinations  he  can  make  the  more  checks  he  will  be  able  to  apply
and  consequently  the  more  confident  he  will  be.^

It  should  not  be  inferred,  however,  that  it  is  only  the  sounds  of
the  street  which  reach  the  observer  in  a  distorted  form.  In  a  great
many  laboratory  experiments  the  characteristics  of  the  sounds  have

^  It  is  interesting  to  note  in  this  connection  that  it  is  not  surprising  that  an  observer
locates  a  complex  tone  with  much  greater  certainty  than  a  pure  tone  when  we  con-
sider how  rapidly  the  number  of  independent  sets  of  data  increases  with  increase
in  complexity  of  sound.  We  have  already  said  that  three  indepsndent  pro  jerties
are  needed  for  the  determination  of  the  three  coordinates  of  the  source.  Hence
if  only  three  are  available,  only  one  determination  can  be  made  and  no  checks  are
possible.  On  the  other  hand,  if  four  are  available,  four  groups  of  three  each  can
be  formed  and  therefore  four  separate  determinations  can  be  made.  Similarly,
10  determinations  can  be  made  from  5  properties,  20  from  6,  and  120  from  10.

been  inconsistent,  and  in  some  cases  thc>'  have  not  e\en  corresponded
to  any  actual  source  whatever.  Under  these  circumstances,  if  an
image  is  formeci  at  all,  some  purely  ps\'chological  factors  must  enter
in.  For  pure  tones  it  has  been  found  possible  to  explain  much  of  the
experimental  data  obtained  under  circumstances  such  as  this  by
assuming  that  the  observer  subconsciously  judges  one  or  more  of  the
characteristics  to  be  in  error  and  applies  such  corrections  as  will
make  all  of  the  data  correspond  to  an  actual  source.  As  a  criterion
for  determining  which  characteristics  will  be  altered,  it  is  assumed
that,  in  general,  those  are  chosen  which  require  the  smallest  changes.

Let  us  now  consider  what  characteristics  are  available  for  locating
sounds  of  different  kinds.  A  pure  tone  from  a  source  at  rest  with
respect  to  the  observer  has  at  any  point  only  two  physical  character-
istics which  are  subject  to  change  with  the  position  of  the  source.
They  are  its  amplitude  and  phase.  Corresponding  to  each  position
of  the  source  there  is  a  particular  amplitude  and  phase  at  each  of  the
two  ears  so  that  a  total  of  four  properties — the  loudness  of  the  sound,
the  average  phase,  the  difference  in  amplitude  (which  mayconven-
iently  be  expressed  as  a  ratio)  and  the  difference  in  phase  at  the  two
ears— are  available  for  determining  the  position  of  the  source.  It  is
inconceivable  that  the  average  phase  can  have  anything  to  do  with
the  location  of  the  sound  since  it  may  be  changed  at  will  without
altering  the  position  of  the  source.  The  same  remark  applies  to  the
loudness  of  the  sound  except  in  those  instances  where  the  observer
is  familiar  with  the  source  to  such  an  extent  as  to  know  how  loud
it  may  be  expected  to  be.  Hence,  if  we  restrict  ourselves  to  the
cases  in  which  prejudicial  information  of  this  sort  does  not  exist,
we  find  that  the  observer  has  only  two  quantities  from  which  he  may
deduce  the  position  of  the  source.  We  should  therefore  expect  that
these  two  quantities  would  make  it  possible  to  locate  the  tone  with
respect  to  two  coordinates  only.  This  is  found  to  be  in  general
agreement  with  experiment,  for  most  observers  locate  all  sources  of
pure  tones  in  the  same  horizontal  plane  with  their  heads  and  determine
only  the  distance  and  angular  departure  from  the  median  plane.  If
the  source  is  more  than  a  few  yards  away  the  intensity  ratio  and  phase
difference  change  very  slowly  with  distance  so  that  in  this  case  even
the  sense  of  distance  is  not  keen  and  a  feeling  of  certainty  exists  with
respect  to  the  direction  only.

In  many  experiments  the  tones  at  the  two  ears  have  been  varied
arbitrarily  so  as  to  give  combinations  having  equal  phases  and  un-
equal intensities  or  vice  versa — combinations  which  cannot  arise
from  actual   physical   sources  in   the  absence  of  distortion.     Under

these  conditions  the  observer  generally  corrects  one  to  a  value  con-
sistent with  the  other  except  in  extreme  cases  where  the  correction
required  for  this  purpose  would  be  inordinately  large.  When  this
occurs  he  may  either  assume  both  to  be  correct  and  form  two  images —
one  based  on  the  phase  difference  together  with  a  mentally  supplied
intensity  ratio  consistent  with  it,  and  the  other  similarly  derived
from  the  observed  intensity  ratio — or  he  may  fail  to  have  a  sense
of  location  at  all.

Before  considering  the  available  characteristics  of  complex  sounds
in  general  let  us  confine  our  attention  for  a  time  to  those  which  are
made  up  of  a  limited  number  of  sustained  pure  tones  such  as  an  organ
note  with  its  series  of  overtones,  or  a  group  of  tuning  forks.  Here  the
number  of  characteristics  increases  rapidly  with  the  number  of  com-
ponent tones.  For  each  component  tone  there  are  two  quantities:
intensity  ratio  and  phase  difference.  In  addition,  at  either  ear  alone
the  relative  intensities  of  any  two  of  the  tones  changes  with  the
position  of  the  source,  owing  to  the  diffraction  of  the  sound  waves
around  the  head  being  different  for  different  frequencies.  There  are
therefore  as  many  of  these  observable  intensity  ratios  as  there  are
pairs  of  components.  Similarly,  for  any  two  tones  whose  frequencies
are  commensurable,  the  relative  phases  of  the  two  at  the  same  ear
depend  upon  the  position  of  the  source.

Not  all  of  these  characteristics  are  capable  of  contributing  to
binaural  as  distinct  from  monaural  location.  In  fact,  only  the  phase
differences  and  intensity  ratios  of  the  separate  components  are  bi-
naural. A  man  who  is  deaf  in  one  ear  has  available  all  of  the  rela-
tions between  the  intensities  and  phases  of  the  various  components
at  his  normal  ear.  That  these  relations  do  actually  contribute  to
sound  location  is  supported  by  experimental  evidence.  Myers  ^
found  that,  after  familiarizing  himself  with  a  complex  sound,  a  blind-
folded observer  could  locate  its  position  with  considerable  accuracy,
even  when  it  was  moved  about  in  the  median  plane,  but  that  his
accuracy  could  be  destroyed  by  varying  the  relative  intensities  of  the
components.'  It  is  not  surprising  then,  that  for  complex  sounds  the
accuracy  is  about  the  same  whether  the  location  is  binaural  or  mo-
naural.*    The  observed  failure  of  monaural  location  in  the  case  of  a

'  It  should  be  noticed  that  this  effect  must  have  been  purely  psychological  since  it
could  be  produced  without  moving  the  source  at  all.  It  therefore  lends  plausibility
to  the  assumption  upon  which  our  theory  is  based:  that  when  discordant  or  unusual
stimuli  are  experienced,  a  mental  readjustment  of  the  stimuli  is  made  in  order  to
render  them  more  nearly  consistent  with  every-day  experience.

*  As  shown  by  the  experiments  of  Angell  and  Fite  upon  persons  deaf  in  one  ear.
Psychol.  Rev.,  vol.  8,  pp.  225-246,  1911.

pure  tone  follows  directly  from  the  absence  of  other  frequencies  with
which  the  pure  tone  may  be  compared.

As  we  are  here  concerned  with  binaural  phenomena  we  shall  con-
fine our  attention  to  the  relative  phases  and  intensities  at  the  two  ears.
The  question  at  once  arises:  does  the  observer  actually  hear  the  differ-
ent tones  separately,  and  if  so,  does  he  assign  a  location  to  each
separately?

To  what  extent  the  listener  locates  each  component  separately
depends  upon  the  ease  with  which  the  tones  can  be  distinguished.
The  experiments  which  bear  most  directly  upon  this  point  are  those
in  which  the  component  tones  at  the  two  ears  are  arbitrarily  adjusted
to  give  values  of  phase  difference  corresponding  to  different  locations.
This  is  done  under  conditions  where  the  location  of  each  component
separately  is  largely  determined  by  the  phase  difference.  More  ^
experimented  with  two  tones,  transmitting  them  to  the  ears  through
tubes  of  adjustable  lengths.  This  permitted  him  to  change  the  phase
difference  at  the  two  ears  while  keeping  the  intensities  substantially
equal.  He  observed  the  apparent  location  for  various  settings  when
each  tone  was  applied  by  itself  and  when  both  were  applied  together,
using  forks  of  256  and  320  cycles.  With  the  paths  equal  the  tones
combined  into  a  chord  located  in  the  median  plane  and  the  separate
components  could  not  be  heard.  With  a  setting  for  which  the  two
components  separately  appeared  on  opposite  sides  of  the  head,  one
component  was  heard  distinctly  by  the  right  ear  only  on  the  right
side,  and  the  other  by  the  left  ear  only  on  the  left  side.  At  the  same
time  the  chord  was  heard  rather  indistinctly  near  the  median  plane
but  tending  slightly  toward  the  side  of  the  lower  tone.

Apparently  the  observer  does  not  consciously  separate  the  chord
into  its  components  unless  he  is  forced  to  do  so  by  some  inordinate
discrepancy  between  the  positions  of  the  images  formed  from  them.
There  is  no  evidence  in  the  case  of  equal  paths  to  show  that  he  did
or  did  not  subsconsciously  locate  the  separate  components  and  find
them  to  be  in  agreement.  In  view  of  the  second  experiment  it  seems
probable  that  he  did.  In  this  latter  experiment  he  obviously  found
that  the  two  components  corresponded  to  different  locations  and
assigned  different  sources  to  each.  At  the  same  time  his  experience
told  him  that  tones  which  would  combine  to  form  a  musical  sound
generally  have  a  common  source.  Hence  he  may  have  concluded
subconsciously  that  the  sound  waves  had  probably  been  distorted
in  coming  from  a  common  source  and  so  he  corrected  his  observations
*  Louis  T.  More:  Phil.  Mag.  XVIII,  1909,  p.  308.

on  both  tones  to  make  them  consistent  and  arrived  at  an  image  of
the  chord  between  the  other  two.

Similar  results  were  obtained  with  forks  of  256  and  384  cycles
per  second,  except  that  in  general  the  lower  tone  was  completely
blotted  out.  The  higher  tone  was  usually  quite  distinct  and  defin-
itely located.  The  image  of  the  chord  was  nearer  to  the  image  formed
when  the  higher  component  was  sounded  by  itself  than  to  the  image
formed  from  the  lower  one  alone.  With  settings  for  which  the  direc-
tions of  the  tones  separately  were  the  same,  whether  right,  left,  or
middle,  the  upper  tone  disappeared  leaving  only  the  chord.  In
experiments  with  forks  of  256  and  512  cycles  it  was  difificult  to  dis-  f
tinguish  the  separate  notes.  With  settings  for  which  the  two  separ-
ately were  on  opposite  sides  the  combination  was  on  the  side  of  the
lower  fork.  This  can  be  interpreted  as  meaning  that  the  octave
relationship  is  inherently  difficult  to  resolve,  or  else  that  tones  an
octave  apart  so  generally  come  from  a  common  source  that  the  ob-
server was  unwilling  to  make  any  other  assumption.

Although  the  explanation  of  these  results  is  not  yet  thoroughly
understood,  they  show  very  definitely  that  in  locating  complex  sounds
made  up  of  pure  tones  the  observer  does  within  limits  locate  the
components  separately.  If  they  agree,  a  single  image  is  formed;  if
they  do  not,  he  may  either  locate  the  tones  separately  or  form  a  single
compromise  image  or  do  both.

It  is  in  this  way  that  the  theory  developed  for  pure  tones  is  ap-  |
plied  to  complex  sounds  made  up  of  pure  tones.  The  next  step  is  to
extend  it  so  as  to  include  complex  sounds  in  general.  To  do  this  we
must  picture  the  observer  as  resolving  each  sound  into  sinusoidal
components  locating  the  components  separately  and  forming  one  or
more  images  based  on  a  combination  of  the  apparent  sources  as  in-
dicated by  the  separate  components.  While  it  is  fairly  easy  to  effect
such  a  resolution  mathematically  it  is  somewhat  less  easy  to  interpret
the  result  in  a  manner  satisfactory  to  our  intuitive  conceptions  of  the
phenomena  involved;  also,  granted  the  theoretical  possibility  of  the
resolution,  there  remains  the  question  of  what  physical  or  psycho-
logical limitations  there  may  be  to  its  application.

In  view  of  the  fact  that  a  really  pure  component  tone  has  no  begin-
ning or  end,  and  no  fluctuations  in  its  amplitude,  it  is  not  at  once
apparent  how  a  single  discrete  sound  such  as  the  bark  of  a  dog  can  be
resolved  into  components  of  that  nature.  However,  if  enough  com-
ponents are  available  it  has  been  established  beyond  question  that
by  properly  choosing   their   frequencies,   amplitudes,   and   phases,   a

combination  may  be  anixcd  at  in  which  the  algebraic  sum  of  all  the
components  is  zero  for  all  instants  before  and  after  the  period  occupied
by  the  sound  and  equal  to  the  instantaneous  value  of  the  sound
wave  for  instants  within  that  period.  This  combination  is  known  to
mathematicians  as  the  Fourier  Integral  corresponding  to  the  wave,
and  the  formula  for  the  phase  and  amplitude  of  each  component
sinusoid  is  known.  It  is  an  extension  of  the  well  known  Fourier
series  expansion  used  for  resolving  sustained  periodic  disturbances.

The  physical  interpretation  of  this  integral  may  be  facilitated  by
reviewing  the  steps  in  its  evolution  from  the  Fourier  series.  It  is
well  known  that  if  the  sound  in  question  were  repeated  at  regular
intervals  the  resulting  periodic  wave  could  be  resolved  by  Fourier
analysis  into  a  series  of  sinusoidal  components,  the  frequencies  of  all
of  which  are  integral  multiples  of  the  frequency  of  repetition  of  the
sound.  Successive  components  therefore  differ  in  frequency  by  an
amount  equal  to  this  frequency  of  repetition.  Now  it  is  not  essential
that  the  repetitions  of  the  sound  follow  each  other  immediately.
Instead,  they  may  be  separated  by  intervals  of  silence.  The  effect
of  such  silent  intervals  is  to  reduce  the  frequency  of  repetition  and
therefore  also  the  fundamental  frequency.  As  a  result  the  com-
ponent frequencies  are  brought  closer  together  and  the  number  within
any  particular  frequency  range  is  increased.

Suppose  now  that  the  interval  between  repetitions  is  indefinitely
increased.  As  this  is  done  the  efTect  of  any  one  occurrence  of  the
sound  becomes  more  and  more  independent  of  the  others,  and  in  the
limit  when  the  sounds  next  preceding  and  next  following  the  one
under  consideration  are  infinitely  far  removed,  we  have  the  case  of  a
discrete  sound.  As  this  limiting  case  is  approached  the  fundamental
frequency  becomes  smaller  and  smaller  and  the  component  frequen-
cies, which  are  multiples  of  it,  are  separated  by  infinitesimal  frequency
differences.  While  the  amplitude  of  each  component  also  decreases,
the  number  of  components  increases  at  such  a  rate  that  the  aggregate
energy  of  all  the  components  within  a  given  frequency  range  remains
finite.  In  this  way,  the  distribution  of  the  sound  energy  over  various
frequencies — that  is,  the  "energy  spectrum" — can  be  obtained.

It  is  evident,  then,  that  when  an  aperiodic  complex  sound  is  resolved
mathematically  there  results  an  infinity  of  component  tones,  each
having  a  characteristic  intensity  and  phase.  If  an  observer  were
capable  of  an  equally  complete  resolution  he  would  have  at  his  dis-
posal an  infinity  of  sets  of  data  from  which  an  infinity  of  images
could  be  formed.  In  the  absence  of  distortion  these  should  all  co-
incide.

Practically,  of  course,  no  such  refinement  of  resolution  is  possible.
The  ability  to  distinguish  differences  in  pitch  varies  from  person  to
person,  but  the  minimum  intervals  employed  in  musical  composition
probably  give  a  rough  measure  of  the  normal  resolving  power  of  the
ear.  Even  with  this  limitation  the  broad  sound  spectrum,  such  as  an
irregular  sound  produces,  is  capable  of  yielding  a  very  large  number  of
separable  components;  and  hence  a  large  number  of  individual  im-
ages. It  is  this  fact — that  with  a  very  complex  sound  the  number  of
independent  determinations  of  the  image  is  limited  only  by  the  re-
solving power  of  the  observer — which  makes  his  accuracy  of  binaural
location  as  well  as  his  sense  of  certainty  much  greater  for  such  sounds
than  for  pure  tones.

So  long  as  the  images  of  all  the  components  coincide,  it  is  of  little
importance  how  fine  the  resolution  is,  for  further  refinement  only
serves  to  increase  the  sense  of  certainty  by  adding  to  the  volume  of
accordant  evidence.  However,  when  the  images  are  not  in  agree-
ment the  problem  is  more  complicated  and  the  degree  of  resolution
becomes  important.  Here  also  purely  physical  considerations  cease
to  be  adequate  and  psychological  factors  must  be  considered  similar
to  those  involved  in  the  location  of  a  pure  tone  for  which  the  intensity
ratio  and  phase  difference  do  not  correspond  to  any  actual  source.
When  an  observer  is  faced  with  discordant  results  he  must  make
some  subconscious  judgment.  For  small  discrepancies  such  as  occur
in  every-day  experience,  he  probably  assumes  those  images  which
depart  most  from  the  rest  to  be  misplaced  because  of  distortion  dur-
ing transmission  and  so  either  corrects  or  ignores  them.  If  the
discrepancies  are  large  he  may  find  it  difficult  on  the  ground  of  ex-
perience to  believe  that  so  much  distortion  could  occur.  In  such  an
event  he  will  most  likely  form  several  images  from  different  com-
ponents or  in  extreme  cases  lose  the  sense  of  location  altogether.

Bowlker  found  separate  images  to  occur  experimentally  both  for
band  music,  which  approaches  a  collection  of  tones  and  for  the
irregular  barking  of  dogs.  He  placed  tubes  of  unequal  length  to  his
two  ears  thereby  upsetting  the  normal  diffraction  around  the  head
and  interposing  a  longer  path  on  one  side  than  on  the  other.  Obvi-
ously, the  distortion  produced  in  this  manner  is  of  a  type  not  likely
to  be  met  in  every-day  life  and  affects  different  frequencies  in  widely
different  fashions.  He  reports  that  when  listening  to  "a  band  of
three  or  four  instruments  played  in  the  open — the  notes  will  be  found
to  be  scattered  over  a  wide  range,  most  being  to  the  side  of  the  short
tube,  some  being  in  front  and  some  being  to  the  side  of  the  long  tube.
In  listening  with  such  a  pair  of  tubes  to  two  dogs  furiously  barking

the  effect  is  at  first  quite  alarming — one  seems  to  be  in  the  middle
of  a  pack  of  dogs  some  of  which  are  rushing  viciously  at  one's  throat."
An  illustration  of  failure  to  form  any  image  is  found  in  a  phenomenon
observed  in  the  use  of  binaural  compensators  for  determining  the
direction  of  submarine  sounds.  The  sound  is  picked  up  by  two  sub-
marine telephone  transmitters  and  led  to  the  ears  through  inde-
pendent paths.  By  adjusting  the  lengths  of  the  paths  the  image
can  be  shifted  from  side  to  side  and  for  practical  purposes  the  setting
of  the  instrument  is  made  by  bringing  the  image  exactly  to  the  middle.
A  fairly  definite  sound  image  is  formed,  but  observers  report  that  part
of  the  sound  does  not  merge  into  this  sound  image  and  move  in  re-
sponse to  the  adjustment,  but  instead  appears  as  a  diffuse  back-
ground of  noise.®  This  may  be  explained  on  the  assumption  that,
while  the  images  formed  from  most  of  the  sound  components  agree
sufificiently  well  that  the  observer  corrects  them  to  a  single  position,
certain  components  are  so  distorted  by  resonance  effects  inherent
in  the  apparatus  that  their  images  are  scattered  more  or  less  at  ran-
dom. The  lack  of  agreement  among  any  considerable  number  of
these  prevents  the  formation  of  a  second  image  and  causes  the  sense  of
diffusedness.

As  the  distortion  becomes  still  more  extreme  we  should  expect
the  experimental  results  to  depend  more  and  more  upon  the  observ-
er's power  of  resolution,  for  as  the  distortion  is  progressively  in-
creased a  condition  must  finally  be  reached  where  the  positions  of  the
images  are  appreciably  different  for  two  components  whose  frequencies
are  so  nearly  alike  as  to  make  their  recognition  as  separate  tones
dillficult  if  not  impossible.  This  condition  actually  occurred  in  an
experiment  of  Baley's  with  a  sound  consisting  of  a  mixture  of  sus-
tained tones.  Its  effect  on  the  listener  is  interesting  from  the  stand-
point of  subconscious  readjustment  of  discordant  data.

Baley's  ^  experiment  consisted  in  applying  a  number  of  sustained
tones  to  one  ear  of  a  musically  trained  observer  and  a  number  of  differ-
ent tones  to  the  other  ear,  and  testing  his  ability  to  assign  them  to
their  proper  sides.  So  long  as  the  intervals  between  the  tones  were
fairly  large,  the  observer  never  failed  to  locate  them  correctly.  Con-
sidering the  entire  stimulus  as  a  complex  sound  we  may  think  of  the
observer  as  locating  the  tones  individually  and  finding  them  to  fall
definitely  into  two  groups  whose  images  are  located  one  at  each  ear.

*  This  interesting  phenomenon  was  called  to  our  attention  by  Mr.  Richard  D.
Fay  of  the  Submarine  Signalling  Corporation  who  tells  us  that  it  has  been  noted
by  a  large  number  of  observers.

However,  when  he  used  six  tones  which  were  separated  from  each
other  by  a  single  tone  interval,  the  separate  components  could  not
be  distinguished  and  a  painful  sensation  was  produced.  The  ob-
server was  apparently  faced  with  the  situation  that  to  make  the  ob-
served intensity  ratios  and  phase  differences  correspond  to  a  single
source  would  involve  extremely  large  corrections  in  the  observed
data.  On  the  other  hand,  his  power  of  tone  resolution  was  insufficient
to  separate  the  components  and  assign  them  to  different  sources.  It
is  not  surprising,  then,  that  the  difficulty  manifested  itself  by  painful
sensations.  While  this  illustration  is  taken  from  an  extreme  condi-
tion of  laboratory  experiment  and  may  appear  to  have  little  bearing
on  the  every-day  location  of  sounds,  it  is  really  significant  because  of
the  manner  in  which  it  illustrates  the  importance  of  psychological
factors  in  all  cases  in  which  the  sound  waves  are  distorted.

In  the  foregoing  discussion  an  attempt  has  been  made  to  bring  out
the  main  features  involved  in  extending  the  theory  of  the  binaural
location  of  pure  tones  to  cover,  qualitatively  at  least,  the  location
of  complex  sounds.  It  has  virtually  been  assumed  that  the  latter
involves  three  processes:  first,  the  resolution  of  the  sound  into  its
component  tones;  second,  the  independent  (generally  subsconscious)
location  of  each  separate  component;  and  third,  the  formation  of  a
conscious  judgment  of  the  position  of  the  source  based  on  the  locations
of  the  individual  images.  The  greatly  increased  amount  of  data
available  when  the  sound  is  complex  has  quite  different  effects  on  the
final  result  according  as  the  different  images  do  or  do  not  coincide.
If  they  do,  the  accuracy  of  location  and  the  sense  of  certainty  are
increased.  If  they  do  not,  confusion  arises,  subconscious  corrections
are  called  for,  and  the  final  result  is  likely  to  depend  very  consider-
ably on  the  psychological  processes  and  individual  prejudices  of  the
particular  observer.

Synopsis:  The  art  of  electrical  communication  owes  a  great  and  incrcas-
inj;!y  recognized  debt  to  Oliver  Heaviside  for  his  work  in  developing  and
emphasizing  a  correct  theory  of  electrical  transmission  along  wires  and  in
particular  for  his  insistance  on  the  importance  of  inrluctance.  His  oper-
ational methods  of  solving  the  differential  etjuations  which  are  fundamental
of  the  theory  of  electric  circuits,  although  not  widely  known,  are  important.
These  methods  are  peculiarly  applicable  to  many  important  problems  of
electrical  transmission.  The  present  paper,  while  theoretical  in  char-
acter, therefore  deals  with  a  subject  of  practical  importance  to  the  com-
munication engineer.

dt
braic  equations  by  replacing  the  differential  operator  by  the  symbol  p  and
by  this  expedient  a  purely  symbolic  solution  is  obtained.     This  syrnbolic
solution  is  called  the  operational  formula  of  the  problem.

In  order  to  interpret  the  purely  symbolic  operational  formula,  Heaviside
proceeded  as  fellows:  By  direct  comparison  of  the  operational  fornmla  of
specific  problems  with  their  known  explicit  solutions  he  was  led  to  assign
a  definite  significance  to  the  operator  p.  Thereupon,  he  obtained  by  in-
duction generalized  specific  criteria  or  rules  for  solving  the  operational
formula.

The  present  paper,  by  attacking  the  problem  from  a  different  standpoint,
shows  that  the  Heaviside  operational  formula  is  a  shorthand  equivalent  of
an  integral  equation  from  which  the  methods  and  rules  of  his  operational
calculus  are  deducible. — Editor.

AVERY  interesting  and  by  no  means  the  least  valuable  part  of
Heaviside's  researches  relates  to  operational  methods  of  solving
the  differential  equations  of  a  class  of  physical  problems  of  which
electric  circuit  theory  problems  are  typical;  in  fact  Volume  II  of  his
Electromagnetic  Theory  is  almost  entirely  devoted  to  this  subject.
The  methods  of  solution  which  he  originated  and  employed  are  of
extraordinary  directness  and  simplicity  in  a  very  large  class  of  prob-
lems in  applied  mathematics.  In  fact  it  would  be  difhcult  to  exagger-
ate the  value  of  his  work  along  this  line,  and  nowhere  is  it  more  im-
mediately and  usefully  applicable  than  in  the  theoretical  problems
of  electro-technics.

Heaviside  is,  however,  by  no  means  easy  reading  and,  in  spite  of
the  considerable  number  of  published  studies  relating  to  his  opera-
tional calculus,  it  is  less  generally  understood  and  applied  than  its
value  warrants.  The  writer  has  had  occasion  to  apply  Heaviside's
methods  quite  extensively  in  electrical  problems  and  in  the  course
of  his  study  was  led  to  a  general  formula  which  to  him  at  least,  has
proved  useful  in  interpreting  and  rationalizing  the  operational  cal-

cuius.  This  formula  is  presented  and  discussed  in  the  present  paper
with  the  hope  that  it  may  be  of  service  to  students  of  Heaviside  in
understanding  and  applying  his  methods.  The  paper  may  also  serve
as  a  brief  recapitulation  of  some  of  the  outstanding  methods  ap-
plicable to  the  solution  of  problems  in  electric  circuit  theory.

The  type  of  problem  to  which  the  operational  calculus  is  applicable
and  Heaviside's  method  of  solution  may  be  illustrated  in  a  sufficiently
general  manner  for  didactic  purposes  in  connection  with  the  solution
of  the  system  of  equations

We  are  concerned  with  the  determination  of  the  variables  Xi  .  .  x„
as  functions  of  the  independent  variable  t  for  the  following  boundary
conditions;  the  known  functions  F]  .  .  F„  and  the  variables  Xi  .  .  :v:„
are  identically  zero  for  values  of  the  independent  variable  t^O.  In  other
words,  the  system  is  initially  in  a  state  of  equilibrium  when  the
"  forces  "  Fi  .  .  .  F„  are  applied.  These  boundary  conditions  are
extremely  important  in  physical  problems.

Owing  to  the  linear  character  of  the  equations  we  may  without  loss
of  generality  set  all  the  F  functions  equal  to  zero  except  one,  say
Fi{t),  and  write

The  function  on  the  right  hand  side,  written,  in  accordance  with
the  Heaviside  notation,  as  unity  is  identically  zero  for  /<0  and
unity  for  />0  and  hi  .  .  .  h„  are  identically  zero  for  /<0.

H^quations  (4)  formulate  the  problem  actually  dealt  with  by  Heavi-
side who  did  not  explicitly  consider  the  more  general  equations  (3).
His  method  of  attack  was  as  follows;  Writing  p"  for  the  differential
operator  d"/dt"  equations  (4)  become  formally  algebraic  and  yield  a
purely  symbloic  solution

Equation  (6)  is  the  Heaviside  operational  formula;  as  it  stands,
however,  it  is  purely  symbolic  and  the  problem  remains  to  find  the
significance  of  the  equation  and  to  deduce  therefrom  the  value  of
h  =  h(t)  as  a.  function  of  /.

Heaviside's  method  from  this  point  on  was  one  of  pure  induction.
From  the  known  solution  of  specific  problems  he  inferred  general
rules  for  expanding  and  interpreting  the  operational  formula:  the
body  of  rules  thus  developed  for  solving  the  operational  equation
may  be  appropriately  termed  the  Heaviside  Operational  Calculus.

The  contribution  of  the  present  paper  to  the  theory  of  the  Heavi-
side operational  calculus  depends  on  the  following  proposition  and
its  immediate  corollary.^

The  integral  equation  is  an  identity  for  all  positive  real  values  of  p  and
consequently  determines  hj(t)  uniquely.

'  This  formula  has  been  established  in  previous  papers.     It  is  briefly  discussed
in  .Appendix  I.

It  follows  as  an  immediate  corollary  that  the  Heaviside  operational
equation

The  significance  of  the  operational  equation  and  the  rules  of  the  Heaviside
operational  calculus  are  therejore  deducible  from  the  latter  equation.
The  whole  problem  is  thus  reduced  to  the  purely  mathematical  problem
of  solving  the  integral  equation.

It  should  be  remarked  in  passing  that,  while  the  Heaviside  opera-
tional calculus  has  been  elucidated  in  connection  with  the  solution
of  a  set  of  differential  equations  involving  a  finite  number  of  variables,
it  is  not  so  limited  in  its  applications.  It  is  applicable  also  when  the
number  of  variables  is  infinite  and  to  such  partial  differential  equ-
tions  as  the  telegraph  equation.  The  foregoing  theorem  applies  also
to  all  such  physical  problems  where  an  operational  formula  A  =  \/H{p)
is  derivable.

Before  discussing  the  solution  of  the  integral  equation  (9)  and  de-
ducing therefrom  some  of  the  rules  of  the  operational  calculus,  a
simple  but  interesting  and  instructive  example  of  the  way  the  oper-
tional  formula  is  set  up  will  be  given.

Consider  a  transmission  line  of  infinite  length  along  the  positive
X  axis  and  let  it  have  a  distributed  inductance  L  and  capacity  C  per
unit  length.  Let  a  unit  voltage  be  applied  to  the  line  at  the  origin
re  =  0  at  time  /  =  0;  required  the  line  current  /  and  voltage  V  at
any  point  x  at  any  subsequent  time  /.

Now  by  the  conditions  of  the  problem  Vq  is  zero  before,  unity  after
time  /■  =  0;  hence  the  foregoing  equations  are  operational  formulas
and  by  (9)

which  are,  of  course,  the  well  known  solutions  of  the  problem.  The
directness  and  simplicity  of  the  solution  from  the  definite  integrals  is,
however,  noteworthy.

By  virtue  of  the  foregoing  analysis  the  Heaviside  operational  cal-
culus becomes  identical  with  the  methods  and  rules  for  the  solution
of  integral  equations  of  the  type

An  integral  equation  is,  of  course,  one  in  which  the  unknown  func-
tion appears  under  the  sign  of  integration;  the  process  of  determining
the  unknown  function  is  the  solution  of  the  equation.  Integral
equations  of  the  form  of  (9)  were  first  employed  by  Laplace  and  may
be  referred  to  as  equations  of  the  Laplace  type.  More  recently  they
have  become  of  importance  in  the  modern  theories  of  divergent  series
and  summability.  The  solution  of  a  large  number  of  integral  equa-
tions of  the  Laplace  type  has  been  worked  out;  however  the  procedure
is  usually  peculiar  to  the  particular  problem  in  hand.  In  this  con-
nection it  is  noteworthy  that,  from  a  purely  mathematical  stand-
point, Heaviside's  operational  calculus  is  a  valuable  contribution  to
the  systematic  solution  of  this  type  of  integral  equations.  That  is  to
say,  methods  which  he  developed  for  the  solution  of  his  operational
equation  suggest  systematic  procedure  in  the  solution  of  the  integral
equation  (9),  as  might  be  expected  from  the  relationship  pointed  out
in  the  present  paper.

As  stated  above  a  large  number  of  infinite  integrals  of  the  type
appearing  in  equation  (9)  have  been  worked  out.  Consequently  the
solution  of  (9)  can  frequently  be  written  down  by  inspection.  When
this  is  not  the  case,  however,  the  appropriate  procedure  is  usually
to  expand  the  function  \/pH{p)  in  such  a  form  that  the  individual
terms  are  recognizable  as  identical  with  infinite  integrals  of  the  re-
quired type.

An  interesting  expansion  of  this  kind  and  one  which  is  applicable
to  a  large  number  of  physical  problems  is  as  follows:

This  expansion  is  purely  formal  and  the  series  is  divergent.  It  is
summable,  however,  in  the  sense  that  it  may  be  identified  with  its
generating  function  l/pH(p).  It  is  also  summable  in  accordance
with  Borel's  definition  of  the  sum  of  a  divergent  series  by  the  Borel
integral  *

J     dt  e-^^^y\  ant^/n\
This  suggests  that  these  two  series  are  equal  and  consequently  that

provided  this  series,  which  is  called  by  Borel  the  associated  function  of
the  divergent  expansion,  is  itself  convergent.  This  is  the  case  in  all
physical  problems  to  which  this  form  of  expansion  has  been  applied.^

The  foregoing  will  be  recognized  as  identical  with  Heaviside's
power  series  solution,  obtained  by  the  empirical  rule  of  identifying
\/p^  with  t"/n\  in  the  asymptotic  expansion  of  l/H{p).

Another  form  of  solution  of  very  considerable  practical  value
depends  on  a  partial  fraction  expression  which  can  be  carried  out  in  a
large  number  of  physical  problems.     It  is

which    will    be   recognized    as    the   celebrated    Heaviside    Expansion
Solution.

As  illustrating  the  flexibility  of  the  integral  identity  (9),  another
form  of  solution  will  be  given  which  is  often  of  value  in  practical
problems  where  an  explicit  solution  cannot  be  obtained.  Suppose
that   l/pH(p)   can   be  written  as

'The  terms  a  +  c/p^  in  this  expansion  were  suggested   by  Dr.  O.  J.  Zobel  and
must  be  included  in  a  number  of  important  problems  in  electric  circuit  theory.

As  a  final  example  of  the  foregoing  discussion  we  shall  consider  a
specific  problem  of  some  practical  interest  in  itself  and  which  involves
Heaviside's  so-called  "  fractional  differentiation  "  and  his  resulting
asymptotic  solutions.  The  physical  problem  is  as  follows:  a  "  unit-
voltage  "  (zero  before,  unity  after  time  /  =  0)  is  applied  through  a
terminal  condenser  Co  to  an  infinitely  long  cable  of  resistance  i?  and
capacity  C  per  unit  length.  Required  the  Voltage  V  at  the  cable
terminals.

Taking  the   last   form   of   l/pH{p),   expanding    asymptotically    and
recognizing  that

up.  VP  -fe-'-  (2„  -  1)  [zf-  3) .  .  .  1  7=i
the  resulting  series  solution  can  be  recognized  and  summed  as

•This  formula  is  quite  useful;  it  is  applied  in  the  solution  of  the  last  example  of
thie  present  paper.

the  series  is  truly  asymptotic  in  the  sense  that  the  error  is  less  than
the  last  term  included.

Another  mode  of  procedure,  however,  suggests  itself,  which,  by
the  aid  of  equation  (10)  gives  the  solution  directly  without  series
expansion.     We  have

The  solution  h{t)  =  hi{i)  +  hiit)  agrees  with  the  preceding  derived
from  the  asymptotic  expansion,  and  is  considerably  more  direct  and
simple.

It  is  interesting  to  compare  this  solution  with  Heaviside's  own
operational  solution  (Electromagnetic  Theory  Vol.  II,  p.  40)  w^hich
amounts  to  the  following.     The  operational  formula  is  written

which  agrees  with   the  foregoing  and   is  the  actual   asymptotic  ex-
pansion.^

The  foregoing  discussion  is  sufficient,  it  is  hoped,  to  show  the  place
of  the  integral  formula  (9)  in  relation  to  the  Heaviside  operational
calculus.  It  is  believed  to  be  particularly  applicable  in  connection
with  a  number  of  questions  relating  to  divergent  series  and  solutions
which  Heaviside's  work  has  raised  and  which  have  received  too  little
attention  from  mathematicians.

This  equation  may  be  regarded  as  well  established  and  can  in  fact
be  deduced  in  a  quite  general  manner  by  synthetic  arguments.  It  is
derived  and  employed  in  papers  by  the  writer  (Trans.  A.  I.  E.  E.,
1911,  pp.  345-427,  and  Phys.  Rev.  Feb.  1921,  pp.  116-134)  and  is
deducible  at  once  from  the  work  of  Fry  (Phys.  Rev.  Aug.  1919,  pp.
115-136).

On  the  basis  of  equation  (5)  the  deduction  of  formula  (9),  in  which,
however,  no  pretense  to  rigor  is  made,  proceeds  as  follows;

If  the  function  F{t)  in  equations  (3)  is  set  equal  to  e^',  the  complete
solution  (5)  includes  the  particular  solution  ^

which  irfvolves  /  only  through  the  exponential  term.     The  complete
solution  must,  therefore,  admit  of  reduction  to  the  form

'  The  procedure  by  which  Heaviside  arrived  at  the  foregoing  asymptotic  solution
is  not,  however,  always  so  fortunate  For  example  if  a  terminal  inductance  is  sub-
stituted for  the  terminal  condenser  of  the  preceding  problem,  precisely  the  same
procedure  gives  an  incomplete  result.  Heaviside  recognized  this  and  added  an
extra  term  without  explanation  (Elm.  Th.  Vol.  H,  p.  42)  but  his  solution  appears
to  be  doubtful  in  the  light  of  some  recent  work  by  the  writer  in  applying  the  formula
of  the  present  paper  to  the  same  problem.

*  Provided  H  {p)  '^  o.  This  restriction  is  of  no  consequence  in  physical  prob-
lems, where  the  roots  of  H  (p)  are  in  general  complex  with  real  part  negative.

Now  the  first  term  of  the  expression  involves  /  only  through  the  ex-
ponential term  while  the  second  term  involves  t  through  the  lower
limit  of  the  integral  which  ultimately  vanishes  and  therefore  includes
no  term  involving  /  only  through  the  exponential.  Consequently
the  first  term  of  {b)  is  identifiable  as  the  particular  solution  of  (a)  and
by  direct  equation  it  follows  that

The  most  important  restriction  which  is  implicit  in  the  foregoing
is  that  in  splitting  up  the  definite  integral  of  (5)  we  have  tacitly  as-
sumed that  hit)  is  finite  for  all  values  of  /;  a  restriction  which  is
necessary  in  order  that  the  infinite  integral  shall  be  convergent  for
all  positive  real  values  of  p.  This  condition  is  satisfied  in  all  physical
problems  and  therefore  introduces  no  practical  limitation  of  im-
portance.

However,  even  w^hen  this  restriction  does  not  hold  formula  (9)  may
be  valid  and  uniquely  determine  h{t)  if  p  is  restricted  to  values  which
make  the  infinite  integral  convergent,  or  when  the  problem  is  such
that  e~^'h{t)   is  an  exact  derivative.     As  an  example,  suppose   that

where  a  is  a  real  positive  quantity.     It  may  be  otherwise  shown  that
k{t)  =  e°'  and  formula  (9)  becomes

The  discussion  in  the  text  does  not  pretend  to  be  a  proof  of  the
power  series  expansion  in  any  strict  sense.  A  more  satisfactory
<iiscussion  proceeds  as  follows:

We  shall  here  introduce  a  necessary  restriction  on  the  function  1/H{p).
It  must  include  no  function  which  is  represented  asymptotically  by
a  series  all  of  whose  terms  are  zero;  that  is  a  function  <p{p)  such  that
the  limit,  as  p  approaches  oo,  of  p"(l>ip)  is  zero  for  every  value  of  n.
The  function  e~^  is  such  a  function.  (See  Whittaker  &  Watson,
p.  154.)

With  this  restriction  understood,  start  with  the   integral   (9)  and
integrate  by  parts;  we  get

Now  let  p  again  approach  infinity;  in  the  limit  the  integral  vanishes,
and  the  right  hand  side,  by  virtue  of  the  asymptotic  expansion,
approaches  the  limit  Ui,  whence  h''^^  (o)  =  ai.  Proceeding  in  this
manner,  repeated  integrations  by  parts  establish  the  relation
h^"^  (o)  —  a„.     But  provided  the  series  is  absolutely  convergent,  then

The  power  series  solution  is  applicable  to  a  large  class  of  physical
problems  and  has  been  rigorously  established  under  certain  restric-
tions by  other  methods  than  that  employed  above  (see  papers  by
Bromwich,  Phil.  Mag,  May  1920,  p.  407;  Fry,  Phys.  Rev.  Aug.
1919,  p.  115;  and  the  writer,  Trans.  A.  I.  E.  E.  1919,  p.  345).

On   the  basis  of   tlie   preceding  and   with   the  aid   of  fornuihi   (10),
expansions  of  the  type

!//)//(/))  ~ -i-    ^bn/P"  +  '  =  f^     e~''h{l)dt
which  occur  in  physical  problems,  can  be  dealt  with.     For  since

The  Physical  Characteristics  of  Audition  and
Dynamical  Analysis  of  the  External  Ear

Synopsis:  This  paper  discusses  some  of  the  characteristics  of  the
ear  which  have  become  important  in  the  design  and  development  of  tele-
phone apparatus  and  circuits.  The  field  of  audition,  bounded  by  the
curves  of  minimum  and  maximum  loudness  as  functions  of  frequency,
has  been  determined  for  a  large  number  of  ears,  and  the  smaller  included
area  most  used  in  speech  has  been  mapped.  The  nature  of  these  fields  in
certain  cases  of  abnormal  hearing  has  also  been  determined  and  the  condi-
tions which  must  be  observed  in  designing  apparatus  to  satisfactorily
relieve  deafness  are  discussed.

The  sensitivity  of  the  ear  is  given  in  terms  of  the  r.  m.  s.  pressure
measured  by  a  calibrated  condenser  transmitter.  It  is  printed  out  in  the
appendix  that  this  pressure  is  not  necessarily  equal  to  that  which,  when
applied  to  the  ear  drum,  would  just  give  rise  to  the  sensation  of  sound.
However,  it  is  the  nearest  approach  to  the  value  of  this  pressure  which  can
be  determined  at  present,  and  as  the  dynamical  properties  of  the  ear
become  more  fully  known  it  is  pointed  out  how  the  relation  between  the
two  pressures  can  be  more  accurately  stated. — Editor.

1.  Introduction.  It  has  become  important  in  the  design  and
development  of  telephone  apparatus  and  circuits  to  know  quantita-
tively the  various  functional  characteristics  of  the  ear  since  the  ear  is
an  important  dynamical  unit  in  the  long  series  of  vibration  transmitting
apparatus  constituting  a  telephone  system.  A  complete  analysis  of
this  problem  involves  not  only  the  properties  of  the  physical  circuit,
but  also  the  characteristics  of  the  ear  and  voice  and  of  the  air  passages
between  the  mouth  and  transmitter  and  between  the  ear  and  receiver.
It  is  the  purpose  of  the  present  paper  to  discuss  some  of  the  character-
istics of  the  ear  and  its  outer  air  passages.

Much  has  been  learned  about  the  normal  ear  by  the  investigation
of  the  characteristics  of  abnormal  ears.  This  has  incidentally  had
an  application  to  otological  diagnosis  and  the  design  and  building  of
amplifying  apparatus  for  the  deaf.

This  paper  is  a  summary  of  the  conclusions  reached  to  date  regard-
ing the  absolute  sensitivity  of  normal  and  abnormal  ears,  the  maximum
sound  to  which  the  ear  can  accommodate  itself,  the  much  discussed
points  of  "upper  and  lower  frequency  limits  of  audition,"  the  "quality"
of  audition,  a  brief  mention  of  the  binaural  sense  and  the  principles  of
rigorous  dynamical  analysis  of  the  ear  as  a  mechanism.  A  brief
description  of  the  apparatus  used  is  also  given.

The  function  of  the  auditory  sense  is  to  detect  sounds  of  various
kinds  and  wave  shapes  varying  over  a  range  of  pressure  on  the  ear
drum  of  from  about  .001  to  1,000  dynes  per  cm^  and  over  a  consider-
able part  of  this  range  to  differentiate  with  certainty  between  complex

sounds  so  ncarl>-  alike  that  no  existing  physical  apparatus  can  separate
them.  The  binaural  feature  adds  a  sense  of  orientation  with  respect
to  a  source  and  uniform  sensitivity  for  sounds  approaching  from  differ-
ent directions.  The  abnormal  auditory  sense  may  be  regarded  as
lacking  niore  or  less  in  (a)  range  of  sensation  (frequency  and  intensity) ;
(b)  quality  of  sensation  in  various  regions  of  the  range;  (c)  the  bi-
naural sense.  Apparatus  and  methods  have  been  developed  by  means
of  which  the  outstanding  features  of  these  functions  can  be  measured
and  to  a  limited  extent  compensated  for.

2.  Minimum  Audibility.     Fig.  1  shows  a  plot  of  the  logarithmic
average  of  minimum  audible  pressure  on  72  normal  ears  taken  through-

out  a  range  of  frequency  from  60  to  4,0C0  cycles.^  Both  the  intensity
and  frequency  scales  are  logarithmic.  Although  all  skew  errors  in  the
determination  of  the  average  curve  have  not  been  eliminated,  an
investigation  has  shown  that  they  are  so  small  as  not  to  affect  the
utility  of  the  curve  for  the  purpose  of  measuring  deafness.  Among
the  errors  which  obviously  tend  to  raise  this  curve  might  be  men-
tioned, noise  in  the  observing  room,  abnormality  of  hearing,  lack  of
attention,  and  low  mentality  of  the  observer.  Care  was  taken  to
reduce  these  errors  to  a  minimum  without  actually  making  separate

'This  curve  has  already  been  pubhshed;  The  Frequency  Sensitivity  of  Normal
Ears,  by  H.  Fletcher  and  R.  L.  Wegel,  Proceedings  pf  the  National  Academy  of  Sciences,
January,  1922,  and  Physical  Review,  June,  1922.

quantitative  measurements  of  each  of  them  on  a  rigorous  statistical
basis.

The  statistical  deviation  from  the  mean  varies  irregularly  with  fre-
quency; very  likely  this  is  due  mostly  to  the  external  anatomical
variations  in  ears  which  cause  deviations  in  the  dynamical  constants
of  the  transmission  system  from  sound  source  to  the  ear  drum.  The
dotted  lines  following  the  curve  of  minimum  audibility  represent
approximately  the  "standard  deviation."

3.  Maximum  Andibility.  The  curve  marked  "Maximum  audi-
bility" represents  the  logarithmic  average  pressure  on  48  normal  ears
required  to  produce  the  sensation  of  feeling.  This  represents  the
threshold  of  feeling  in  the  same  way  that  the  minimum  audibility
curve  represents  the  threshold  of  audition.  A  sound  much  louder
than  this  is  painful.  The  measurements  were  taken  through  a  range
of  from  60  to  3,000  cycles.  The  standard  deviation  lines  are  also
given  from  which  it  will  be  seen  that  this  curve  is  quite  as  definite  as
that  of  minimum  audibility.  While  this  point  of  feeling  probably  has
no  relation  to  the  auditory  sense  it  does  serve  as  a  practical  limit  to
the  range  of  auditory  sensation.  A  few  observations  indicate  that
people  with  abnormal  ears  have  a  point  of  feeling  sound  which  is  not
greatly  different  from  that  of  normal  ears,  but  this,  of  course,  depends
on  the  type  of  abnormality.  The  intensity  for  feeling  is  about  equal
to  that  required  to  excite  the  tactile  nerves  in  the  finger  tips.

4.  Loiver  and  Upper  Frequency  Limits  of  Hearing.  The  curves  of
minimum  and  maximum  audibility  in  Fig.  1  will  be  seen  to  have  been
extrapolated  to  the  points  of  intersection  at  high  and  low  frequencies.
The  feeling  sensation  in  the  middle  range  of  frequency  is  first  a  tickling
sensation  and  then  becomes  acutely  painful  as  the  loudness  is  in-
creased. As  the  frequency  is  decreased  the  sensation  of  feeling  becomes
milder  until  frequencies  around  60  cycles  it  is  sensible  as  a  flutter,
but  still  quite  different  from  the  sense  of  audition.  As  the  frequency
is  still  further  decreased  to  a  point  where  the  hearing  and  feeling  lines
appear  to  intersect,  it  is  difficult  to  distinguish  between  the  sense  of
hearing  and  that  of  feeling.  The  low  point  of  intersection  of  the  two
normal  curves  of  minimum  audibility  and  feeling  sense  may,  there-
fore, be  taken  arbitrarily  as  the  lower  tone  limit  of  audibility.  For
frequencies  lower  than  this  it  is  easier  to  feel  than  to  hear  the  air
vibration.  The  point  of  intersection  cannot  be  determined  by  direct
observation  due  to  the  diflficulty  in  distinguishing  between  the  two
sensations.  A  .similar  intersection  of  the  two  curves  occurs  at  some
very  high  frequency.  Sound  waves  of  frequencies  below  the  lower
intersection  and  above  the  upper  intersection  are  more  easily  sensed

by  feeling.    Soiiiul  waxes  between  these  limits  are  more  easily  sensed
by  audition. 2

This  suggests  a  rational  way  of  defining  and  determining  the  two
frequency  limits  of  audibility.  Measurements  of  these  limits  which
have  been  made  in  the  past  are  questionable  because  the  intensity
factor  has  been  neglected.  At  the  lower  limit  of  audibility  the  ex-
cursions of  the  diaphragm  and  ossicles  of  the  middle  ear  are  probably
so  large  that  the  nerves  feeding  these  movable  parts  are  stimulated.
This  observation  at  low  frequencies  as  indicated  in  this  work  lends
color  to  the  hypothesis  of  otologists  that  abnormalities  in  the  hearing

frequencies  is  considered  an  indication  of  obstructive  deafness  if  there

^  The  extrapolation  upward  of  the  curve  of  minimum  audibility  is  consistent
with  some  recent  observations  of  Mr.  C.  E.  Lane  at  the  University  of  Iowa,  Physi-
cal Review,  May,  1922.

characteristic  of  the  normal  ear.  Any  point  within  this  area  repre-
sents a  definite  auditory  sensation  in  frequency  and  intensity.  The
area  of  sensation  is  analogous  to  the  field  of  vision  of  the  eye.  The
part  of  this  area  which  is  most  utilized  in  the  interpretation  of  speech
is  represented  approximately  by  the  shaded  area  in  Figs.  1  and  2
and  corresponds  in  a  way  to  the  center  of  the  field  of  vision.  A
normal  listener  tries,  by  keeping  at  a  certain  distance  from  a  speaker,
to  bring  this  part  of  his  sensation  area  into  play  in  the  same  way  that
when  examining  an  object  he  directs  his  eyes  so  that  it  falls  in  the
center  of  the  field  of  vision.

An  abnormal  ear  may  be  regarded  as  having  an  area  of  sensation
which  is  smaller  than  the  normal  area  but  included  within  it.  Fig.  2
is  a  plot  of  the  minimum  audibility  of  the  right  and  left  ears  for  a
man  (CHK)  having  a  "catarrhal"  deafness.  The  areas  between
these  curves  of  minimum  audibility  and  the  curve  of  feeling  are  his
areas  of  sensation.  It  will  be  seen  that  CHK  retains  about  50  or  60
per  cent  of  the  normal  amount  of  sensation.  He  hears  and  interprets
conversation  with  some  difficulty.

Since  the  CHK  curves  pass  through  the  speech  region,  part  of  it '
is  entirely  inaudible  and  the  remainder  is  near  minimum  audibility'
for  him.  In  order  to  make  him  hear  well,  the  speech  area  must  be'
raised  to  a  higher  level  of  intensity  or  loudness  as  indicated  by  the
dotted  curve.

In  general  it  takes  a  loss  of  about  20  per  cent  of  the  sensation  area
to  become  noticeable  and  much  more  is  disagreeable.  A  loss  of  50
per  cent  requires  the  use  of  deaf  apparatus.  A  loss  of  75  per  cent
can  be  aided  considerably  by  the  use  of  high  powered  amplifying
apparatus.

6.  Importance  of  Various  Intensities  in  Speech.  It  is  interesting
to  speculate  on  how  CHK  interprets  speech.  It  has  been  shown  '
that  the  intensity  of  speech  may  be  varied  over  perhaps  70-80  per
cent  of  the  range  of  sensation  without  serious  loss  of  intelligibility
to  the  normal  ear.  As  the  sound  intensity  is  decreased,  the  in-
telligibility drops  very  suddenly  to  zero  at  minimum  audibility.  A
similar  drop  is  to  be  expected  at  an  intensity  so  loud  as  to  be  painful.
It  is  evident,  therefore,  that  the  range  in  which  speech  is  intelligible  for
CHK  is  very  considerably  limited  as  compared  to  normal.  It  is
possible  to  design  a  deaf  set  which  raises  the  intensity  of  the  principal
speech  region  to  any  desired  place  within  the  abnormal  sensation  area
and  so  in  a  measure,  compensate  for  this  narrowed  range.  The
region  in  Fig.  1  "Region  of  Lesser  Importance  in  Speech,"  corre-
'  H.  Fletcher,  Journal  of  the  Franklin  Institute,  June,  1922.

spends  to  stimuli  in  conversation  of  lesser  energy  content,  such  as
the  minor  shadings  and  fainter  consonant  sounds.  While  it  is  physi-
cally possible  to  produce  an  amplification  of  speech  so  that  this  region
is  raised  into  the  diminished  area  it  is  impracticable  to  do  so  because
of  the  pain  which  would  be  caused  by  the  louder  components.  A
diminution  in  sensation  area  can,  therefore,  be  only  partially  com-
pensated for.  In  case  the  area  is  extremely  narrow  a  deaf  set  fur-
nishing optimum  volume  can  only  serve  as  an  aid  to  lip  reading.

"sustained,"  "smooth,"  "pure,"  etc.  Such  a  description  may,  in
fact,  be  taken  as  a  reasonable  indication  that  the  quality  of  sensation
at  the  point  in  question  is  normal.  Abnormal  ears  sometimes  ex-
perience a  subjective  degeneration  of  quality  of  pure  stimuli  which
they  describe  as  "rough,"  "harsh,"  "sharp,"  "buzzing,"  "vibrating,"
"hissing,"  etc.  This  subjective  degeneration  is  independent  of  any
tinnitus  or  head  noises  which  the  patient  may  have.  Fig.  3  shows
various  regions  of  the  sensation  area  which  are  degenerated  in  the
case  of  CHK,  left  ear.  The  shaded  area  was  not  explored.  The
boundaries  of  the  degenerated  regions  are  usually  more  sharply
marked  than  the  outer  boundaries  of  the  sensation  area.  The  sensa-
tions in  these  areas  are  so  radically  different  from  the  sensation  of  a

pure  tone  that  it  is  with  difficulty  that  the  patient  is  convinced  that
the  stimulation  is  the  same  pure  tone  to  which  he  has  been  listening
at  the  other  intensities.  The  subject  of  these  tests  is  a  violinist  and
capable  of  better  descriptions  and  finer  distinctions  than  average.

Since  all  speech  sounds  may  be  considered  as  stimuli  composed  of
various  frequency  components  of  certain  intensities,  the  sensation
caused  by  such  a  sound  may  be  represented  on  this  plot  by  points,
or  by  a  line  provided  the  sound  has  a  band  spectrum.  If  the  points
or  line,  falls  within  the  sensation  area  the  sound  is  audible.  It  is
easy  to  see  that  if  the  points  or  the  part  of  the  line  which  represent
those  frequency  components  most  essential  to  interpretation  of  the
sound,  fall  within  any  of  these  abnormal  areas,  the  sound  is  very
likely  to  be  misinterpreted.  This  adds  a  further  source  of  loss  in
intelligibility  to  that  already  observed  due  to  a  narrowing  of  the
sensation  range.  When  an  amplifying  deaf  set  is  designed,  due  care
should  be  taken  to  raise  the  principle  speech  region  in  such  a  way
as  to  cause  a  minimum  overlapping  with  the  abnormal  areas.

Many  practically  normal  ears  have  verv  small  abnormal  areas.
They  have  always  been  found  near  minimum  audibility  and  "f  this  is
always  true  would,  therefore,  have  little  influence  on  the  hearing  of
the  individual.  They  seem  to  be  associated  with  "catarrhal"  con-
ditions although  this  cannot  be  stated  positively.

8.  Binaural  Sense.  The  normal  individual  has  learned  to  interpret
the  differential  sensations  of  the  two  ears  to  advantage.  It  helps
him  to  locate  the  direction  from  which  sounds  come,  to  have  a  sort  of
sense  of  orientation  with  respect  to  sounds  approaching  from  different
directions,  and  whether  for  physical  or  for  purely  psychological
reasons  to  assist  in  focusing  of  the  attention  on  one  sound  of  a  large
number.  Two  ears  also  assist  the  individual  in  perceiving  equally
well  sounds  coming  from  different  directions.

When  one  ear  becomes  less  sensitive,  even  though  the  loss  is
small,  the  use  of  the  binaural  sense  disappears  an]  after  a  time  is  not
missed,  the  subject  depending  upon  other  means  of  locating  sounds.
For  the  binaural  sense  to  be  most  effectively  utilized  it  is  necessary
that  the  ears  be  very  nearly  alike.  When  a  binaural  deaf  set  is  made
and  fitted  to  a  person  with  compensating  sensitivity  for  the  two  ears
so  that  both  hear  the  sounds  equally  loud,  the  sensation  is  usually
so  novel,  that  if  the  patient  is  actually  able  to  experience  a  binaural
sensation  he  is  very  much  pleased.  Usually,  however,  he  has  not
used  his  binaural  sense  for  so  long  a  time  that  it  takes  a  considerable
amount  of  practice  before  he  is  able  to  have  binaural  experiences.  It
may  be  noted   in   this  connection   that  the  same  experience  is  en-

countered  in  fittinj^  the  eyes  with  jjlasses.  It  is  found  that  people
with  two  eyes  which  are  slightly  different  do  not  see  stereoscopically
but  if  glasses  are  made  so  as  to  compensate  and  make  the  eyes  nearly
alike,  it  usually  takes  a  certain  amount  of  practice  before  the  sense
of  perspective  can  be  brought  back.

As  a  source  of  sound,  a  small  thermal  receiver  unit  was  used.  This
consisted  ot  about  twenty  very  small  loops  of  Wollaston  wire  con-
tained in  a  brass  case  small  enough  to  be  inserted  in  the  external  ear
canal  and  entirely  stop  it  up.  In  the  average  ear  a  volume  of  about
1  cm.^  of  air  is  included  between  it  and  the  drum  membrane.  A  direct
heating  current  is  passed  through  the  receiver  and  an  alternating
current  of  the  desired  frequency  and  intensity  is  superimposed  to
modulate  its  temperature.  This  modulation  in  temperature  causes
alternate  expansion  and  contraction  of  a  very  thin  film  of  air  covering
its  surface  and  so  produces  alternations  in  pressure  in  the  ear  canal
of  the  frequency  of  the  impressed  alternating  current.  The  intensity
is  proportional  to  this  alternating  current  if  it  is  maintained  small
compared  with  the  direct  current.  This  arrangement  permits  of
producing  alternating  or  sound  pressure  on  the  ear  drum  with  a
comparatively  simple  dynamical  relation  between  the  source  of
sound  and  the  ear  drum.  The  thermal  receiver  is  also  dynamically
one  of  the  simplest  sources  of  sound  known.

The  sound  or  alternating  pressure  was  determined  by  calibration.
This  was  done  by  inserting  the  thermal  receiver  in  an  air  cavity  of
1  cm.^  volume  in  front  of  a  condenser  transmitter  diaphragm  by  which
the  alternating  pressure  developed  by  a  given  current  in  the  receiver
could  be  measured.^  By  measurement  of  the  current  for  minimum
audibility  or  "maximum  audibility"  or  for  any  other  intensity  the
pressure  in  the  ear  canal  is  determined.

10.  Dynamical  Principles  of  Ear  Measurements.  From  a  dynamical
standpoint  the  phrase  "sensitivity  of  the  ear"  as  it  is  usually  used  is

*  For  further  details,  see  "The  Frequency  Sensitivity  of  Normal  Ears,"  H.  Fletcher
and  R.  L.  Wegel,  Physical  Review,  June,  1922.

*  For  the  method  of  calibration  of  the  condenser  transmitter,  see  article  by  H.  D.
Arnold  and  I.  B.  Crandail,  Physical  Review,  July,  1917.

rather  indefinite.  When  a  figure  is  given  in  ergs  per  second,  the  rate
of  flow  of  energy  through  an  area  equal  to  that  of  the  ear  opening  in
an  unobstructed  wave,  is  commonly  meant.  This  has  no  simple
relation,  theoretically  at  any  rate,  to  the  net  rate  of  flow  of  energy
into  the  ear  when  the  head  is  placed  as  an  obstruction  to  the  wave.
The  distortion  of  the  sound  field  by  the  head  varies  greatly  with
frequency.  Similarly,  there  is  no  simple  relation  between  the  energy
flowing  into  the  ear  and  that  transmitted  to  and  absorbed  by  the  ear
drum  or  by  the  cochlea.  In  the  experiments  recorded  above,  atten-
tion was  paid  to  the  experimental  set-up  so  as  to  make  the  figures
given  have  a  more  definite  dynamical  significance.  Sensitivity  is
given  in  terms  of  the  alternating  (root  mean  square)  pressure  to
produce  a  minimum  audible  sensation.  The  term  "pressure"  has  so
far  been  used  in  a  rather  loose  sense.  Just  why  this  is  so  will  be  seen
from  the  following  argument.

r  =  frictional  resistance  to  motion,  with  respect  to  a  station-
ary body  and  involves  dissipation  of  energy  at  a  rate
of  Pr  where  x  is  the  root  mean  square  value  of  the
relative  velocity.  The  velocity  x  will  be  assumed
simply  sinusoidal  in  what  follows,

ni  =  mass  or  inertia  constant  involving  an  average  storage
kinetic  energy  of  x^m  through  one  cycle,

s  =  stiffness  constant  involving  an  average  storage  of
potential  energy  through  one  cycle  of  x^s/w^.

If  the  r.  m.  s.  alternating  force  acting  is  F,  the  motion  at  any
frequency  is  given  by

as  "lunipc'd,"  that  is  in  which,  for  the  pur[K)sc  of  {iractical  sohition,
a  finite  number  of  degrees  of  freedom  may  be  assumed,  the  method
is  to  find  the  most  useful  way  of  "lumping"  these  constants.  The
motions  are  then  represented  by  a  series  of  equations,  one  for  each
degree  of  freedom,  between  the  forces  acting  and  the  impedances
and  velocities.  The  determinant  of  the  coefficients  of  these  equations
is  the  Lagrange  determinant  of  the  system.  The  only  caution  to  be
observed  in  lumping  the  constants  is  that  the  reciprocal  relation,
which  is  a  property  of  any  linear  system  holds  also  for  the  physical
system  which  the  assumed  Lagrange  determinant  is  supposed  to
represent.

The  dynamical  system  used  in  calibration  with  the  condenser
transmitter  consists  of  three  parts:

(a)  The  very  thin  pulsating  air  film  over  the  thermal  receiver
filaments.  The  expansion  of  air  around  the  wires  is  represented  by
the  "diffusion"  equation,  the  solution  of  which  in  such  a  case  of
cylindrical  symmetry  is  given  as  a  Bessel's  function  of  the  distance
from  the  wire.^  This  wave  is  so  quickly  damped  in  travelling  away
from  the  wire  as  to  be  negligible  beyond  the  first  zero  point  of  the
Bessel's  function.  The  vibrating  system  of  this  receiver  may  then
be  considered  as  a  cushion  of  air  next  to  the  wire  of  a  thickness  a  little
less  than  the  first  half  wave  length  of  the  heat  w'ave.  The  thickness
of  this  cushion  is  an  inverse  function  of  the  frequency.

(b)  The  air  chamber  between  the  thermal  receiver  and  con-
denser transmitter  diaphragm  having  a  volume  of  1  cm.'  and  en-
closed by  practically  unyielding  w^alls  w^ith  no  openings.

(c)  The  condenser  transmitter  diaphragm,  being  stretched  very
tightly  and  air  damped.  It  may  also  be  regarded  as  unyielding,  or  as
having  an  impedance  very  high  compared  to  that  of  the  connecting
air  chamber.

If  for  simplicity  the  mass  reaction  and  internal  losses  in  the  air
chamber  may  be  neglected,  it  may  be  seen  that  the  moving  system
of  the  receiver  may  be  regarded  as  a  weightless  and  frictionless
"diaphragm"  surrounding  the  wires  at  a  distance  equal  to  the  effective
thickness  of  the  active  air  film  and  may  be  shown  to  have  an  intrinsic
stiffness  reactance  of:

In  this  expression,  7  is  the  adiabatic  constant  of  air,  po  the  atmos-
pheric pressure,  ai  the  area  of  the  fictitious  diaphragm,  and  Vi  the
volume  of  air  in  the  film.  This  diaphragm  is  loaded  externally  by
the  air  chamber,  when  the  transmitter  diaphragm  is  prevented  from
moving,  by  a  stiffness  reactance  of

in  which  v  is  the  volume  of  the  air  chamber.  Similarly,  the  load  of
the  air  chamber  on  the  transmitter  diaphragm,  whose  area  is  02,  is

The  air  chamber  also  acts  as  a  mutual  impedance  between  the
thermal  unit  and  the  transmitter  diaphragm  equal  to

If,  further,  the  intrinsic  impedance  of  the  transmitter  diaphragm,
which  may  be  any  function  of  frequency,  be  denoted  by  Z2,  the
equations  of  motion  of  the  system  may  be  written

In  these  equations,  F  is  the  force  acting  on  the  thermal  receiver
"diaphragm"  due  to  alternating  current,  Xi  the  velocity  of  its  motion
and  Xi,  the  velocity  of  motion  of  the  condenser  transmitter  diaphragm.
A  rough  calculation  shows  that  Vi  is  very  small  compared  with  v,
so  that  Si  may  be  neglected  compared  to  Si  and  that  the  reaction
yiyiXi  may  be  neglected.  The  analysis  of  the  condenser  trans-
mitter shows  Z2  to  be  very  large  compared  to  M'^.  These  equations
may  then  be  rewritten

The  equations  of  motion,  when  the  receiver  is  inserted  in  the  ear,
may  be  derived  in  a  similar  way.  In  this  case,  although  the  volume
of  air  between  the  receiver  and  ear  drum  is  the  same  as  before,  the

walls  may  yield  appreciably,  particularly  in  some  frequency  ranges.
The  mutual  impedance  between  the  receiver  and  ear  drum,  is,  there-
fore, not  necessarily  a  simple  stiffness  reactance.  Also  the  loads  due
to  it  on  the  thermal  receiver  and  ear  drum,  which  in  this  case  takes  the
place  of  the  transmitter  diaphragm,  are  not  simple  stiffness  reactances.
The  constants  in  the  case  of  the  ear  system  will  be  denoted  by  the
same  letters  as  those  used  in  the  calibration  but  with  the  primes
dropped,  with  the  exception  that  the  intrinsic  impedance  of  the  ear
drum  is  denoted  by  D.  D  includes  the  reactions  of  the  ossicles  of
the  middle  ear  and  the  cochlea  and  is  probably  a  complicated  function
of  frequency.  If,  as  may  be  expected,  nature's  design  is  efficient,
then  D  must  be  of  the  same  general  order  of  magnitude  as  the  load  on
the  ear  drum,  M12,  of  the  ear  canal.  This  probably  constitutes  the
largest  difference  between  the  calibration  and  the  observational
systems.  Strictly,  of  course,  the  condition  for  maximum  power
absorption  by  the  ear  drum  from  the  air  is  that  D  be  the  conjugate
of  the  impedance  of  the  load  on  it  due  to  the  unobstructed  ear  canal.
This  condition  is  not  obtained  in  nature  because  of  such  requirements
placed  on  the  design  as  protection  from  injury,  etc.

In  the  case  of  the  ear,  Mi  may  again  be  neglected,  compared  to
Zi,  and  the  reactance,  M12  ^2  may  be  neglected.     Then

where  .V2  represents  the  velocity  of  motion  of  the  ear  drum.  Suitable
variations  with  frequency  are  implied  in  each  of  the  "  constants  "
of  this  system.

We  are  now  in  a  position  to  see  just  what  has  been  measured  and
called,  for  the  sake  of  brevity  or  want  of  a  better  name,  "  minimum
audible  pressure  "  in  the  first  part  of  this  paper.

Let  X\  now  represent  the  velocity  of  the  receiver  diaphragm  in
both  systems  corresponding  to  that  necessary  to  obtain  a  minimum
audible  sensation  in  the  ear,  and  F  the  corresponding  force.  Then
X2  will  be  the  velocity  of  the  ear  drum  corresponding  to  minimum
audibility  in  equation  (2).  In  the  calibration,  the  pressure  P'  on  the
condenser  transmitter  diaphragm  corresponds  to  Xi.  The  total  force
acting  on  this  diaphragm  is  p'a'  where  now  a'  designates  its  area.
Since  this  force  is  relieved  by  the  motion  of  the  diaphragm,  it  is  seen
from  equation  (1)  to  be  equal  to  \

Similarly  if  the  actual  pressure  on  the  ear  drum  is  p,  and  its  effec-
tive area,  a,  the  total  force  on  the  ear  drum  pa  =  D  x^-  Combining
equations  (2)  and  (3)  gives

The  pressure  p  is  the  actual  pressure  on  the  ear  drum.  The
pressure  p'  is  that  measured  and  plotted  in  the  diagram.  If  the  walls
of  the  ear  canal  and  the  ear  drum  were  unyielding,  p  and  p'  would  be
identical  for  then  M  =  M'  and  M^  Xija  would  vanish.  If  the  yield
of  the  ear  canal  walls  were  such  as  to  relieve  half  the  pressure  in  the
canal  and  that  of  the  ear  drum  about  the  same,  the  difference  would  be
considerably  less  than  one  of  the  divisions,  in  the  diagrams,  on  the
intensity  scale.  If  the  drum  impedance  D  should  be  found  to  be
negligible  compared  to  its  load  Mi  the  difference  would  be  consider-
able. This,  however,  is  hardly  to  be  expected  even  through  narrow
ranges  of  frequency.  If  the  impedances  in  the  formulas  were  measured
the  energy  flow  into  the  ear  drum  could  be  computed.

In  conclusion,  the  present  status  of  the  ear  problem  may  be  sum-
marized. The  philosophy  of  external  ear  dynamics  has  been  touched
on  but  there  still  remain  difficult  problems  both  theoretical  and  ex-
perimental. A  start  has  been  made  on  a  sound  basis  in  the  explana-
tion of  the  action  of  the  cochlea  by  Roaf,  "  Analysis  of  Sound  Waves
by  the  Cochlea,"  Philosophical  Magazine,  February  1922.  Nothing
dependable  has  as  yet  been  published  on  the  action  of  the  middle
ear  for  audio  frequencies.  It  is  usually  assumed  that  the  various  parts
undergo  relative  displacements  at  audio  frequencies  in  the  same  way
as  they  react  to  static  forces  but  this  is  very  likely  far  from  the  truth.

THE  Theory  of  Probabilities  lends  itself  to  the  solution  of  many
important  telephone  problems.  These  problems  arise  not  only
in  connection  with  the  trunking  of  calls  but  also  in  statistical
studies  which  underlie  the  making  of  fundamental  plans,  in  studies
carried  on  in  physical  research  and  in  the  manufacturing  of  telephone
apparatus.

The  purpose  of  the  present  paper  is  to  discuss  certain  simple  types
of  trunking  problems  which  can  readily  be  handled  to  a  sufificient
degree  of  approximation  by  well-known  probability  methods.  It
would  be  quite  impossible,  within  the  scope  of  a  single  paper  to  give
a  complete  discussion  of  trunking  problems  in  general.  For  years  ^
it  has  been  known  that  light  could  be  shed  on  these  problems  by  the
application  of  probabilities  and  many  articles  ^  have  appeared  on
this  subject;  however  the  treatment  to  be  found  in  the  literature  is,
as  yet,  by  no  means  comprehensive.

About  1905,  the  development  of  machine  switching  systems  arrived
at  a  stage  where  the  relative  efficiencies  of  different  sizes  of  trunk
groups  became  of  prime  importance.

In  designing  and  engineering  machine  switching  systems,  it  is
necessary  to  compare  the  costs  of  various  plans  using  trunk  groups
of  widely  different  sizes,  in  order  to  choose  the  cheapest  arrangement.
Some  plans  use  trunk  groups  as  small  as  5  and  others  groups  as  large
as  90.

Machine  switching  development,  therefore,  gave  a  great  impetus
to  the  application  of  the  Theory  of  Probabilities  to  telephone  engineer-
ing and  in  the  Bell  System  work  along  this  line  has  been  in  progress,
systematically,  for  many  years.  This  work  has  included  not  only
the  theoretical  solutions  of  various  trunking  problems,  but  has  also
involved  the  computation  of  special  probability  tables  and  collec-
tion of  data  by  means  of  which  theoretical  results  have  been  closely
checked.

In  the  articles  which  have  hitherto  appeared,  little  or  no  effort
has  been  made  to  present  the  mathematical  theory  of  trunking  in  a

'  G.  T.  Blood  of  the  A.  T.  &  T.  Co.  in  1898  found  a  close  agreement  between  the
terms  of  a  binomial  expansion  and  the  results  of  observations  on  the  distribution
of  busy  calls.  The  first  comprehensive  paper  was  one  written  by  M.  C.  Rorty  in
October  1903  and  was  quite  widely  circulated  within  the  Bell  System.

manner  that  can  be  understood  by  those  who  are  not  experts  on  the
subject.  It  is  hoped  that  this  article  will  assist  the  reader  in  under-
standing both  what  has  been  and  will  be  written  on  the  subject.  As
Poisson  ^  has  said  "a  problem  relative  to  games  of  chance  and  proposed
to  an  austere  Jansenist  by  a  man  of  the  world,  was  the  origin  of  the
calculus  of  probabilities,"  and  today  the  reader  will  find  that  in  the
majority  of  text  books  the  subject  is  introduced  by  the  solution  of
games  of  chance  and  particularly  of  dice  problems.  This  established
custom  will  be  followed  by  the  present  writer  who,  in  the  course  of
this  article,  will  show  how  various  fundamental  trunking  problems
can  be  transformed  into  equivalent  dice  problems.  This  being  done,
solutions  will  be  found  to  be  at  hand.

Three  trunking  problems,  each  one  step  more  complicated  than
the  preceding,  will  be  dealt  with.  In  order  to  facilitate  the  trans-
formation to  the  three  equivalent  dice  problems  it  is  desirable  that
the  basic  assumptions  made  be  as  simple  as  possible.  The  asump-
tions  made  in  all  three  problems  are:

Conditions  substantially  approximating  this  assumption  frequently
occur  in  practice.

B — If  a  call  when  initiated  obtains  a  trunk  immediately  it  retains
possession  of  that  trunk  for  exactly  two  minutes.  In  other  words,  a
constant  holding  time  of  two  minutes  duration  will  be  assumed.

In  practice,  holding  times,  of  course,  vary  from  a  few  seconds  to
many  minutes  and  it  may  at  first  sight  seem  that  the  assumption  of
a  constant  holding  time  might  lead  to  results  deviating  too  much
from  practice  to  be  of  value.  On  this  point,  the  theory  of  probabilities
itself  sheds  some  interesting  light.  As  will  be  pointed  out  in  the
following  problems,  the  assumption  of  a  constant  holding  time  is
the  equivalent  of  a  dice  problem  in  which  a  single  die,  or  several  iden-
tical dice  are  considered.  The  telephone  problem  with  variable
holding  times  may  be  reduced  to  the  consideration  of  many  dice,
each  with  a  different  number  of  faces.  Suppose  600  throws  are  made
with  a  die  having  6  faces  so  that  on  the  average  3^  of  600  or  100  aces
would  be  expected.  With  Bernoulli's  formula  it  is  easy  to  find  the
probability  that  the  number  of  aces  which  turn  up  shall  lie  between
75  and  125,  that  is  to  say,  within  25  on  each  side  of  the  average.  Now
suppose  200  throws  are  made  with  a  die  having  20  faces,  200  with  a

10  face  die,  100  with  a  5  fac-e  die  and  finally  100  with  a  2  face  die.
These  600  throws  would  also  give  on  the  average  100  aces.  Using
Poisson's  generalization  of  the  Bernoulli  formula'  we  can  calculate
the  probability  that  these  (iOO  throws  with  various  kinds  of  dice  shall
gi\e  a  number  of  aces  lying  between  75  and  125.  This  probability
will  be  greater  than  in  the  case  of  the  600  throws  with  the  die
with  a  constant  number  of  faces,  i.e.,  the  chance  that  the  result  will
come  outside  the  range  75  to  125  is  less.

The  thought  is  at  once  suggested  that  for  the  same  total  volume  of
traffic  and  a\-erage  holding  time,  fewer  calls  would  be  lost  when  the
holding  time  is  not  constant.'*  The  above  theory  was  tested  in  practice
a  few  \ears  ago  by  the  engineers  of  the  American  Telephone  and  Tele-
graph Company,  who  made  pen  register  records  of  hundreds  of  thou-
sands of  actual  calls  as  handled  by  groups  of  machine  switching
trunks  at  Newark,  New  Jersey.  A  pen  register  was  made  which
operated  as  follows:  Each  trunk  in  the  group  was  represented  by  a
pen.  These  pens  were  mounted  side  by  side  and  each  was  controlled
by  a  magnet  in  such  a  manner  that  when  the  trunk  was  busy  the  pen
made  a  mark  on  a  wide  strip  of  paper  driven  at  constant  speed  under
the  pens.  There  was  thus  obtained  a  record  showing  when  each  call
originated  and  when  it  was  concluded.  An  artificial  record  was  now
made  showing  what  would  have  happened  if  each  call  had  lasted  for
the  average  holding  time  as  determined  from  the  original  record.
Some  100,000  calls  w^ere  analyzed  in  this  manner  and  it  w^as  found  that
with  a  group  of  trunks  of  a  size  to  carry  the  calls  of  the  original  record
with  only  a  small  loss,  30  per  cent,  more  calls  would  have  been  lost  if
the  traffic  had  been  as  shown  by  the  artificial  record.  It  should  be
borne  in  mind,  however,  that  a  30  per  cent,  change  in  a  probability
of  the  order  of  one  in  one  hundred,  considering  the  values  we  are  deal-
ing with,  is  practically  negligible.

This  assumption,  although  artificial,  simplifies  materially  the  analy-
sis of  the  problems.     Just  what  happens  in  practice  to  every  call

which  fails  to  get  a  trunk  immediately  is  unknown.  It  is  obvious,
however,  that  when  the  number  of  trunks  is  such  that  the  liability  of
the  call  failing  to  get  a  trunk  immediately  is  very  small — for  example:
of  the  order  of  one  in  one  hundred — the  reaction  of  these  calls  on  other
calls  must  be  negligible  independently  of  whatever  assumption  ^  is
made  in  place  of  C.

it  comes  to.  The  20  points  of  all  switches  are  multipled  together  so
that  a  single  group  of  20  trunks  must  handle  the  calls  originating  from
these  269  lines.

Referring  to  Fig.  2  let  point  P  represent  the  unknown  instant
within  the  hour  at  which  X  calls.  Consider  the  two  minutes  imme-
diately preceding  the  instant  P.  Evidently,  by  assumption  C,  calls
falling  outside  of  this  particular  two-minute  interval  can  not  prevent
X  from  obtaining  a  trunk.

*  It  is  well  known  that  the  Erlang  formula  which  is  based  on  an  assumption  dia-
metrically opposed  to  assumption  C,  namely  that  calls  which  find  all  trunks  busy
do  not  wait  for  a  trunk  to  become  idle,  gives  essentially  the  same  results  (for  small
probabilities,  which  are  the  only  ones  of  interest  in  practice)  as  the  Poisson  furmula
which  assumes  C.

It  is  evident  then,  that  the  probability  that  X  fails  to  get  a  trunk
immediately  is  the  same  as  the  probability  of  throwing  at  least  20  aces
if  268  throws  are  made  with  a  30-face  die.  To  facilitate  the  de-
termination of  this  probability  and  the  solution  of  similar  problems,
probability  tables  of  a  type  shown  in  Table  I  have  been  computed.*^
In  the  table,  the  average  number  of  times  an  event  may  be  expected
is  represented  by  a.  The  probability  that  the  event  occurs  at  least
a  greater  number  of  times  c  =  a  -[-  d  \s  represented  by  P.  In  the
problem  under  consideration,  the  average  number  of  aces  expected  is

the  table,  we  find  that  corresponding  to  c  =  20  and  a  =  8.96,  the
value  of  the  probability  P  is  .OOL  In  the  particular  telephone  prob-
lem under  consideration  this  means  that  once  in  a  thousand  times

or  choices.  The  reader  unfamiliar  with  automatic  systems  may
consider  a  10  level  selector  as  one  from  which  calls  may  be  sent  in  10
difTcrent  directions.  Assume  that  each  level  is  equipped  with  8
trunks  to  second  selectors.  The  591  line  switches  are  multipled
together  so  that  one  group  of  35  first  selectors  must  handle  the  calls
originating  from  these  591  lines.  The  35  first  selectors  are  multi-
pled  together  so  that  one  group  of  8  second  selectors  must  handle
the  calls  originating  from  the  591  lines  for  a  particular  level.  It  is
assumed  that  the  591  calls  are  distributed  at  random  with  reference
to  the  10  levels  of  the  first  selectors.

The  probability  of  Y  fulfilling  the  first  condition  is  equal  to  the
probability  of  throwing  the  ace  with  a  30  face  die.  The  probability  of
Y  fulfilling  the  second  condition  is  equal  to  the  probability  of  throw-
ing the  ace  with  a  10  face  die.

The  question  may  then  be  stated  in  the  form  of  a  dice  problem  as
follows:  591  throws  are  made  with  a  30  face  die  giving  C  aces.  C
throws  are  made  with  a  10  face  die  giving  D  aces,  and  the  question
is  the  probability  that  D  is  not  less  than  8.  Assuming  no  restric-
tion ^  on  the  value  of  Cthis  probability  is  the  same  as  that  of  throwing
at  least  8  aces  in  591  throws  with  a  die  having  (30)  (10)  =  300  faces.

The  average  number  of  aces  to  be  expected  is  (591/300)  =  1.97  and
with  this  average  the  tables  tell  us  that  once  in  a  thousand  times
we  may  expect  at  least  8  aces.

'  Since  it  is  assumed  that  X  obtained  a  first  selector  it  follows  that  in  the  2  minutes
preceding  the  instant  when  X  called  the  number  of  calls  must  have  been  less  than
the  number  of  first  selectors  and  we  should,  therefore,  not  count  the  throws  giving
values  of  C  which  are  not  less  than  the  total  number  of  first  selectors.  This  res-
triction becomes  of  practical  importance  only  where  a  large  proportion  of  the  calls
from  the  first  selectors  go  to  one  level.  To  take  an  extreme  case,  assume  that  all
the  calls  went  to  one  level,  and  that  therefore  each  10  first  selectors  would  require
10  second  selectors  to  handle  the  traffic.  Placing  no  restriction  on  the  value  of  C,
since  C  exceeds  the  number  of  first  selectors  occasionally,  we  would  get  the  result
that  10  second  selectors  were  not  enough  to  handle  all  the  calls  from  10  first  selectors,
which  is  of  course  absurd.  Where,  however,  the  values  of  C  e.xceeding  the  number
of  first  selectors  are  assumed  to  be  distributed  over  all  10  levels  of  the  first  selectors
their  effect  on  the  number  of  second  selectors  is  negligible.

In  practice,  a  modification  of  Problem  II  frequently  arises.  As-
sume an  arrangement  similar  to  that  of  Problem  II  except  that  the
number  of  lines  is  multiplied  by  a  factor  of  perhaps  3  or  more,  each
line  switch,  however,  still  having  access  to  all  first  selectors.  The
required  number  of  first  selectors  will  also  be  larger  but  not  in  ex-
actly the  same  ratio  because  the  margin  of  idle  selectors  need  not  be
relatively  as  great  in  the  large  system  as  in  the  small.  An  enlarged
group  of  trunks  running  from  the  first  selectors  to  the  second  selectors
will  now  be  required,  and  it  will  be  assumed  that  there  are  four  times

as  many  trunks  coming  from  each  level  of  the  first  selectors  as  there
are  points  of  contact  on  each  level.  To  meet  this  situation,  the
first  selectors  and  their  outgoing  trunks  are  divided  into  four  sub-
groups as  shown  in  Fig.  4.  The  corresponding  sub-groups  of  second
selectors  are  designated  by  d,  G2,  G3,  G4,  the  number  of  trunks  to
each  sub-group  being  10.  The  solution  of  this  problem  depends
primarily  on  the  manner  in  which  the  line  switches  distribute  calls
to  the  first  selectors.     Three  cases  will  be  considered.

Referring  to  Fig.  4  consider  a  group  of  n  =  1486  lines,  and  let  the
traffic  be  divided  among  the  ten  levels  or  directions  available  in
such  a  way  that  on  the  average  V3  of  the  calls  are  made  for  a  particular
direction  or  level.  Let  us  suppose  the  circuit  connections  between
the  line  switches  and  first  selectors  to  be  such  that  the  calls  are  dis-
tributed individually  at  random.  By  this  is  meant  that  the  first
selector  seized  by  a  calling  line  is  as  likely  to  be  one  having  access
to  sub-group  Gi  as  to  sub-group  G2,  G3  or  G4.  Note  carefully  that
this  distribution  is  assumed  whether  or  not  the  calling  line  wants
the  particular  level  under  consideration.  One  way  of  securing  this
random  distribution  by  sub-groups  would  be  to  allow  the  line  switches
first  to  choose  by  chance  one  of  the  four  sub-groups  of  first  selectors
and  then  to  choose  an  idle  first  selector  in  the  sub-group.

As  before  we  are  interested  in  the  calls  made  during  the  two  minutes
preceding  the  instant  at  which  X  calls.  Let  the  number  of  these  calls  be
C.  Of  these  C  calls  a  certain  number  D  want  the  level  for  which  X
has  called.  If  at  least  10  of  these  D  calls  were  distributed  by  the
line  switches  to  first  selectors  having  access  to  the  same  sub-group
as  the  one  to  which  the  first  selector  seized  by  X  has  access,  then
there  will  be  no  idle  trunk  in  the  sub-group  for  X.  Our  telephone
trunking  problem  evidently  transforms  to  the  following  series  of
dice  problems.

1st.       1486  throws  are  made  with  a  30  face  die  giving  C  aces.
2nd.     C  throws  are  made  with  a  3  face  die  giving  D  aces.
3rd.      D  throws  are  made  with  a  4  face  die  giving  x  aces,  and  the
question  is  the  probability  that  x  is  not  less  than  10.

By  the  theory  of  dice  (assuming  no  restriction  ^  on  the  value  of
C)  the  probability  is  the  same  as  that  of  throwing  at  least  10  aces  in
1486  throws  with  a  die  having  30  X  3  X  4  =  360  faces.  The  average
number  of  aces  to  be  expected  being  1486/360  =  4.13  the  probability
tables  give  .01  as  the  answer.

As  in  Case  1  assume  that  on  the  average  3^  of  the  calls  are  for
the  level  under  consideration,  but  take  n  =  1725  for  the  number  of
lines.     Now  suppose  the  circuit  connections  between  line  switches

and  first  selectors  to  be  such  that  the  calls  are  distributed  uniformly
to  the  first  selectors,  meaning  that  if  at  any  instant  C  calls  exist,  C/4
of  them  are  on  first  selectors  having  access  to  the  10  trunks  of  sub-
group Gi,  C/4  are  on  first  selectors  having  access  to  the  10  trunks
of  sub-group  G2  and  so  on.  With  a  constant  holding  time  such  as
assumed  this  result  could  be  secured  by  a  device  common  to  all  line
switches  which  would  route  the  first  call  to  the  first  sub-group,  the
second  call  to  the  second  sub-group,  etc.

X  will,  as  before,  be  interested  in  the  calls  falling  in  the  two  minutes
preceding  him.  By  hypothesis  y^  of  these  will  have  been  distributed
to  first  selectors  having  access  to  the  same  sub-group  of  second  selec-
tors as  the  first  selector  seized  by  X.  Finally,  the  probability  is  %
that  one  of  these  calls  wants  the  level  in  which  X  is  interested.  The
equivalent  dice  problem  is  therefore:

aces  which  turn  up  are  noted.     Let  this  number  be  C.
2nd.     C/4  throws  are  made  with  a  3  face  die.

What  is  the  probability  that  this  sequence  of  throws  results  in  at
least  10  aces?  This  probability  is  not  that  of  getting  at  least  10  aces
if  1725  throws  are  made  with  a  die  having  30  X  3  =  90  faces.  We
must  write  separately  the  formula  for  each  of  the  two  steps  of  the
problem,  then  multiply  them  together  and  finally  sum  the  product
for  all  values  of  C/4  from  10  up.  If  this  is  done,  again  ignoring  the
restriction  on  the  upper  limit  of  C,  the  answer  will  come  out  0.01.
Note  that  whereas  in  Case  1  the  average  volume  of  traffic  carried
by  a  sub-group  of  10  trunks  was  4.13,  in  this  case,  with  the  same
probability  of  failure,  it  is  1725  (1/30)  (1/4)  (1/3)  -  4.79.

Number  each  first  selector  and  a  corresponding  card;  shufifle  the
cards  and  deal  out,  for  example,  37  of  them.  The  distribution  under
consideration  is  such  that  when  37  calls  exist  the  probability  that
they  occupy  a  specified  set  of  37  selectors  is  equal  to  the  probability
that  the  cards  dealt  have  the  corresponding  numbers.  This  dis-
tribution of  calls  would  be  measurably  secured  by  arranging  the  line
switch  multiple  so  that  the  trunks  to  the  first  selectors  appear  so  far
as  possible  in  a  different  order  before  every  line  switch.  This  case  of
distribution  differs  from  that  of  Case  1.     In  Case  1,  if  the  first  call

falls  on  a  first  selector  liaxing  access  to  sub-group  d,  for  example,
the  second  call  still  has  the  same  chance  of  falling  on  a  first  selector
ha\ing  access  to  sub-group  Gi  as  on  one  having  access  to  any  one  of  the
other  three  sub-groups.  In  Case  3,  however,  the  busy  first  selectors
tend  to  be  distributed  uniformly  between  the  4  sub-groups,  so  that
if  any  sub-group  should  have  a  preponderance  of  busy  first  selectors
the  probability  of  its  receiving  another  call  is  less  than  the  probability
that  one  of  the  other  sub-groups,  with  more  idle  first  selectors,  should
receive  it.     The  full  discussion  of  this  case  is  reserved  for  the  future.

If  it  is  known  that  one  of  two  events  must  occur  in  any  trial  or
instance,  and  that  the  first  can  occur  in  u  ways  and  the  second  in  v
ways,  all  of  which  are  equally  likeh-  to  happen,  then  the  probability
that  the  first  will  happen  is  mathematically  expressed  by  the  fraction

the  last  equation  following  from  the  first  two,  and  being  the  mathe-
matical expression  for  the  certainty  that  one  of  the  two  events  must
happen.

If  the  probabilities  of  two  independent  events  are  pi  and  p2  re-
spectively, the  probability  of  their  concurrence  in  any  single  instance

of  several  independent  events,  and  P  the  probability  of  their  con-
currence, then

Consider,  now,  what  may  happen  in  n  trials  of  an  event,  for  which
the  probability  is  p  and  against  which   the  probability  is  q.     The

where  the  factor  p  appears  n  times;  that  is  the  probability  is  p".
The  probability  that  the  event  will  occur  («  —  1)  times  in  succession
and  then  fail  is  p""'^  q.

But  if  the  order  of  occurrence  is  disregarded,  this  last  combination
may  arrive  in  n  different  ways;  so  that  the  probability  that  the  event
will  occur  («  —  1)  times  and  fail  once  is  n^"~^  q.  Similarly,  the  prob-
ability that  the  event  will  happen  {n  —  2)  times  and  fail  twice  is
^"~2  g2  multiplied  by  n{n  —  l)/2,  etc.  That  is,  the  probabilities
of  the  several  possible  occurrences  are  given  by  the  corresponding  terms
of  the  binominal  expansion  of  {p  +  qV-     Let

Then  P  =  probability  that  the  event  happens  exactly  n  times,  plus  the
probability  that  it  happens  exactly  {n  —  1)  times  .  .  .  plus

If  the  series  for  P  contains  few  terms  it  may  be  computed  easily.
In  general,  however,  it  is  impracticable  to  compute  P  by  means  of
the  above  binomial  expansion.  Other  forms  for  the  value  of  P
must,  therefore,  be  developed.

One  of  the  most  convenient  approximations  for  P  when  p  is  small
has  been  developed  by  Poisson.  It  is  known  as  Poisson's  Exponen-
tial Binomial  Limit  and  gives  the  value  of  P  by  the  following  ex-
pansion

The  following  Table  gives  corresponding  values  of  P,  a,  c  satisfying
equation  (2).

Averages  (a)    Corresponding  to  Deviation   (d)   plus  Average  (a)   to  be  Expected  with

The  Relation  Between  Rents  and  Incomes,  and
the  Distribution  of  Rental  Values

Synopsis:  Many  parts  of  telephone  plant,  such  as  central  office  buildings
and  equipment,  conduits,  underground  and  aerial  cable  at  the  time  of
installation  must  have  the  capacity  to  handle  not  only  the  immediate
demand  for  telephone  service,  but  also  to  take  care  of  growth  for  a  number
of  years  to  come.  In  order  to  engineer  such  items  of  telephone  plant
economically  it  is  necessary  to  know  in  advance  as  accurately  as  possible
what  the  demand  for  telephone  service  will  be  five,  ten,  or  twenty  years
in  the  future.  Forecasts  of  the  future  market  are  very  necessary
for  plant  engineering,  operating  plans,  rate  treatment,  and  other  purposes,
in  multi-central  office  cities.  In  such  cities  detailed  estimates  are  made
of  the  market  some  twenty  years  ahead  and  of  its  telephone  development
under  stated  rate  conditions.  Such  estimates  are  called  commercial  surveys,
and  they  involve  a  study  of  the  various  factors  which,  in  the  course  of  events,
will  be  likely  to  control  the  industrial,  commercial  and  residential  develop-
ment of  the  city  concerned.

In  the  course  of  such  a  survey,  a  rental  classification  of  all  families  is
obtained  and  at  the  same  time  a  record  is  made  of  existing  telephone  service
in  each  rental  class.  The  rent  data  of  this  article  have  been  gathered  in
representative  large  cities  throughout  the  country  and  the  results  as  here
set  forth  are  being  used  together  with  many  other  kinds  of  data  to  guide
the  engineering  of  future  additions  to  the  plant  of  the  Bell  Telephone  System.

In  general  the  income  of  a  family  is  an  index  of  the  market  it  creates  for
various  commodities  including  telephone  service.  Rental  values  may  also
be  considered  as  such  an  index  and  the  present  study  seeks  to  correlate  rents
with  incomes.  Rents  can  be  readily  recorded  and  classified,  whereas  it  is
not  feasible  to  determine  the  money  incomes  of  large  numbers  of  families.
While  it  may  be  ideally  possible,  by  a  study  of  rent  data,  to  compare  the
inherent  markets  for  telephone  service  and  also  the  strength  of  the  tele-
phone habit  in  various  cities,  there  are  many  practical  limitations  to  such
a  procedure.  Comparison  of  the  residence  market  for  telephone  service
in  different  cities,  as  determined  by  rent  values,  is  made  difficult  by  the
fact  that  the  variation  between  cities  in  rentals  paid  for  substantially  similar
dwellings  is  considerably  greater  than  the  variation  in  prices  for  food  or
clothing.  Further,  there  is  considerable  variation  in  rent  levels  even  in
different  sections  of  any  one  city.  Attempts  to  compare  rent  distribu-
tions by  application  of  the  usual  statistical  measures  of  dispersion  and
skewness  have  proved  unsatisfactory.  However,  a  method  of  charting
has  been  found  by  which  rent  distributions  may  be  readily  compared
with  one  another  and  an  index  of  spread  or  dispersion  determined.  It
has  been  found  that  cumulative  curves  of  rent  distribution  may  be  plotted
on  logarithmic  probability  paper  to  yield  straight  lines  for  a  large  number
of  cities.  These  are  called  logarithmic  skew  distributions.  Although  it
has  not  been  found  possible  to  assign  any  special  significance  to  the  par-
ticular value  of  the  index  of  rent  dispersion  in  any  city,  this  index  appears
to  remain  practically  constant  for  that  city  regardless  of  changes  in  the
level  of  prices.  In  the  appendix  the  mathematical  features  of  the  loga-
rithmic skew  curve  are  discussed. — Editor.

TT  is  a  well  recognized  fact  that  the  better  class  families,  i.e.,  those
-■-  with  higher  incomes,  are  a  better  market  for  telephone  service
than  the  poorer  families.  For  purposes  of  market  analysis  in  com-
mercial surveys  it  is  not  feasible  to  determine  the  money  incomes
received  by   families  but  the   rental  values  of  dwellings,   which,  as

will  be  shown,  are  a  measure  of  the  incomes  of  their  occupants,  are
comparatively  readily  collected  and  classified.  Rent  data  obtained
in  the  course  of  a  commercial  survey  show  the  "character"  of  a  city
and  are  used  as  a  basis  for  estimates  of  the  future  residence  telephone
market.

In  view  of  the  importance  of  these  rent  data,  it  seems  desirable
to  study  them  in  some  detail  to  find  out  just  what  their  limitations
are.

There  may  be  set  down  in  advance  certain  things  which  it  is  desirable
to  know,  as,  for  instance,  the  relationship  betw-een  money  incomes
and  house  rents  and  methods  and  limitations  of  comparison  of  different
cities  on  the  basis  of  rental  values.  On  the  first  point,  as  applied  to
any  particular  city,  a  knowledge  of  the  relation  between  incomes  and
rents  is  desirable  in  a  general  way,  although  there  is  no  necessity  to
translate  the  telephone  market  expressed  in  terms  of  rent  types  into
a  scale  of  incomes.  On  the  second  point,  the  comparison  of  different
cities,  it  should  be  ideally  possible  by  a  study  of  rent  data  to  compare
the  inherent  economic  markets  for  telephone  service,  and  also  to
measure  differences  in  the  strength  of  the  telephone  habit,  but  in
practice  only  rough  approximations  may  be  made.

Certain  limitations  to  work  of  this  kind  are  fairly  evident.  The
most  obvious  difficulty  is  the  fact  that  rent  levels  have  changed
along  with  the  general  price  level.  Rent  lev^els  in  various  cities  differ
according  to  the  varying  degrees  of  housing  congestion  and  the
varying  social  standards  of  the  population.  Furthermore,  the  varia-
tion in  rent  levels  extends  to  different  sections  of  any  one  city.  The
mere  fact  that  a  given  family  paid  say  $30  rent  is  not  an  indication
of  that  family's  economic  condition  or  its  value  as  a  telephone  pros-
pect, unless  there  is  also  known  the  city  and  the  part  of  the  city  in
which  that  family  lived,  and  the  time  when  the  given  rent  was  paid.
Therefore  rent  data  from  different  cities  and  of  various  dates  are
not  directly  comparable  at  their  face  value.  To  adjust  the  money
values  of  house  rents  for  an  accurate  comparison  of  the  telephone
markets  in  different  cities  w'ould  require  a  knowledge  of  the  relative
proportions  of  income  spent  for  rent  in  the  different  cities,  of  the
relative  levels  of  incomes  and  rents  at  the  time  of  the  surveys  as
compared  w^ith  their  levels  in  some  base  year,  and  perhaps  of  other
factors  equally  difficult  to  estimate.

Various  rent  tabulations  can  not  be  compared  one  with  another
without  knowing  something  of  the  way  in  which  rents  are  distributed
about  their  average.  The  nature  of  the  distribution  is  determined
by  the  house  count  data,  but  from  those  data  in  their  usual  form  it

is  not  easy,  when  making  comparisons,  to  make  proper  allowances  for
differences  in  rent  levels  and  in  the  schedule  of  rent  classes.  In  the
following  pages  there  is  discussed  a  method  of  charting  by  which
rent  distributions  may  be  readily  compared,  and  their  spread  or
dispersion  determined.

Rents  as  a  Market  Index.  The  relation  between  rents  and  incomes
is  concerned  with  the  use  of  rental  values  both  as  an  index  of  tele-
phone market  in  a  given  city,  and  in  comparing  the  markets  in  differ-
ent cities.  In  what  follows  it  is  not  always  possible  to  separate  these
two  views,  but  the  distinction  should  be  borne  in  mind  by  the  reader.

The  goal  of  an  analysis  of  residence  telephone  market  is  to  determine
the  future  sales  possibilities.  In  theory  either  incomes  or  rents  may
be  considered  as  an  index  of  the  telephone  market.  The  market
index  adopted  in  commercial  surveys  is  the  rental  of  dwellings.
This  may  be  considered  either  as  a  direct  measure  of  the  ability
and  desire  of  families  to  subscribe  to  telephone  service,  or  as  an
indirect  index,  if  incomes  are  considered  the  real  measure  of  the
market.  If  the  first  viewpoint  is  accepted,  it  may  be  logically  con-
cluded, although  not  proved,  that  rents  are  a  better  index  of  tele-
phone market  than  are  incomes.  Incomes,  as  measured  in  money,
are  the  nearest  approach  which  may  be  made  to  a  measure  of  the
position  of  families  on  an  imaginary  scale  of  economic  welfare.  An
attempt  to  translate  rent  data  to  an  income  basis,  as  a  working
method  in  commercial  surveys  would  introduce  errors  with  no  com-
pensating advantage,  but  a  translation  of  this  kind  is  more  or  less
unconsciously  made  in  making  comparisons.

Sources  of  Information.  Much  of  the  literature  on  the  question  of
house  rents  versus  incomes  is  generalization  based  on  limited  or
antiquated  data.  Such  careless  statements  as  "rent  approximates
about  one-third  of  the  average  worker's  income,"  may  be  found  in
the  literature  of  the  subject.  Adam  Smith,  the  father  of  Political
Economy,  "made  the  assertion,  surprising  to  us  in  these  days,  that
the  proportion  of  income  spent  in  house  rent  is  highest  among  the
rich."  Frederick  Engels  concluded  in  1857  that  rent  was  12  per
cent  and  heat  and  light  5  per  cent  of  the  workingman's  expenditure,
regardless  of  the  amount  of  his  income.

Investigation  of  budgets  in  recent  years  has  been  confined  almost
entirely  to  the  field  of  the  wage  earning  class.  The  first  really  com-
prehensive study  was  made  by  the  United  States  Bureau  of  Labor

Statistics  in  several  states  in  1901  and  1902,  and  is  detailed  in  the
1903  annual  report  of  that  organization.  It  consisted  chiefly  of  a
study  of  11,156  so-called  "normal"  families,  each  including  a  husband
at  work,  a  wife,  not  more  than  5  children  all  under  14  years  and  no
lodgers  or  servants.  The  average  income  of  these  families  was  S651.
Original  work  on  a  smaller  scale  has  been  done  by  R.  C.  Chapin
(1908)  and  by  the  Philadelphia  Bureau  of  Municipal  Research  (1918).
The  Bureau  of  Labor  Statistics  collected  a  large  amount  of  data  in
1918  and  1919^  concerning  the  incomes  and  expenses  of  12,837  families
in  92  towns  having  an  average  income  of  $1491.  This  investigation
included  families  of  wage  earners  and  low  salaried  men,  but  none  of
the  slum  or  recent  immigrant  classes.  Families  of  the  lowest  type
are  automatically  excluded  from  such  studies  as  this  by  their  inability
to  supply  the  desired  information  from  accounts  or  from  intelligent
estimates.

Distribution  of  Family  Expenses.  Representative  distributions  of
family  expenditures  are  given  in  Table  I.  The  National  Industrial
Conference  Board  has  adopted  for  use  in  computing  their  cost  of
living  index  and  representative  budgets  a  list  of  standard  weights
made  by  combining  the  results  of  a  number  of  studies  made  from
1901  to  1917.  Most  importance  was  assigned  to  the  first  Bureau  of
Labor  Statistics  study,  the  results  of  which  it  closely  resembles.
The  standard  weights  used  by  the  Bureau  of  Labor  Statisics  are  the
result  of  surveys  made  in  22  cities  from  July  31  to  November  30,  1918,
covering  families  whose  average  income  was  $1,434.

From  Table  I  it  may  be  inferred  that  the  per  cent  spent  for  rent
is  reduced  in  a  period  of  inflated  prices,  at  least  during  the  first  part
^  Monthly  Labor  Review,  May-December,  incl.,  1919.

of  that  period.  This  is  reasonable,  since  rents  respond  less  rapidly
than  most  other  prices  to  fluctuations  in  the  general  price  level.  An
extreme  example  of  this  type  is  found  in  Germany  where  rents,
which  are  to  some  extent  under  government  regulation,  "at  the
present  time  absorb  not  more  than  3>^  per  cent  of  total  expenditure
as  against  20  per  cent  before  the  war."  ^

The  percentage  distribution  of  total  expenses  depends  on  the  size
of  the  family,  the  income  received  and  the  city  lived  in.  Of  course,
it  must  be  understood  that  any  particular  family  may  differ  widely
from  general  averages.  Other  things  being  equal,  large  families  spend
more  for  food  and  clothing  and  less  for  rent  and  sundries  than  do
small  families.  Large  families  of  the  lower  middle  class  accommodate
themselves  to  whatever  housing  accommodations  they  can  afford
after  the  more  inflexible  demands  for  other  things  have  been  provided
for.  Less  than  one  room  per  person  is  considered  over-crowding
and  the  recent  Bureau  of  Labor  Statistics  investigation  found  this
condition  to  exist  rarely,  except  in  families  having  more  than  three
children.  Families  with  one  to  three  children  were  found  to  have
LO  to  L3  rooms  per  person  in  almost  all  cities.

Amount  of  Income  vs.  Per  Cent  Spent  for  Rent.  The  extent  to  which
the  distribution  of  expenses  is  modified  by  the  amount  of  income
received  is  known  only  within  the  very  limited  range  for  which  data
are  available.  The  best  recent  figures  are  those  of  the  1918-1919
study  of  the  Bureau  of  Labor  Statistics.  These  are  given  here  for
12,096  white  families  in  92  cities  and  towns:

When  the  original  data  are  examined  in  detail,  it  appears  that  in
almost  every  city  as  incomes  increase  the  per  cent  spent  for  rent
^  M.  Elsas.  Economic  Journal,  September,  1921,  p.  332.

and  fcHxl  decreases  and  the  per  cent  for  clothing  increases.  The
decrease  in  the  per  cent  for  food  as  incomes  increase  is  slight  and  the
increase  in  the  per  cent  for  clothing  is  especially  marked  in  the  higher
incomes  within  the  range  covered.  Thus,  it  appears  that  among
families  of  moderate  incomes  as  incomes  rise  the  increase  is  spent
by  preference  for  clothing  rather  than  for  food  or  rent.  The  relative
decrease  in  expenditure  for  rent  as  incomes  increase  is  significant  in
rental  analysis.  This  means  that  while  a  10  per  cent  difference  in
rents  among  the  lower  rents  in  a  city  indicates  an  average  difference
in  income  of  about  10  per  cent,  a  similar  difTerence  among  the  higher
rents  indicates  a  difference  in  income  of  much  more  than  10  per  cent.

Rent  Levels  in  Various  Cities.  As  nearly  as  may  be  determined
from  the  Bureau  of  Labor  Statistics  data,  there  is  no  regular  tendency
for  Eastern,  Western  or  Southern  cities  to  differ  from  the  average
of  all  cities,  either  in  the  amount  of  wage-earners'  incomes  or  in
amounts  spent  for  food  or  clothing.  In  Southern  cities  somewhat
less  is  paid  for  rent  than  in  other  cities.  This  refers  only  to  w^hite
families.  Negro  families  have  smaller  average  incomes  than  white
families  and  at  any  given  income  they  spend  less  for  rent,  more  for
food  and,  to  a  less  degree,  more  for  clothing  than  white  families.
The  size  of  a  city,  so  far  as  may  be  told  from  these  data,  does  not
determine  either  total  incomes  or  expense  for  food,  rent  or  clothing.

In  different  cities  the  difference  in  rent  levels,  that  is,  variation  in
rentals  paid  for  substantially  similar  dwellings,  is  considerably  greater
than  the  difference  in  levels  of  prices  for  food  or  clothing.  The  varia-
tion in  price  levels  is  about  twice  as  great  for  rents  as  for  food  or
clothing,  reckoned  as  percentages  of  the  amounts  spent  for  each  class.
The  expenditure  for  food  by  the  lower  middle  class  families  included
in  this  investigation  is  more  nearly  the  same  in  different  cities  than
is  the  expenditure  for  rent  or  for  clothing.  Food  expense  is  the  only
one  of  these  classes  in  which  all  cities  are  as  closely  grouped  as  in
total  expenses,  considering  deviations  from  the  averages  on  a  per-
centage basis.  The  amounts  spent  for  rent  show  relatively  wide
variation  between  cities.  It  appears  that  if  a  workman  moves  from
one  city  to  another  to  secure  increased  wages  a  large  proportion  of
the  increase  in  income  goes  for  increased  rent.  This  is  to  be  expected
since  land  rents  and,  to  a  less  extent,  construction  costs  are  peculiar
to  each  individual  city,  much  more  than  food  or  clothing  costs.

A  comparison  of  rent  data  from  the  1918-1919  investigation  of  the
Bureau  of  Labor  Statistics  and  data  from  Commercial  Surveys  leads
to  the  conclusion  that  differences  in  average  rents  in  various  cities
are  due  at  least  as  much  to  differences  in  the  level  of  prices  for  rents

as  to  differences  in  the  grade  of  the  population.  Wage-earners  and
low  salaried  people  of  the  types  studied  by  the  Bureau  of  Labor
Statistics  occupy  about  the  same  position  in  the  community  in  a
large  number  of  cities.  As  a  rule  they  pay  about  80  to  90  per  cent
of  the  median^  rent  in  any  city.  Exception  must  be  made  in  the
case  of  cities  having  an  unusually  large  proportion  of  negro  or  very
low  grade  white  population.  It  is  interesting  in  this  connection  to
compare  wage  rates  for  different  classes  of  labor  in  various  cities.
The  variation  between  cities  in  wage  rates  for  common  labor  is  pro-
portionately much  greater  than  the  variation  in  wages  for  work
requiring  some  skill,  such  as  bricklaying  and  structural  iron  work.

As  examples  of  the  impossibility  of  accurately  rating  the  grade
of  a  city's  population  by  its  median  rent  alone,  we  may  take  four
cities  where  surveys  were  made  in  1921.  Spokane  and  Houston  had
practically  identical  median  rents  of  $23.00  and  $23.40  respectively,
but  Houston  is  not  as  good  a  telephone  market  as  Spokane.  In
Cleveland  and  Minneapolis  the  median  rents  were  found  to  be  $35.50
and  $31.00  respectively,  but  this  is  no  measure  of  the  grades  of  the
two  cities.

Rent  Data  from  Various  Sources,  Including  England.  Some  addi-
tional rent  data  is  presented  here  without  extended  comment.  The
two  following  tables  show  the  proportion  which  rent  bears  to  total
expense  in  different  communities.

The  first  four  of  these  "standard"  budgets  are  by  the  National
Industrial  Conference  Board,  and  the  others  in  order  b\-  the  Bureau
of  Municipal  Research  (Philadelphia),  Professor  W.  F.  Ogburn,
and  the  U.  S.  Bureau  of  Labor  Statistics.

It  has  already  been  mentioned  that  the  per  cent  spent  for  rent
shows  a  tendency  to  decrease  with  increasing  incomes.  This  trend
is  confined  by  data  from  other  sources,  as  follows:

Although  no  data  are  av'ailable  for  families  above  the  lower  middle
class,  the  relationship  may  be  extended  by  conjecture  into  the  higher
income  levels.  That  this  is  reasonable  is  brought  out  in  subsequent
pages  in  comparing  distribution  curves  of  rental  values  and  incomes.

Some  interesting  conclusions  from  English  experience  are  given
by  Sir  J.  C.  Stamp. ^  The  rent  corresponding  to  an  income  of  £160
averages  at  least  £5  greater  in  London  than  outside  that  city.  Among
the  lower  incomes,  say  up  to  £1000,  the  variation  or  dispersion  of  the
percentages  paid  for  rent  becomes  less  as  the  amount  of  the  income
rises.  Owner-occupants  live  in  larger  houses  than  tenants  with  the
same  total  income.  It  was  not  found,  as  is  generally  supposed,  that
professional  men  pay  relati\'ely  more  for  rent  than  business  men.  The
following  table  is  from  the  work  abo\e  mentioned ;

The   second   of   these   two   tables   represents  average   conditions   for
Great  Britain.

In  making  comparisons  of  survey  rent  data  it  is  desirable  to  dis-
tinguish differences  in  price  levels  as  they  afTect  rents,  difTerences
in  economic  grade  of  the  population,  and  differences  in  the  distri-
bution of  families  about  their  average  grade.  Failure  to  take  account
of  these  three  factors  will  result  in  misleading  impressions,  which  may
be  illustrated  by  summaries  from  successive  surveys  in  Atlanta.
The  following  table  shows  composites  of  private  residences,  flats  and
apartments:

It  might  be  inferred  from  this  set-up  that  the  condition  of  the
poorer  families  had  been  very  much  improved  or  that  the  average
family  had  attained  a  higher  condition  of  well-being.  It  will  be
shown  later  that  there  was  no  material  change  in  the  distribution  of
rental  values  about  an  average  rent  when  rents  are  considered  as
percentages  of  that  average,  and   it  is  probable  that  the  principal.

if  not  the  sole  cause  of  the  changes  shown  in  the  table  above,  is  the
general  rise  in  the  le\'el  of  prices.

Methods  of  Study — Graphic  Representation.  The  most  convenient
and  practical  method  of  studying  rent  distributions  is  by  the  use
of  graphs  and  charts.  The  distribution  of  values  of  renjs  or  of  other
variables  may  be  charted  in  either  a  detail  or  a  cumulative  form.  A
detail  curve  shows  at  any  value  of  the  independent  variable  the
frequency  of  occurrence  of  items  of  that  value.  A  cumulative  curve
shows  at  any  value  of  the  variable  the  number  (or  better,  the  per
cent)  of  all  cases  which  have  values  below  (or  above)  that  value.
Cumulative  curves  are  better  than  detail  curves  for  presenting  rent
data  since  the  number  of  classes  into  which  the  data  are  divided  is
small  and   the  class  widths  are  non-uniform,   resulting  in   uncertain

curves  of  the  detail  type.'^  Attempts  to  compare  rent  distributions
by  application  of  the  usual  statistical  measures  of  dispersion  and
skewness  have  proved  unsatisfactory.

Typical  rent  distributions  plotted  in  the  cumulative  manner  on
ordinary  coordinate  paper  are  shown  in  Fig.  1.  Diagrams  of  this
type  may  be  used  to  determine  the  rent  paid  by  families  of  correspond-
ing position  in  the  rent  scale  at  the  dates  of  successive  surveys,  but
they  do  not  give  a  very  clear  picture  of  changes  in  the  distribution  of
rents  and  from  them  it  is  not  readily  apparent  whether  rents  are
closely  concentrated  or  widely  distributed  in  any  given  case.

^  Detail  curves  for  rent  and  income  distributions  are  most  easily  drawn  on  paper
with  a  logarithmic  scale  both  ways.

Logarithmic  Probability  Charts.  Cumulative  curves  for  rent  dis-
tributions may  be  plotted  on  logarithmic  probability  paper®  in  which
case  the  resulting  graph  is  a  straight  line  for  a  large  number  of  cities.
Such  a  graph  will  be  said  to  represent  a  logarithmic  skew  distribution.
In  the  appendix  there  is  given  a  discussion  of  frequency  curves,
with  special  reference  to  curves  of  this  type.  The  essential  point
in  reading  charts  on  logarithmic  probability  paper  is  that  the  slope
of  the  line  determines  both  the  spread  or  dispersion  of  the  data  and
the  skewness  or  lack  of  symmetry  of  distribution.  Since  the  hori-
zontal scale  is  logarithmic  it  follows  that  the  dispersion  is  represented
on  a  percentage  and  not  a  linear  basis.  A  steep  slope  indicates  a
close  concentration  of  the  data,  a  less  steep  slope  indicates  a  wider
distribution,  and  parallel  lines  indicate  distributions  which  are  identical
on  a  percentage  basis.  As  explained  in  the  appendix,  the  most  con-
venient index  or  coefficient  for  expressing  the  spread  or  dispersion
of  a  distribution  is  the  ratio  of  the  upper  quartile'^  to  the  median  rent.
If  the  curves  for  a  given  city  are  closely  parallel  for  successiv'e  surveys
it  follows  that  there  has  been  no  material  change  in  the  character  of
the  distribution.  In  other  words,  rents  have  increased  approximately
proportionately  at  all  points  of  the  scale.

Examples  of  charts  of  this  kind  (Figs.  2-4)  are  shown  for  twelve
cities  for  which  successive  surveys  are  available.  Curves  for  suc-
cessive surveys  are  nearly  parallel  in  eight  of  the  twelve  cities.  For
Cleveland,  Dallas  and  Houston  there  are  distinct  differences  in  the
curves  for  the  two  dates,  indicating  changes  in  the  distribution  of
rents,  which  changes  may  be  measured  since  horizontal  distances
between  points  on  the  curves  for  two  dates  represent  the  percentage
increases  in  rents.

When  a  rent  distribution  is  plotted  on  logarithmic  probability
paper  the  points  do  not  always  lie  on  a  straight  line,  but  a  straight
line  of  best  fit  may  be  chosen  by  eye,  giving  greatest  weight  to  points
near  the  middle  of  the  scale  of  ordinates.  Of  the  rent  distributions
for  large  cities  which  have  been  plotted  on  this  paper,  nearly  one-
third  are  very  closely  represented  by  straight  lines,  an  equal  number
are  slightly  concave  upward,  and  the  remainder  are  more  or  less
concave  downward.  Most  of  the  deviations  from  straight  lines  are
slight.  The  examples  submitted  herewith  (cities  in  which  successive
surveys  have  been  made)  are  rather  poorer  than  the  average  in  this

"See  an  article  by  G.  C.  Whipple  in  the  Journal  of  the  Franklin  Institute  for  July
ajid  August,  1916,  for  a  description  of  this  paper  and  some  examples  of  its  use  in  the
field  of  sanitation.

respect.  Concavity  upwards  represents  a  distribution  which  is  less
skew  than  the  theoretical  logarithmic  skew  curve,  and  concavity
downwards  a  distribution  of  greater  skewness.  No  great  importance
can  be  assigned  to  small  differences  of  this  sort,  as  they  are  not  perma-
nent betw^een  successive  surveys,  whereas  the  general  type  of  the
distribution  is  quite  constant  for  a  given  city.

The  justification  for  assuming  that  rents  follow  the  logarithmic
skew  curve  is  made  stronger  by  certain  data  from  Volume  19  of  the
report  of  U.  S.  Immigration  Commission  made  in  1912.  This  com-
mission collected  a  large  mass  of  data  concerning  the  living  conditions
of  families  of  the  immigrant  type.  The  data  are  classified  by  nation-
ality of  head  of  family,  by  income,  etc.  Distributions  of  amounts
paid  for  house  rent  per  apartment,  per  room  and  per  person  for  certain
nationalities  are  shown  in  Fig.  5.  The  data  shown  were  chosen  from
those  classes  which  were  made  up  of  the  largest  numbers,  and  the
deviations  from  straight  lines  shown  by  data  for  other  groups  are  in
both  directions,  so  the  straight  line  relation  may  be  considered  fairly
representative.  It  may  be  noted  that  the  rents  per  month  per  person
show  a  greater  dispersion  than  the  rents  per  room  or  per  apartment.
These  latter  moreover  show  as  small  a  spread  as  do  rents  for  any  of
the  cities  studied  as  a  whole.

Fig.  5  also  shows  the  distribution  of  British  house  rents  at  intervals
during  the  period  1890-1913.  There  has  been  a  gradual  but  steady
decrease  in  the  dispersion  of  rents  during  the  period  covered.  Unless
the  relation  between  rents  and  incomes  has  radically  changed,  this
means  that  the  inequality  of  distribution  of  wealth  has  been  decreased,
and  that  the  condition  of  the  poor  has  been  improved  as  compared
to  that  of  the  rich.  Data  for  1830  indicate  that  the  inequality  of
distribution  was  distinctly  greater  at  that  date  than  in  1890.  Changes
in  the  relative  condition  of  the  rich  and  poor  may  be  readily  demon-
strated by  charts  of  this  kind,  but  of  course  conclusions  regarding
absolute  degrees  of  well-being  must  be  reached  by  other  means.

Distribution  of  Rents  Compared  with  that  of  Incomes.  Significant
conclusions  regarding  the  relation  between  rents  and  incomes  may  be
drawn  from  a  comparison  of  their  respective  distributions.  Fig.  6
shows  a  detail  curve  for  income  distribution  in  the  United  States
based  on  preliminary  data  of  the  National  Bureau  of  Economic
Research.  These  data  are  subject  to  revision  but  are  the  best  avail-
able and  are  sufficiently  accurate  for  comparative  purposes.  The
usual  way  to  chart  income  distribution  assumes  conformity  with
Pareto's  law  which  says  that  the  frequency  curve  of  incomes  may
be  plotted  as  a  straight  line  on  double  logarithmic  paper,  either  on  a

detail  or  cumulative  basis.  This  law  does  not  hold  for  the  lower
income  levels  which  may  be  best  represented  by  a  curve  of  approxi-
mately hyperbolic  form,  as  shown  in  Fig.  6.  The  same  income  data
are  shown  plotted  on  logarithmic  probability  paper  in  an  insert  on

Based  on  Preliminary  Data  from  the
National  Bureau  of  Economic  Resrarch

Fig.  6.  From  the  form  of  this  curve  it  may  be  concluded  that  the
distribution  of  the  lower  two-thirds  of  both  incomes  and  rents  is
similar  but  that  the  spread  of  the  higher  incomes  is  much  greater
than  the  spread  of  the  corresponding  rents.

Another  comparison  of  incomes  and  rents  may  be  made  from  a
second  insert  on  the  same  chart.  It  may  be  readily  demonstrated
that  the  normal  curve  of  error  plots  as  a  parabola  on  semi-logarithmic
paper  and  the  logarithmic  skew  curve  as  a  parabola  on  double  logar-
ithmic paper.  Two  parabolas  which  represent  extreme  conditions  of
spread  and  of  concentration  of  rents  in  large  cities  are  shown.  If
the  degree  of  dispersion  remains  fixed  a  change  in  the  rent  level
merely  shifts  the  parabola  on  the  chart  without  changing  its  shape.
The  parabolic  shape  of  rent  curves  and  the  hyperbolic  shape  of  the
income  curve  indicate  that  rents  are  somewhat  less  concentrated
locally  about  their  mode,^  but  are  more  concentrated  as  an  entire
group  than  are  incomes.  These  curves  can  not  well  be  superposed
for  comparison  since  areas  are  not  equivalent  on  different  parts  of
the  chart.  Those  incomes  which  are  closely  grouped  around  the
mode  represent  wage-earners  of  such  a  type  that  several  may  come
from  a  single  family.  Conclusions  regarding  comparison  of  incomes
and  rents  must  be  made  with  caution  since  rents  are  on  a  family
basis  and  incomes  on  an  individual  basis.  No  satisfactory  data
are  available  to  show  the  variation  in  income  distribution  between
small  subdivisions  of  the  United  States,  as  cities,  but  it  is  reasonable
to  assume  that  there  is  some  such  variation  for  incomes  as  well  as
for  rents,  although  perhaps  not  of  so  great  a  range.

A  third  comparison  of  incomes  and  rents  is  made  possible  by  the
use  of  Lorenz  curves  illustrated  in  Fig.  7.     On  this  form  of  chart  a
*  See  Appendix.

diagonal  line  at  45  represents  a  uniform  distribution  and  the  further
a  given  curve  falls  to  the  right  of  and  below  that  line  the  more  unequal
the  distribution  represented.  If  incomes  were  plotted  on  a  family
basis,  the  resulting  curve  would  lie  somewhat  closer  to  the  diagonal
line  than  the  one  shown,  but  it  is  fairly  evident  that  incomes  are
more  unequally  distributed  than  rents.  For  instance,  the  top  10
per  cent  of  incomes  are  on  the  average  about  42  per  cent  of  the  total
income,  while  the  top  10  per  cent  of  rents  are  from  22  to  32  per  cent  of
the  aggregate  rent  in  most  cities.  These  three  comparisons  confirm
the  idea  discussed  in  the  first  part  of  this  paper,  that  the  proportion
of  income  spent  for  rent  is  less  among  the  larger  incomes.

Of  the  extensive  data  on  income  distributions  few  can  well  be  used
for  comparison  with  rent  data.  In  order  that  a  cumulative  curve
really  mean  anything,  it  must  represent  an  entire  group,  not  merely
items  from  one  end  or  the  other  of  the  complete  scale.  Therefore,  the
various  tables  of  earnings  of  working  class  families  and  individuals
are  of  doubtful  use  here,  although  they  do  show,  plotted  on  double
logarithmic  or  logarithmic  probability  paper,  that  the  type  of  dis-
tribution of  earnings  about  an  average  value  is  practically  identical  for
various  nationalities  in  similar  industries,  or  for  men,  women  and
children  in  all  industries.  However,  the  average  earnings  of  the
various  classes  are  widely  different.  A  few  examples  are  shown  in
Fig.  5.

Income  tax  returns  are  of  some  interest  although  they  are  defective
in  several  respects:  they  only  include  the  upper  part  of  society,  a
large  number  of  persons  fail  to  make  returns  and  large  amounts  of
income  are  tax  exempt.  Federal  income  tax  data,  which  are  available
on  a  uniform  basis  for  the  years  1917-1920,  may  best  be  studied  by
plotting  on  double  logarithmic  paper,  preferably  after  reducing  the
figures  for  the  various  states  to  a  basis  of  returns  per  1000  popula-
tion. There  are  small  changes  from  year  to  year  in  the  position  of
the  curve  for  any  given  state,  which  are  not  significant,  since  they
may  be  due  either  to  changes  in  the  average  income,  or  to  increased
efficiency  of  tax  collection.  Changes  from  year  to  year  in  the  slope
of  the  curve  for  any  one  state  are  small,  indicating  that  there  exists
in  each  state  a  definite  type  of  distribution  of  wealth  and  earning
power.  Differences  in  the  position  and  slope  of  the  curves  for  dif-
ferent, states  are  conspicuous,  indicating  that  both  the  per  capita
income  and  the  distribution  of  the  total  income  among  individuals
are  different  in  different  states.  New  York,  for  instance,  shows  a
wide  spread,  i.e.,  a  relatively  large  number  of  very  high  incomes,  and
Iowa  shows  a  narrow  spread,  i.e.,  a  large  number  of  incomes  around

$2000-5000,  and  comparatively  few  incomes  over  $20,000.  New
Jersey  occupies  an  intermediate  position.  Alabama,  more  or  less
typical  of  Southern  states,  shows  a  much  smaller  number  of  returns
in  proportion  to  population  than  any  of  these  states,  and  a  distribu-
tion nearly,  but  not  quite,  as  closely  grouped  as  Iowa.  The  fact
that  a  particular  shape  of  curve  is  typical  of  a  given  state,  and  that
the  curves  are  different  for  different  states,  corresponds  to  similar
characteristics  of  rent  curves  for  cities.  British  income  statistics
show  about  the  same  degree  of  dispersion  as  do  returns  for  the  United
States  as  a  whole.

Distributions  of  the  logarithmic  skew  type  may  be  found  in  other
fields  than  those  of  incomes  and  house  rents.  The  theory  has  been
advanced  by  some  statisticians  that  while  the  normal  curve  of  error
is  characteristic  of  observational  errors,  errors  of  estimate  agree  with
that  law  if  logarithms  rather  than  actual  estimates  be  considered.
Price  fluctuations,  corporation  earnings,  and  the  profits  of  farmers
are  distributed  in  a  similar  manner.  The  lengths  of  life  of  telephone
contracts  agree  quite  closely  with  this  type  of  distribution,  if  we
allow  for  the  fact  that  very  long  lives  are  relatively  few  in  number
because  they  started  when  the  telephone  business  was  comparatively
small.  A  peculiarity  of  rent  distribution  is  that  if  we  choose  only
families  having  telephone  service,  or  families  having  any  one  class
of  service,  we  obtain  a  logarithmic  skew  distribution  about  as  closely
as  though  we  plotted  all  families  in  a  city.

Application  to  Survey  Data.  The  charting  method  described  above
was  applied  to  rent  data  for  57  cities,  both  for  composites  of  private
residences,  flats  and  apartments  and  for  private  residences  alone.
Table  VIII  gives  the  median  rents  and  values  of  the  rent  dispersion
index  Q^  for  the  composite  data.  Results  for  private  residences
differ  in  most  cases  only  very  slightly  from  the  results  given;  there
is  no  dominant  tendency  for  the  spread  of  private  residence  rents  to
be  greater  or  less  than  that  of  all  rents  in  a  city,  but  the  median  rent
in  private  residences  is  usually  somewhat  greater  than  that  for  the
composite.

An  effort  was  made  to  determine  the  significance  of  the  various
values  of  the  index  Q,  but  the  results  are  chiefly  negative.  There
is  some  tendency  for  the  smaller  cities  to  have  a  wide  spread  of  rent
values;  i.e.,  a  high  value  for  Q,  but  there  is  considerable  scattering
of  the  data.  This  tendency  is  most  apparent  in  the  South,  where  the
smaller  cities  have  extremely  high  values  for  Q.  The  relationship
between  the  index  Q  and  the  per  cent  of  families  with  telephone
•  See  Appendix  for  a  quantitative  definition  of  Q.

service  is  not  very  well  defined.  Cities  with  a  very  high  residence
development  have  low  values  for  the  index  and  Southern  cities  with
poor  residence  development  have  high  values  for  Q,  but  the  inter-
mediate scattering  of  data  is  quite  wide.  It  might  be  supposed
that  cities  with  high  values  for  Q,  which  indicate  a  wide  spread  of
social  strata,  would  have  a  relatively  large  number  of  business  firms,
either  total  or  retail,  to  meet  the  widely  divergent  needs  of  the  popula-
tion. As  a  matteg-  of  fact,  no  such  relationship  is  apparent.  There  is,
however,  positive  correlation  between  Q  and  the  proportion  of  insti-
tutions to  population.  This  may  be  due  in  part  to  the  fact  that  high
values  of  Q  are  found  in  Southern  cities  which  have  separate  churches
and  schools  for  whites  and  negroes.

Although  no  special  significance  has  been  found  for  the  particular
degree  of  rent  dispersion  found  in  any  city,  some  interest  attaches  to
the  fact  that  this  index  remains  practically  constant  in  a  given  city,
regardless  of  changes  in  the  level  of  prices.  The  diagrams  illustrating
this  point  have  already  been  discussed.  If  the  type  of  distribution
is  not  found  constant  in  a  particular  city,  it  would  seem  probable
that  a  change  in  character  of  the  population  is  taking  place,  but  a
change  in  the  average  economic  grade  might  occur  without  any
change  in  the  type  of  distribution.  When  two  distributions,  each  of
which  agrees  with  a  logarithmic  skew  curve,  are  added  together,
the  new  combined  distribution  may  be  represented  by  another  loga-
rithmic skew  curve  only  in  case  both  the  medians  and  coefficients  of
dispersion  for  the  two  original  curves  are  identical.  It  follows  that
if  the  index  of  rent  dispersion  in  a  city  is  found  to  be  the  same  in  suc-
cessive surveys  and  if  it  may  be  assumed  to  have  remained  constant
during  the  interval,  then  the  new  families  which  have  come  into  a  city
at  any  time  comprise  a  group  having  substantially  the  same  coefficient
of  dispersion  and  median  rent  as  the  families  which  made  up  the  original
population.  The  apparent  permanence  of  the  type  of  rent  distri-
bution in  a  city  may  be  considered,  along  with  the  telephone  habit,  as
a  reasonable  explanation  of  the  rather  high  degree  of  stability  of
station  distribution  by  classes  of  service  among  residence  subscribers.

In  commercial  survey  work  a  city  is  divided  into  market  areas,
known  also  as  homogeneous  sections,  which  are  so  laid  out  that  in  any
one  section  the  families  at  any  stated  rent  are  similar  telephone
prospects.  A  study  of  rent  distributions  in  market  areas  was  carried
out  in  a  number  of  cities,  considering  only  those  market  areas  in  each
city  which  had  fairly  large  populations.  There  appears  to  be  no
relationship  between  the  index  of  rent  dispersion  and  either  the  median
rent,  the  per  cent  of  families  in  private  residences,  or  the  per  cent

of  families  with  telcphoiu"  service,  in  the  various  areas  in  any  one
city.  Whether  a  particular  area  is  suburban  or  downtown,  likewise
has  no  apparent  effect  on  the  value  oi  Q.  It  was  found  in  Atlanta,
where  the  di\ision  of  the  city  into  market  areas  was  substantially
the  same  in  successiv'e  surveys,  that  the  distribution  index  which  had
previously  been  found  to  be  stable  for  cities  as  a  whole,  behaved  in
the  same  way  in  separate  sections  of  the  city.  It  was  found  that  the
rent  distribution  index  for  any  single  market  area  is  smaller,  usually
much  smaller,  than  the  index  for  the  entire  city  in  which  the  area
is  located.  One  section  in  Atlanta  is  the  only  exception  found  to
this  rule.  In  market  areas  it  was  noted  that  a  considerable  number
of  the  graphs  on  logarithmic  probability  paper  were  formed  of  two
intersecting  straight  lines.  This  indicates  that  the  sections  are  not
really  homogeneous,  but  contain  elements  of  population  radically
different  in  character.  This  condition  can  not  be  obviated  by  the
most  careful  laying  out  of  section  boundaries  in  case  there  exists  a
mixture  of  families  oi  essentially  different  types,  as  when  negro
residences  are  scattered  among  a  predominantly  white  population.

Indices  of  Rent  Distribution  in  Large  Cities
Composites   of   Private    Residences,    Fiats   and   Apartments

Frequency  curves  may  be  symmetrical  or  skew.  The  particular
symmetrical  distribution  known  as  the  normal  curve  of  error  is  typical
of  distributions  of  observational  errors  and  in  general  of  all  phenomena
obeying  the  laws  of  chance.  It  is  approximated  by  a  number  of  other
distributions  which  have  not  obviously  originated  in  the  same  way,
which  implies  that  "the  variable  is  the  sum  of  a  large  number  of
elements  each  of  which  can  take  the  values  0  and  1,  these  values
occurring  independently  and  with  equal  frequency."  Skew  distri-
butions may  take  a  variety  of  forms  but  the  type  shown  in  the  dia-
gram is  closely  approached  by  a  large  number  of  rent  distributions.
The  essential  characteristic  of  this  curve,  which  may  be  called  the
logarithmic  skew  curve,  is  that  logarithms  of  the  values  of  the  variable
are  distributed  according  to  the  normal  curve  of  error.  This  skew
curve  is  of  course  not  the  only  one  which  might  be  selected  to  repre-
sent rent  data,  but  it  presents  the  fewest  mathematical  difficulties
and  gives  a  sufficiently  close  approximation  for  all  practical  purposes.

where  e  is  2.7183,  the  base  of  natural  logarithms  and  a  is  a  measure
of  dispersion,  known  as  the  standard  deviation.  An  ordinate  of
the  curve  is  called  the  frequency,  and  expresses  the  fraction  of  the
whole  number  of  items  which  occurs  per  unit  interval  of  the  variable  x.

Substituting  log  X  for  x,  a  new  equation  may  be  obtained,  in  which
y  is  the  frequency  per  unit  of  x  (or  log  X).  An  expression  for  the
frequency  per  unit  of  X  is  desired,  which  may  be  called  F.  It  may  be
shown  that  the  desired  equation  is

This  is  the  equation  of  what  we  have  called  above  the  logarithmic
skew  curve,  which  is  really  not  a  curve  of  error  in  the  same  sense  as
equation  (1)  is.

In  the  course  of  this  discussion  it  will  be  convenient  to  refer  to
certain  features  of  the  frequency  curves  by  the  accustomed  terminol-
ogy of  statistics.  The  median  item  of  a  group  is  such  that  one-half
of  all  the  items  are  larger,  and  one-half  are  smaller,  and  is  the  central
item  when  they  are  arrayed  in  order  of  size.  The  quartiles,  upper  and
lower,  together  with  the  median,  divide  the  array  into  four  parts,
each  containing  one-fourth  of  the  items.  The  percentiles  divide  the
array  into  100  equal  parts.  The  mode  is  that  value  of  the  variable
which   is  of  most   frequent   occurrence.

In  the  normal  curve  of  error  a,  the  standard  deviation,  is  tech-
nically defined  as  the  square  root  of  the  mean  of  the  squares  of  the
deviations  of  the  items  from  their  mean.  For  present  purposes  it
may  be  regarded  as  a  measure  of  dispersion  approximately  equal  to
the  difference  between  the  values  of  x  at  the  84th  percentile  and  the
median.  In  the  logarithmic  skew  curve  a  is  the  difference  between
the  corresponding  logarithms.

The  origin  of  x  in  the  normal  curve  of  error  is  the  arithmetic  mean,
median,  or  mode,  which  are  coincident.  When  a  logarithmic  scale
of  abscissas  is  introduced,  the  median  value  of  x  (or  log  X)  corre-
sponds to  the  median  value  of  X,  which  is  smaller  than  the  mean
value  of  X,  and  larger  than  the  mode.  In  a  logarithmic  skew  curve
the  median  may  be  considered  the  origin,  and  at  this  point  x  (or
log  X)  is  equal  to  zero,  and  X  is  equal  to  unity.  When  this  curve
is  applied  to  house  rents  the  median  rent  occurs  at  this  point.  The
relation  between  rents  and  values  of  X  is  a  simple  one.  If  rents  be
denoted  by  R,  and  if  M  be  the  median  rent,  then

The  relationship  of  the  various  scales  is  presented  in  Fig.  9.  The
scales  for  X  and   log  X  may  be  considered   fixed,   and    the  scale  for

R  a  movable  one,  as  on  a  slide  rule,  corresponding  values  always
being  opposite  each  other.

Equation  (2)  above  for  the  logarithmic  skew  curve  gives  the  fre-
quency per  unit  of  X.  The  frequency,  per  unit  of  rent  when  expressed
in  dollars,  is  1/M  times  that  value,  and  substituting  for  X  from
equation  (3),  there  results

If  it  is  desired  to  make  computations  from  this  equation,  it  is  best
to  use  the  base  10  for  logarithms  rather  than  the  natural  base.  For
this  purpose  the  equation  becomes  approximately

although  it  will  very  rarely  be  necessary  to  make  such  computations.
It  has  been  stated  above  that  the  median  value  of  X  (or  rents
expressed  in  dollars)  may  be  logically  regarded  as  the  origin  of  the
logarithmic  skew  curve,  although  X  is  not  equal  to  zero  at  this  point,
but  is  equal  to  1.  If  some  of  the  other  forms  of  statistical  averages  are
also  known,  the  properties  of  the  curve  may  be  better  understood.
To  determine  the  mode,  the  first  derivative  of  equation  (2)  of  the
curve  is  equated  to  zero,  and  there  results

The  arithmetic  mean  for  a  distribution  agreeing  with  the  logarith-
mic skew  curve  probably  can  not  be  defined  by  any  mathematical
expression  sufficiently  simple  for  practical  use.  It  is  a  function  of
<r,  but  its  exact  position  on  the  curve  has  not  been  determined.  As
applied  to  rent  data,  the  mean  may  be  computed  direct  from  a  house
count  summary  with  an  error  of  two  or  three  per  cent.  Thus  found,
its  position  on  the  curve  is  in  the  neighborhood  of  the  65th  to  70th
percentile.

The  geometric  mean  coincides  with  the  median  for  a  logarithmic
skew  distribution.  This  follows  from  the  fact  that  the  median  value  of
X  corresponds  to  the  median,  which  is  also  the  mean,  value  of  log  X.

The  measure  of  dispersion  for  a  logarithmic  skew  curve  is  also  a
measure  of  skewness.  Up  to  this  point  a  has  been  used  as  the  measure
of  dispersion,  in  agreement  with  conventional  usage.  For  practical
purposes  another  measure  may  be  substituted,  which  has  a  more
readily  understood  meaning.  This  is  the  quartile  deviation,  known
also  by  the  misleading  term  probable  error.  The  quartile  deviation
for  a  logarithmic  skew  curve  is  that  deviation  either  above  or  below
the  median  which  includes  one-fourth  of  all  the  items  in  the  array.
It  may,  like  o-,  be  measured  in  logarithms,  and

Perhaps  the  easiest  mathematical  conception  of  a  measure  of  skew-
ness and  dispersion  is  that  of  the  ratio  of  the  upper  quartile  to  the
median.  This  is  identical  with  the  ratio  of  the  median  to  the  lower
quartile,  and  is  the  number  whose  logarithm  is  the  quartile  deviation
as  defined  above.    We  shall  let  this  ratio  be  denoted  by  Q.

Either  a  or  the  quartile  deviation  for  a  given  set  of  data  may  be
best  determined  from  a  straight  line  graph  on  logarithmic  probability
paper.  The  following  table  gives  the  positions  in  the  array  for  certain
convenient  multiples  of  a  and  the  quartile  deviation,  when  measured
in  logarithms.

To  obtain  the  value  of  the  ratio  Q,  take  the  antilogarithm  of  the
quartile  deviation  determined  in  this  manner.  For  ordinary  purposes
it  is  sufficiently  accurate  to  obtain  Q  as  the  ratio  of  the  upper  quartile
to  the  median,  read  from  the  75th  and  50th  per  cent  lines  on  the
graph.

Synopsis:  It  is  shown  that  a  satisfactory  measure  of  power  loss  in  a
dielectric  is  the  product  of  phase  angle  and  dielectric  constant.  Although
the  dielectric  constant  need  not  be  explicitly  considered  in  the  design  of
condensers,  it  i?  important  in  such  cases  as  the  design  of  apparatus  panels,
and  vacuum  tube  bases.  The  method  used  in  measuring  phase  angle  and
dielectric  constant  is  discussed. — Editor.

IN  working  with  electrical  circuits  operating  at  very  high  frequen-
cies and  moderately  high  voltages,  such  as  radio  transmitting
circuits,  it  is  found  that  failure  in  the  insulation  is  seldom  due  to
puncture  or  flashover  as  is  usually  the  case  at  power  frequencies,
but  is  generally  due  to  excessive  heating  which,  in  turn,  causes  both
mechanical  and  chemical  disintegration.  As  this  heating  is  due
almost  entirely  to  the  energy  losses  occurring  in  the  dielectric  itself,
it  is  essential  that  the  factors  involved  in  the  calculation  of  these
losses  be  well  understood.

In  the  past,  various  indices  have  been  used  as  a  measure  of  power
losses  for  the  purpose  of  comparing  different  dielectrics.  Of  these,
power-factor,  phase  difference  and  watts  per  cubic  centimeter  prob-
ably are  the  most  common.  None  of  these,  however,  is  very  satis-
factory for  this  purpose  since  the  first  two  give  only  part  of  the  de-
sired information,  and  the  last  is  not  in  any  sense  a  property  of  the
material,  as  it  is  dependent  on  both  the  voltage  gradient  and  the
frequency.

However,  it  can  be  shown  that  the  product  of  the  phase  difference
and  the  dielectric  constant  of  a  material  is  to  a  sufficient  approxima-
tion an  index  of  its  power  losses.  Let  us  consider  for  a  moment  the
complete  expression  for  dielectric  loss.     In  any  condenser  the  capacity

where  a  is  a  constant  depending  on  the  geometrical  dimensions,  and
K  is  the  dielectric  constant.  If  a  voltage,  E,  is  applied  to  the  con-
denser the  power  loss

where  /  is  the  current  through  the  condenser  and  ^  is  the  phase
difference  of  the  dielectric;    sin  ^  being  the  power  factor.     (Plate

where  w  is  a  constant  depending  on  the  units  used,  A  the  area  of  one
plate,  and  d  the  thickness  of  the  dielectric.

where  m'  =  2  -k  m,  and  m'  K  ^  =  loss  per  unit  volume  at  unit
frequency  and  potential  gradiant.

Thus  it  is  seen  that  while  no  single  factor  of  the  expression  can  be
used  to  represent  the  losses,  the  product  of  phase  difference  and  di-
electric constant  ^  can  be  used  in  this  way.  Furthermore,  for  most
good  insulators,  this  product  remains  fairly  constant  throughout  a
considerable  range  of  voltage  and  frequency.  For  example,  we  have
found  that  for  such  materials  as  wood,  phenol  fibre,  and  hard  rubber,
the  change  of  this  product  with  frequency  is  of  the  order  of  20  per  cent
from  200,000  cycles  to  1,000,000  cycles.  Hence  it  is  possible  to  com-
pare directly  the  losses  in  different  materials  even  though  the  measure-
ments were  not  made  at  exactly  the  same  frequency.

If  ^  is  taken  in  degrees.  Eg  in  volts  per  centimeter,  and/  in  cycles
per  second,  the  constant  w'  reduces  to  0.97X10."^*.  Hence,  for  a
frequency  of  1,000,000  cycles  per  second  and  a  potential  gradient  of
10,000  volts  per  centimeter,  the  product  of  K  and  "^  (in  degrees)  is
within  3  per  cent  of  being  numerically  equal  to  the  dielectric  loss  in
watts  per  cubic  centimeter.

1  The  substitution  of  the  angle  for  its  sine  is  correct  to  better  than  5  per  cent
for  angles  as  large  as  30°.

-  This  relation  has  been  brought  to  the  attention  of  the  Committee  on  Electrical
Insulating  Materials  of  the  American  Society  for  Testing  Materials  and  is  included
in  their  "Tentative  Method  of  Test  for  Phase  Difference  (Power  Factor)  and  Di-
electric Constant  of  Molded  Electrical  Insulating  Materials  at  Radio  Frequencies."

Data  showing  the  variations  with  frequency  and  temperature  of
the  phase  difference,  dielectric  constant,  and  their  product,  for  several
materials  are  given  in  Tables  I.  and  II.  below.

Dielectric  Constant,  Phase  Difference  and  Their  Product  for  Several  Commercial
Insulating  Materials  ^

'All  of  the  samples  had  been  in  the  laboratory  for  some  time  during  summer
weather  without  artificial  drying  or  other  special  preparation.

Variation  with  Temperature  of  Dielectric  Constant,  Phase  Difference  and  Their  Product
for  Some  Commercial  Insulating  Materials  {Frequency  500,000  C.  P.  S.)  *

The  above  data  were  obtained  by  the  resistance  variation  method,*
Fig.  1.  Each  value  of  phase  difference  and  of  dielectric  constant
represents  the  average  of  at  least  five  readings  on  a  single  sample
using  not  less  than  three  different  values  of  the  known  resistance  R.
A  condenser,  the  dielectric  of  which  consists  of  the  material  to  be
tested,  is  connected  in  series  with  a  suitable  inductance,  a  known  re-

*  The  measurements  on  each  sample  were  made  in  the  order  in  which  they  are
given  in  the  table.

sistance  which  can  be  varied,  and  a  radio  frequency  ammeter.  An
oscillator  is  coupled  loosely  to  the  inductance  and  its  frequency  varied
until  resonance  is  obtained  as  indicated  by  maximum  current  through
the  meter.     Without  changing  the  tuning,  the  resistance  is  changed

and  a  second  reading  of  current  is  obtained.  Then,  since  the  e.m.f.
induced  in  the  measuring  circuit  is  the  same  in  both  cases,  if  Ri  and
Ri  are  the  known  resistances,  I\  and  I2  the  corresponding  currents,
and  r  the  resistance  of  the  remainder  of  the  circuit,

A  standardized  variable  air  condenser  having  negligible  resistance
is  then  substituted  for  the  condenser  under  test  and  the  process  re-
peated except  that  the  circuit  is  tuned  to  resonance  by  varying  the
capacity  instead  of  the  frequency.  In  this  way  the  resistance  of  the
circuit  exclusive  of  the  test  condenser  may  be  determined.  The
difference  between  these  two  circuit  resistances  is  the  resistance  of
the  test  condenser  from  which  the  phase  difference  may  be  computed.
The  capacity  of  the  test  condenser  is  equal  to  the  capacity  of  the
standard  condenser  which  produces  resonance.  From  this  and  the
dimensions  of  the  sample,  its  dielectric  constant  may  be  computed.

In  addition  to  the  general  precautions  mentioned  in  the  Bureau  of
Standards  Bulletin,  two  others  should  be  observed  in  the  measure-
ment of  dielectrics.  First,  the  electrodes  must  be  in  intimate  con-
tact at  all  points  with  the  surface  of  the  sample,  as  a  very  small  air
space  will  cause  a  large  error  in  the  values  of  phase  difference  and  di-

electric  constant  obtained  for  the  sample.  For  this  reason  only
mercury  electrodes  have  been  found  suitable,  the  sample  being  floated
on  a  pool  of  mercury  forming  the  lower  electrode  and  the  upper  elec-
trode being  formed  by  pouring  a  pool  of  mercury  inside  a  metal  ring
on  the  upper  surface  of  the  sample.  This  introduces  the  second
difficulty.  The  lower  electrode  being,  of  necessity,  larger  than  the
upper  one,  the  electric  field  spreads  out  considerably  beyond  the
edges  of  the  upper  electrode  and  increases  the  effective  area  by  an
unknown  amount.

To  determine  the  magnitude  of  this  error,  measurements  were
made  on  samples  prepared  as  shown  in  Fig.  2  ^  is  the  upper  electrode,
B  is  the  sample  under  test  and  C  is  a  tinfoil  guard  ring  shellaced
to  the  lower  surface  of  the  sample  but  separated  from  the  lower  elec-
trode Z)  by  a  sheet  of  paper  shellaced  over  the  guard  ring.  The
guard  ring  covers  all  of  the  lower  surface  of  the  sample  except  the
area  equal  to  the  upper  electrode  and  directly  under  it.  The  direct
capacity  ^  between  A  and  D  is  measured  using  the  guard  ring  as  a
shield  to  intercept  the  flux  which  spreads  out  around  the  upper
electrode,  diverting  it  away  from  the  measuring  circuit.  This  measure-
ment is  made  at  audio  frequency  on  a  completely  shielded  substitu-
tion bridge.  The  difference  between  this  capacity  and  the  capacity
o{  A  to  D  without  the  guard  ring  is  approximately  the  correction  due
to  this  edge  effect.  Using  samples  6  inches  square  with  an  upper
electrode  5  inches  square,  this  correction  was  found  to  be  about  7
per  cent  for  samples  }4  inch  thick  and  14  per  cent  for  samples  ^
inch  thick.  All  values  of  dielectric  constant  given  above  have  been
corrected.  The  phase  difference  is  not  affected  appreciably  since  it  is
dependent  only  on  the  ratio  of  resistance  to  reactance  and  does  not
involve  the  area  of  the  sample.

^  Direct  Capacity  Measurement,  George  A.  Campbell,  The  Bell  System  Technical
Journal,  July,  1922.

care  was  taken  to  avoid  capacity  couplings.  The  measuring  circuit
was  shielded  from  the  observer  by  a  metal  screen.  In  spite  of  these
precautions  the  results  obtained  on  the  same  sample  at  different
times  do  not  agree  as  well  as  might  be  desired  although  the  individual
readings  taken  at  the  same  time  agree  in  most  cases  to  within  5  per
cent.  Other  observers  have  found  that  measurements  made  on  the
same  sample  at  intervals  of  a  few  hours  often  differ  by  more  than
the  apparent  error  of  the  measurements  and  have  attributed  it  to
actual  changes  in  the  properties  of  the  material.''  Hence  it  is  possible
that  at  least  part  of  the  apparent  variation  with  frequency  shown
above  is  due  to  unknown  errors  in  the  measurements  or  unknown
changes  in  the  samples  or  both.

As  an  illustration  of  the  error  involved  in  taking  only  phase  differ-
ence as  a  measure  of  power  loss,  suppose  we  wish  to  compare  hard
rubber  having  a  phase  difference  of  about  0.5  degree  and  a  dielectric
constant  of  3.,  with  a  certain  grade  of  glass  having  a  phase  difference
of  about  0.3  degree  and  a  dielectric  constant  of  7.  On  the  basis  of
phase  difference  alone  the  hard  rubber  appears  very  much  worse  than
the  glass,  but  when  the  dielectric  constant  is  taken  into  account,  the
glass  is  found  to  give  a  40  per  cent  higher  power  loss.  Similarly,  some
untreated  woods  were  found  to  have  considerably  lower  losses  than
the  phenol  fibres  although  their  phase  differences  are  nearly  the  same.

In  the  case  of  ordinary  insulation  where  the  object  is  to  provide  a
mechanical  separator  or  support,  the  product  of  phase  difference  and
dielectric  constant  is  a  true  measure  of  the  energy  loss  per  unit  volume
as  shown  by  the  equation  (1).  In  the  case  of  a  condenser  where  the
object  is  to  obtain  a  given  capacity,  the  phase  difference  alone  de-
termines the  power  loss  since  in  this  case  the  effect  of  the  increased
dielectric  constant  is  exactly  balanced  by  the  smaller  volume  of
dielectric  required.

^  R.  Mesing — L'Onde  Electrique,  April,  1922,  p.  235  and  Augustin  Frigon — Comptes
Renins,  May  22,  1922,  p.  1339.

Synopsis:  This  article  points  out  that  radio  and  wire  communication
systems  are  subject,  fundamentally,  to  the  same  general  requirements,
and  its  purpose  is  to  develop  for  radio,  points  of  view  which  are  familiar
to  wire  transmission  engineers.  The  transmission  characteristics  over  a
wide  range  of  distances  are  compared.  For  short  distances  the  comparison
is  favorable  to  wires.  Although  over  great  distances,  the  attenuation  of
electric  waves,  guided  by  wires,  may  be  greater  than  the  unguided  waves
of  radio,  it  is  pointed  out  that  at  the  present  time  intermediate  amplifiers
can  be  more  economically  applied  in  wire  transmission  than  in  radio  to
boost  the  message  energy.  Economy  of  transmission  requires  the  handling
of  messages  at  as  low  an  energy  level  as  possible  and,  as  the  author  points
out,  wire  transmission  satisfies  this  requirement  much  better  than  radio.
Referring  to  the  transcontinental  line  with  radio  extensions,  which  was
used  recently  to  talk  from  Catalina  Island  in  the  Pacific  Ocean  to  a  ship
in  the  Atlantic  Ocean,  it  is  stated  that  had  all  of  the  necessary  energy  been
introduced  at  one  end  of  the  circuit,  there  being  no  intermediate  amplifica-
tion, the  total  power  required  would  have  been  1.8  x  10'^  kilowatts,  an
amount  unavailable  in  the  world.  In  the  actual  system,  distributing
the  amplification  along  the  transmission  line,  the  power  required  sums
up  to  something  less  than  1  kilowatt.

Interference  between  messages  and  extraneous  disturbances  is  discussed,
and  the  requirements  involved  in  keeping  message  energy  well  above  the
energy  level  of  the  disturbances  in  both  systems  are  pointed  out.  The
limitations  on  two-way  operation  resulting  from  "singing"  of  the  entire
system  are  considered  for  both  cases  and  for  combination  wire  and  radio
circuits  as  well.  The  method  of  improving  the  efficiency  of  transmission
by  suppressing  the  carrier  and  one  side  band  is  discussed.  Finally  the
factors  involved  in  obtaining  high  grade  quality  of  transmission  are  enumer-
ated.— Editor.

ONE  of  the  most  interesting  aspects  of  the  development  of  radio
during  the  last  few  years,  and  particularly  of  radio  telephony,
is  the  obvious  convergence  of  its  technique  with  that  of  wire  trans-
mission. It  is,  of  course,  the  advent  into  both  of  these  arts  of  that
remarkable  device,  the  electron  tube,  which  is  responsible  for  the
close  technical  relations  which  now  exist  between  them.

This  community  of  interest,  however,  altho  thus  greatly  stimu-
lated by  a  device  of  such  range  of  utility  as  to  find  important  applica-
tions in  both  arts,  is  not  due  primarily  to  any  device  per  se,  but  rather
to  the  fact  that  both  type  of  systems  are  subject  fundamentally,  as
communication  systems,  to  the  same  general  requirements  and  design
considerations  concerning  their  intelligence-carrying  capabilities.
These  underlying  communication  requirements  lead  to  similar  con-
siderations in  both  types  of  systems  as  to  the  efficiency  and  fidelity
with  which  the  transmission  of  intelligence  is  effected  and  give  rise

•  Presented  before  The  Institute  of  Radio  Engineers,  New  York,  January  23,
1922.  Received  by  the  Editor  April  17,  1922,  Also  printed  in  the  Procd.  Radio
Institute  for  October,  1922.

The  engineering  handhng  of  the  transmission  problems  which  arise
from  these  fundamental  communication  requirements  has  been  quite
highly  developed  in  the  older  of  the  two  arts — ^wire  transmission — in
connection  with  telephone  repeaters  and  carrier  telephone  and  tele-
graph systems.  It  should  be,  therefore,  interesting  and  profitable
to  apply  some  of  the  transmission  technique  thus  developed  in  the
wire  art  to  several  of  the  more  important  radio  problems.  In  so
doing,  we  obtain  rather  new  viewpoints  of  radio  transmission  and  a
useful  correlation  of  it  with  the  better  established  wire  methods.  It
is  hoped,  therefore,  that  the  picture  which  is  presented  of  radio  and
wire  transmission,  treated  from  a  common  standpoint,  may  con-
tribute to  a  better  appreciation  of  both  arts  by  radio  and  wire  engineers
alike  and  may  make  clear  the  underlying  transmission  principles
which  are  common  to  them.

Principal  among  the  problems  of  electric  communication  is  the  one
of  delivering  at  the  receiving  end  the  required  volume  of  signal  with
the  necessary  freedom  from  interference.  The  delivering  of  the
required  volume  is  a  matter  of  overcoming  the  transmission  losses
of  the  system  by  amplification;  while  the  obviating  of  interference  is,
of  course,  concerned  with  the  reduction  of  the  ratio  of  the  interfering
to   the   signaling  energy.

In  considering  these  factors  we  will  take  up  first  the  primary  one
of  the  losses  which  are  suffered  by  the  carrier  waves  as  they  are
propagated  thru  the  transmission  medium.  In  both  wire  and  radio
transmission,  of  course,  the  actual  propagation  of  the  electromagnetic
wave  energy  occurs  in  the  "ether,"  the  difference  being  that  in  the
wire  case,  the  waves  are  bound  to  a  guiding  path,  whereas  in  the  radio
case  they  are  transmitted  freely  in  all  directions  and  bound  merely
to  the  earth's  surface.  This  difference  in  the  mechanism  of  trans-
mission gives  rise  to  an  important  difference  in  the  transmission
losses  occurring  in  the  two  cases.  In  order  to  assist  in  visualizing  the
two  cases  they  are  indicated  diagrammatically  in  Fig.  1.

Referring  first  to  the  wire  case,  the  law  in  accordance  with  which
the  current  and  voltage  strength  decrease  as  the  transmission  wave
travels  along  the  wire,  is  the  familiar  one  of  attenuation.

which  simply  expresses  the  fact  that,  as  the  wave  proceeds  along
the  wire,  the  losses  in  the  resistance  of  the  conductor  and  in  the  insu-
lation, extract  for  each  mile  a  certain  definite  proportion  of  the  volt-
age and  current  which  arrives  at  that  point.  After  traveling  (/)
miles  the  original  current  /i  is  attenuated  down  to  a  value  /i«~"'
which  represents  the  received  current  h-  This  is  the  same  general
law  of  damping  as  applies  to  the  dying  down  of  the  voltage  and  cur-
rent in  an  oscillation  circuit,  except  that  here  the  damping  is  with
respect  to  distance  along  the  line  rather  than  time.  We  are  assuming,
of  course,  that  the  circuit  is  so  terminated  as  to  avoid  reflection
effects  at  the  terminals — a  condition  readily  met,  by  making  the
terminal  impedance  equal  to  the  characteristic  line  impedance.  This
is  indicated  in  the  figure  by  the  designations,  Z  (internal)  equals  Z
(line).  A  similar  relation  is  taken  for  the  radio  case.  The  "  line  "
impedance  is  here  the  antenna  radiation  resistance  while  the  "  termi-

nal  "  impedance  is  the  resistance  internal  to  the  antenna  and  the
apparatus,  assuming  resonance;  thus  R  (internal)  equals  R  (radiation).

We  know  that  in  radio  there  are  tw^o  distinct  causes  of  the  trans-
mission loss:  (1)  that,  due  to  the  spreading  out  of  the  waves,  which
is  characteristic  of  non-guided  wave  transmission;  and  (2)  that  due
to  absorption  in  the  air  and  earth's  surface,  which  extracts  a  definite
percentage  loss  for  each  mile  of  the  radio  circuit  and  which  conforms,
therefore,  to  an  exponential  law  similar  in  its  general  nature  to  that
of  wire  attenuation.

formula,  is  given  in  the  Appendix. ^  In  order  to  express  the  radio
transmission  loss  in  some  general  manner  which  will  be  comparable
to  the  expression  of  wire  transmission  loss,  these  conditions  have  been
taken  for  the  radio  case:

(1)  That  we  will  use  as  the  measure  of  the  transmission  loss  the
ratio  of  the  square  root  of  the  power  radiated  from  the  sending
antenna  to  the  square  root  of  the  power  delivered  in  the  re-
ceiving antenna.  This  is,  of  course,  the  same  criterion  as  is
used  for  wire  transmission.

(2)  The  radiation  resistance  of  the  two  antennas,  sending  and
receiving,  are  made  equal,  analogous  to  the  equality  of  line
impedance  at  the  two  ends  of  the  wire  system.

(3)  Also  the  internal  antenna  resistance,  which  corresponds  to
the  terminating  impedance  in  the  wire  case,  is  made  equal  to
the  radiation  resistance  for  both  ends.  This  is  the  condition
of  maximum  power  transfer  between  the  "  line  "  and  the
terminal.

These  assumptions  set  up  the  two  cases,  radio  and  wire,  on  a  com-
parable basis  and  facilitate  a  comparison  of  them.  They  are  favor-
able to  radio  in  that  they  do  not  take  account  of  practical  limitations
which  obtain  in  antennas.  The  radio  curves  should  be  read,  there-
fore, as  giving  the  minimum  possible  losses  for  daylight  transmission
over  water.

These  curves  show  the  manner  in  which  the  transmission  loss
varies  with  distance,  for  various  frequencies,  for  both  radio  and  wire.
The  ordinates  are  plotted  in  terms  of  the  logarithm  of  the  ratio  of  the
sent  to  the  received  currents,  or  voltages,  in  circuits  of  equal  im-
pedances. In  so  doing  we  are  plotting  the  losses  on  the  straight
attenuation  basis  upon  which  they  are  usually  plotted  in  the  wire
art;  that  is,  the  ordinates  represent  the  exponent  («/)  of  the  wire
attenuation  law,  and  may  be  directly  interpreted  in  terms  of  miles
of  standard  cable^  by  multiplying  by  21.  approximately.  The  ad-
vantage of  dealing  with  the  exponent  rather  than  the  current  ratio

*  Measurements  on  ship-shore  transmission  made  since  the  above  was  written,
indicate  that  the  Austin-Cohen  law  holds  quite  well  for  frequencies  as  high  as  about
1,000,000  cycles.

'For  the  mile  of  standard  cable  the  attenuation  a  (at  800  cycles)  equals  0.109.
Therefore  the  equation  for  current  ratio,  in  terms  of  miles  of  standard  cable,  becomes

itself  is  the  very  considerable  one  which  is  characteristic  of  logarithms,
namely,  that  when  thus  expressed  the  individual  losses  and  gains
thruout  a  system  may  be  summed  up  algebraically,  and  the  over-
all transmission  equivalent  of  the  system   thus  readily  determined.

It  should  be  noted  that  the  transmission  loss  given  in  the  radio
curves  is  that  obtaining  between  the  point  at  which  power  is  delivered
to  the  ether  at  the  sending  end  and  that  at  which  it  is  delivered  to  the
dissipative  load  of  the  receiving  antenna  circuit.  In  Fig.  1  these
points  are  represented  by  Ry  at  the  transmitter  and  /?,  at  the  receiver.
If  at  the  sending  end,  we  start  with  the  power  developed  within  the
generator,  meaning  in  Ri  instead  of  R^,  then  the  power  ratio  is  sim-
ply doubled,  for  the  conditions  assumed,  and  the  attenuation  is
0.15  units  or  about  3  miles  greater  than  given  in  the  curves.  The
curves  can  be  used  for  obtaining  the  loss  in  any  practical  case  simply
by  taking  the  minimum  loss  as  given  by  the  curves  and  adding  thereto
the  additional  loss  obtaining  in  the  actual  antenna.

Referring  now  to  Fig.  2 — the  transmission  losses  in  the  two  cases
are  given  for  distances  up  to  200  miles  (320  km.).  The  straight
lines  represent  the  wire  losses,  the  bending-over  curves  the  radio
losses.  Of  the  radio  curves,  the  dash  lines  give  the  spreading-out
losses  alone,  while  the  full  lines  give  the  total  losses,  including  ab-
sorption.

The  first  thing  one  observes  is  the  difference  in  the  nature  of  the
two  sets  of  curves — the  wire  losses  being  represented  by  straight
lines,  because  of  their  exponential  law  and  the  fact  that  it  is  the
logarithm  or  the  exponent  itself  which  is  being  plotted,  while  the  radio
curves  jump  up  rapidly  at  first  and  then  straighten  out,  in  accordance
with  the  "  inverse-with-distance  "  law.

The  second  thing  one  notes  is  the  fact  that  as  a  result  of  the  large
initial  (or  "  jump  off  ")  loss,  the  radio  values  run  on  the  whole  higher
than  do  the  wire  for  the  more  usable  wire  frequencies,  and  very  much
greater  than  the  wire  losses  at  telephone  frequencies  (1  k.c.).'*  For
the  wire  case  the  number  8  Birmingham  wire  gauge  open  wire  circuit  is
taken.^  This  is  the  standard  long  distance  telephone  circuit  of  the
United  States.     The  constants  are  given  in  the  appendix.

A  third  characteristic  which  one  notes  in  the  radio  curves  is  that
the  losses  are  greater  for  the  higher  frequencies  or,  conversely,  lower
for  the  lower  frequencies.  This  is  because  the  efficiency  of  the  an-
tenna has  been  kept  constant  for  all  frequencies.     In  practice  the

transmission   losses   at   the   lower   frequencies   are   higher   than   here
indicated  because  of  limitations  in  antenna  heights.

Were  we  to  take  the  ideal  condition  as  regards  the  transmission
medium  itself,  where  for  wires  there  is  no  conductor  or  dielectric  loss,
and  for  radio  there  is,  likewise,  no  earth  or  air  absorption  loss,  we
would  note:  (1)  that,  for  wires,  there  would  be  no  attenuation  what-

Radio  Dispersion  and  Attenuation
Dashed  Curves-Loss  Due  to  Dispersion  Only.

ever,  the  curve  following  along  the  X  axis;  (2)  for  radio,  there  would
remain  the  loss  due  to  dispersion,  inherent  in  the  unguided  method
of  transmission,  the  magnitude  of  which  loss  is,  of  course,  very  sub-
stantial. The  dash-line  radio  curves  show  the  radio  losses  without
attenuation,  the  full  line  curves  with  attenuation.

in  the  transmitting:;  medium,  we  fmd  that  for  moderate  distances,
up  to  200  miles  (320  km.),  as  plotted  in  Fig.  2,  the  wire  losses  are  in
general  less,  and  at  telephone  frequencies  very  much  less,  than  the
radio  losses.  The  low  wire  attenuation  at  telephone  frequencies  is,
of  course,  in  keeping  with  experience  and  accounts  for  the  economical
terminal  apparatus  which  is  employed  in  telephone  practice.  Like-
wise the  relatively  high  losses  for  radio  accounts  for  the  large  amplifica-
tion at  either  the  sending  or  receiving  end  or  both,  which  experience
has   proven    to    be    necessary.     This   brings   in   an   interesting   side-

light,  namely,  that  altho  in  radio  the  transmission  medium  is  provided
by  nature,  the  effective  use  of  this  medium  is  not  as  economical  as
might  be  expected  because  it  requires  considerable  equipment,  ampli-
fiers at  both  ends  for  overcoming  the  large  attenuations,  selective
means  for  dividing-up  the  frequency  range  and  thereby  "multiplex-
ing" the  ether,  and  antennas  for  getting  into  the  medium  and  out
again.

For   the   higher   frequencies,   the  wire  attenuations   increase   rela-
tively more  rapidly  than  the  radio,  thus  limiting  the  frequency  range

which  can  be  employed  on  wires  without  Hkewise  running  into  large
amplification  requirements.  For  example,  the  loss  at  100,000  cycles
for  a  distance  of  200  miles  (320  km.)  is  about  as  great  over  wires  as
the  minimum  loss  which  it  is  theoretically  possible  to  obtain  over
radio.

Referring  now  to  the  attenuations  for  longer  distances,  as  given  in
Fig.  3,  it  is  of  interest  to  note  that  for  distances  of  the  order  of  2,000
to  3,000  miles  (3,200  to  4,800  km.)  the  lower  radio  frequency  curves
cross  the  1,000  cycle  wire  curve,  meaning  that  for  these  distances
it  is  possible  for  radio  transmission  to  be  as  efficient  as  straight  tele-
phone transmission.  The  wires  present  to  carrier  frequencies  for
these  long  distances  losses  which  are  generally  greater  than  prevail
for  radio.

These  attenuation  relations  cannot  be  directly  converted  into  an
economic  comparison,  however,  for  the  economies  depend  not  upon
the  attenuation  itself  but  upon,  among  other  factors,  the  cost  in-
volved in  overcoming  the  losses  by  means  of  amplification;  and  this
cost  in  turn  depends  largely  upon  the  extent  to  which  the  amplifica-
tion can  be  applied  at  weak  powers,  as  by  the  frequent  application
of  telephone  repeaters.  By  applying  repeaters  every  few  hundred
miles  in  the  wire  case,  the  attenuation  is  prevented  from  piling  up
and  the  amplification  is  handled  at  relatively  weak  and  therefore
economical  power  levels.  This  brings  us  to  the  point  of  requiring
that  the  attenuation  values  given  above,  be  considered  in  reference
to  the  amplification  and  power  required  to  overcome  them  and  yield
the  necessary  volume  of  transmission  at  the  receiving  end  over  and
above  interference.

In  both  the  radio  and  wire  cases  there  is  always  present  in  the
transmission  medium  a  certain  amount  of  stray  wave  energy  which
tends  to  interfere  with  the  proper  reception  of  the  message-carrying
waves.  It  is  necessary  that  the  communication  waves  arrive  at  the
receiving  end  of  the  system  with  such  power  as  to  be  large  compared
with  the  interfering  waves — by  a  factor  determined  by  the  type  and
grade  of  communication  involved.  Inasmuch  as  the  stray  energy
always  has  some  finite  value,  this  requirement  of  freedom  from  inter-
ference will  determine  in  the  radio  case  as  well  as  in  some  types  of
wire  transmission  the  minimum  wave  power  required  at  the  receiving
end  of  the  transmission  system.

In  the  wire  system  the  minuinuin  power  requirement  may  be
expressed  directly  in  terms  of  a  power,  or — as  it  is  usually — a  current,
in  the  recei\ing  apparatus,  the  "transfer"  between  the  line  and  the
receiver  being  a  constant  and  efficient  relation.  In  radio  the  power
delivered  out  of  the  ether  or  "line"  into  the  receiving  antenna  is  so

largely  a  function  of  the  antenna  dimensions  that  it  is  necessary  to
express  the  necessary  received  power  in  terms  of  the  received  field,
usually,  simply  as  a  field  intensity — and  not  as  a  certain  current  in
the  terminal  apparatus.  Of  course,  the  transmission  loss  occasioned
by  getting  from  the  "ether"  into  the  receiving  circuit  does  not  affect

the  interference  relation  but  merely  the  absolute  amount  of  terminal
amplification  required.  On  the  other  hand  the  transmission  loss
occasioned  by  getting  into  the  "ether"  at  the  sending  end  aflfects
the  interference  relation  vitally,  as  we  shall  see.

This  necessity  of  having  to  keep  the  power  of  the  received  waves
above  the  interference  level  may  be  visualized  by  reference  to  Fig.  4.
Here  we  have  what  in  wire  practice  is  called  a  "transmission  level"
diagram.  Such  a  diagram  is  useful  in  showing  what  goes  on  in  the
system  from  the  power  and  interference  standpoints.  The  vertical
scale  is  plotted  in  terms  of  the  transmission  level  expressed  as  the
logarithm  of  the  current  or  field  intensity  ratios,  and  the  horizontal
scale  represents  progression  along  the  system.  For  illustration
purposes,  the  presence  of  interference  is  indicated  at  the  bottom  of
the  transmission-level  scale  by  the  shading.

The  point  of  "zero "level  is  taken  roughly  as  that  corresponding  to
the  power  delivered  into  a  telephone  circuit  by  a  certain  telephone
transmitter  when  spoken  into  by  the  average  talker,  and  is  here  taken
to  be  0.01  watt.  As  the  voice  currents  are  amplified  to  power  pro-
portions in  the  transmitting  station,  at  the  left,  the  transmission  level
is  greatly  increased,  as  illustrated  by  the  vertical  jump  in  the  curve.
The  amplified  voice  currents  are  assumed  to  be  converted  by  modula-
tion into  high  frequency  currents  at  this  high  power  level  and  put  into
the  antenna.  The  high  frequency  loss  in  the  antenna  system  is  in-
dicated by  the  perpendicular  jog  in  the  curve.  The  drooping-off  curve
then  commences,  starting  with  a  point  which  represents  the  power
usefully  applied  to  the  ether  in  accordance  with  the  expression  PR,
where  /  is  the  antenna  current  and  R  is  the  radiation  resistance.
The  level  curve  falls  off  in  accordance  with  the  transmission  loss
curves  previously  discussed,  as  it  extends  across  the  transmitting
medium  to  the  receiving  station.  It  will  not  do  to  permit  the  trans-
mission level  to  fall  as  low  as  that  of  the  interference,  so  I  have  shown
that  the  transmission  reaches  the  receiving  station  before  dropping
down  very  far  into  the  interference  level.  At  the  receiving  point  a
further  transmission  loss  occurs  in  getting  into  the  receiving  antenna
circuit,  shown  by  the  drop  in  the  curve,  but  this  loss  obtains  for  the
interference  as  well  as  the  desired  signals  and  does  not  affect  the
interference  ratio.  The  terminal  amplification  brings  the  level  up
to   that  required   for  suitable  audition   and   the  difference  between

where  this  level  leaves  off  and  the  original  zero  level,  measures  the
over-all  transmission  equivalent  of  the  circuit,  shown  in  this  case  as

■I2
responds  to  a  current  ratio  of  about  4,  a  value  ample  for  good  "  talk."
Of  course,  in  a  one-way  circuit  the  terminal  amplification  can  be
raised  to  any  value  desired.  In  a  two-way  circuit,  however,  a  limit
in  the  terminal  amplification  is  imposed  by  interference  between  the
two  transmissions,  as  will  be  understood  subsequently.

1.  The  net  transmission  equivalent  represents  the  difference  be-
tween the  over-all  loss  and  the  over-all  gain.

2.  The  over-all  gain  is  divided  betw^een  the  transmitting  and  re-
ceiving ends.  We  should  like  to  throw  as  much  of  this  amplifica-
tion as  possible  to  the  receiving  end  because  of  the  economy
with  which  amplification  can  be  provided  at  low  powers.

3.  The  extent  to  which  we  can  do  this,  however,  is  distinctly  limited
by  the  fact  that  the  transmission  level  obtaining  at  the  receiving
end  in  the  transmission  medium  must  be  held  above  a  certain
amount  in  order  to  overcome  interference.

4.  It  is,  then,  the  absolute  intensity  of  the  interference  which
determines  the  receiving  power  level  required,  and  in  turn  this
together  with  the  attenuation  back  to  the  transmitting  station
which  determines  the  transmitting  power  required.

Thus  the  two  transmission  features  most  fundamentally  important
in  a  radio  communication  system  are  (1)  the  interference  level  and
(2)  the  transmission  loss  thru  the  medium.  These  once  given,  the
other  engineering  considerations  follow  naturally.  There  are  an-
alogously fundamental  factors  in  wire  communication  systems.  In
the  latter  case,  however,  the  art  has  advanced  to  a  point  where  means
of  controlling  the  interference  level  are  available,  so  that  the  ratio  of
interference  to  transmitted  power  may  be  made  small  by  decreasing
the  former  rather  than  increasing  the  latter.

The  working  value  w^hich  should  be  assumed  for  the  ratio  between
the  transmission  level  of  the  received  signals  and  the  interference,
depend  upon  the  type  of  communication  involved,  whether  it  is
telephone  or  telegraph,  for  example,  and  upon  the  grade  of  service
to  be  given.  There  is  a  wide  difference  between  the  transmission
level  which  will  enable  telephonic  signals  to  be  barely  discerned  by  an

expert  ear  and  that  which  is  required  for  a  pubUc  service  communica-
tion system  which  must  provide  sufificient  operating  margin  to  enable
the  average  person  to  converse  with  ease  and  certainty  under  all
ordinary  conditions.  Under  favorable  static  conditions,  the  trans-
mission level  can  be  permitted  to  fall  to  extraordinarily  low  values.
When  this  condition  is  accompanied  by  a  substantial  reduction  in  the
effective  attenuation,  which  sometimes  occurs  at  short  wave  lengths
especially  at  night,  apparently  due  to  the  effective  absence  of  either
absorption,  then  it  becomes  possible  to  "get  thru"  over  relatively
long  distances  with  powers  diminutive  as  compared  with  those  re-
quired for  giving  a  regular  service.  With  these  exceptional  trans-
mission conditions  we  are,  of  course,  familiar.  They  are  exemplified
by  the  long  distances  reached  at  night  by  the  amateurs,  as  across  the
Atlantic,  and  by  the  hearing  of  the  normally  30-mile  (48  km.)  Catalina
Island  system  in  Australian  waters.  The  transmission  curves  of
Fig.  3  account  for  these  unusual  long  distance  transmissions  if  we
assume  that  the  attenuation  due  to  absorption  is  eliminated  on  these
occasions  by  some  natural  cause.  Thus,  at  3,000  miles  (4,800  km.)
the  curves  for  1,000  kilocycles  (300  meters),  for  example,  show  that
were  the  absorption  eliminated,  the  transmission  equivalent  would  be
improved   by   the  difference   between   about    10.8  and   5.2   for  logio

standard  cable.  The  remaining  or  purely  spreading-out  loss  of  about
5  units,  or  100  miles  of  standard  cable,  is  then  taken  care  of  by  the
sending  and  receiving  amplification.

Interference  may  occur  in  either  or  both  of  two  ways — by  the
interference  level  rising  to  a  point  comparable  with  the  normal  trans-
mission level  at  the  receiving  end  of  the  ether  circuit,  or  by  the
transmission  level  of  the  waves  themselves  dropping  so  low,  due  to
excessive  atmospheric  absorption,  as  to  fall  below  that  of  the  atmos-
pheric disturbances.  For  reliable  transmission  it  is  necessary,  there-
fore, to  deliver  normally  at  the  receiving  end,  a  wave  intensity  suffi-
cient to  allow  for  the  fluctuations  which  occur  in  atmospheric  absorp-
tion and  in  the  intensity  level  of  the  atmospherics.  The  importance
of  working  to  transmission  level  standards  which  give  an  adequate
operating  margin  against  interference,  for  the  types  of  service  re-
quired, will  be  appreciated  from  the  foregoing.  The  following  values
of  minimum  transmission  levels  will  be  of  value  to  know:

(a)   For  carrier  wire  telephone  transmission  at  frequencies  in  the
tens  of  thousandths  of  cycles,  the  limiting  interference  may  be

(b)  While  for  radio  telephone  transmission  the  available  data  are
as  yet  very  meagre,  we  have  obtained  a  few  order-of-magnitude
figures  which  should  be  of  interest.  For  the  Catalina  Island
radiophone  system,  for  example,  the  minimum  field  intensity
is  estimated  at  roughly  1,000  microvolts  per  meter.  The
circuit  is  sometimes  quite  noisy  during  the  summer  months
altho  not  prohibitively  so.  In  our  ship-to-shore  radio  tele-
phone experiments  along  the  Atlantic  coast,  we  have  on  occa-
sions worked  with  lower  field  intensities,  as  low  as  100  micro-
volts per  meter.  The  latter  figure,  however,  gives  a  grade  of
service  far  below  wire  standards.

(c)  The  best  data  on  the  minimum  permissible  transmission  level
for  radio  telegraphy  are  those  obtained  from  the  experience  in
trans-Atlantic  telegraph  operation.  The  figures  prevailing
for  present  trans-oceanic  radio-telegraph  operation  are  under-
stood to  lie  in  the  order  of  10  to  100  microvolts  per  meter,
depending  upon  individual  cases  and  the  time  of  the  year.

The  net  over-all  transmission  equivalent  of  the  system  is  measured
by  the  ratio  of  the  transmitted  to  the  received  signaling  power,  and  is
shown  in  Fig.  4  as  the  difference  between  the  transmission  levels  at
the  two  ends.  This  relatively  small  loss  represents  the  difference
between  two  large  values,  the  transmission  loss  and  the  transmission
gain  thruout  the  system.  Relatively  small  changes  in  either  the  at-
tenuation or  amplification  may,  therefore,  cause  large  changes  in  the
net  equivalent  of  the  circuit,  thus  tending  to  give  rise  to  instability
in  the  transmission  performance  of  the  circuit.

This  problem  of  fluctuation  becomes  very  serious  with  the  use  of
very  high  frequencies,  whether  transmitted  by  wires  or  by  radio.
Were  we  to  attempt  to  employ,  for  example,  a  million  cycles  for  wire
carrier  transmission  over  considerable  distances,  as  has  been  proposed,
not  only  would  the  losses  be  very  large,  but  they  would  be  unstable,
changing   with   weather   conditions,    so   that   the   maintenance   of   a

constant  volume  of  transmission  would  become  extremely  difficult.
Similarly  in  radio  transmission,  the  fluctuations  in  the  ether  attenu-
ation, particularly  at  short  wave  lengths  where  over  long  distances
we  experience  the  well  known  "swinging"  or  fading  efTects,  render  the
maintenance  of  a  satisfactory  volume  of  transmission  a  difficult
problem.  As  noted  above  these  fluctuations,  particularly  as  between
day  and  night  transmission  with  very  high  frequencies,  may  be
enormous.

siderably  larger  transmission  equivalents  can  be  talked  over.  The
long  distance  toll  lines  themselves  are  usually  designed  for
transmission  equivalents  of  0.5  to  0.75  or  10  to  15  miles  of  standard
cable.  These  figures  will  serve  as  a  general  guide  for  the  transmission
equivalents  which  radio  telephone  circuits  should  provide.  Where  a
radio  circuit  forms  a  link  in  a  direct  wire  circuit  as,  for  example,  in
the  case  of  Catalina  Island,  it  is  desirable  to  work  the  radio  link  as
close  to  a  zero  equivalent  as  possible,  that  is,  to  give  out  at  the  receiv-
ing end  a  volume  nearly  equal  to  that  fed  in  at  the  transmitting  end.

When  the  two  one-way  radio  channels  are  merged  at  their  two
ends  into  a  regular  telephone  circuit  for  connection  to  the  wire  net-
work, as  illustrated  in  Fig.  5,  then  there  is  a  limit  in  the  transmission
equivalent  which  can  be  given  over  the  radio  part  of  the  circuit.

This  limit  will  be  appreciated  by  reference  to  Fig.  5.  It  is  im-
posed by  the  tendency  of  the  two  one-way  channels  to  form  a  round-
trip  circuit  by  "feeding-back"  from  one  to  the  other  via  the  voice
frequency  connecting  circuit.  If  the  total  amplification  around  the
circuit  including  the  voice-frequency  line,  exceeds  the  total  losses  in
the  circuit,  "singing"  will  result.  Were  no  line  balance  provided  at
the  voice  frequency  terminals,  then  it  would  be  impossible  to  operate
the  circuit  at  a  zero  equivalent.  By  setting  up  a  balancing  circuit  at
each  end  in  the  manner  illustrated,  a  transmission  loss  is,  in  effect,
inserted  between  the  sending  and  receiving  sides  of  the  voice  circuit
which  tends  to  prevent  this  sing-around  action.  Actually,  there  is  a
limitation  in  the  degree  of  balance  which  can  be  realized  between  the

telephone  line  and  the  balancing  network,  especially  if  tlie  telephone
line  is  to  be  switched  at  a  nearby  central  office,  and  this  factor,  to-
gether with  the  margin  of  safety  which  is  required  between  the  oper-
ating condition  and  the  singing  condition,  prevents  the  radio  channels
from  being  operated  much  better  than  the  zero  equivalent.  This
whole  matter  of  realizing  in  practice  an  adequate  transmission  equiva-
lent, will  be  appreciated  to  be  an  especially  difficult  problem  in  the
case  of  marine  radio  telephony,  where  the  connection  is  switched
from  one  vessel  to  another  at  varying  distances.

It  should  be  noted  further,  with  reference  to  two-way  operation,
that  the  difficulty  of  effecting  simultaneous  sending  and  receiving
at  a  station  arises  primarily  from  the  large  attenuation  which  must  be

overcome  and  the  resulting  large  ratio  between  the  energies  trans-
mitted into  and  received  from  the  ether.  The  receiver  must  be  pre-
vented from  being  overloaded  by  the  home  transmitter  and  this,
in  general,  requires  that  there  be  provided  between  the  high  frequency
side  of  the  transmitter  and  that  of  the  receiver,  a  transmission  loss
comparable  in  size  to  that  obtaining  over  the  radio  circuit  itself.  This
"separating"  transmission  loss  is  ordinarily  provided  (a)  by  fre-
quency-selecting circuits  (tuned  circuits  and  filters),  the  sending  and
receiving  transmissions  being  placed  on  different  frequencies;  (b)  by
balance,  as  w'hen  using  the  blind  spot  of  a  loop-antenna  receiver,
and  (c)  by  spatial  separation  between  sending  and  receiving  points,
where  the  large  step-off  loss  is  used  to  advantage.

It  will  be  of  interest  to  trace  thru  the  approximate  transmission
levels  which  obtain  for  a  radio  system  linked  up  with  a  long  repeat-
ered  land  line  system.

In  Fig.  6,  there  is  taken  a  rather  striking  example  of  this  case  in
the  transcontinental  telephone  line  as  connected  up  to  radio  ex-
tensions at  its  termini — to  Catalina  Island  on  the  Pacific  and  to  a
vessel  at  sea  on  the  Atlantic.  The  transmission  illustrated  is  that
occurring  from  east  to  west.  The  voice  currents  start  out  from  the
vessel  at  zero  level,  are  amplified  to  a  relatively  high  level  and  upon
being  transmitted  to  the  shore  150  miles  (240  km.)  away,  drop  to  a
very  low  level.  At  the  shore  radio  station  they  are  boosted  up,  at
New  York  amplified  again,  and  put  upon  the  transcontinental  circuit.
Regularly  at  about  300  miles  (480  km.)  the  telephone  repeaters  pull
back  the  transmission  level  to  about  its  original  value.  In  the  radio
link  at  the  w-estern  end  the  currents  are  again  amplified  to  a  high  level
at  the  transmitting  station,  drop  down  to  a  very  low  level  at  the  re-
ceiver and  are  brought  back  to  a  level  at  which  they  can  be  heard.
Actually  in  the  receiving  telephone  the  transmission  is  about  logio

"  down."  The  total  loss  and  the  total  gain  in  the  circuit  is  enormous,
as  is  shown  by  the  figures  given  in  the  diagram.  This  is  a  rather
striking  illustration  of  the  extent  to  which  amplification  properly  dis-
tributed and  maintained  can  be  used  to  overcome  attenuations  enor-
mous in  the  aggregate.  Just  to  give  a  better  idea  of  what  these  values
of  attenuation  and  amplification  mean,  it  may  be  noted  that  were  it
necessary  to  supply  at  the  transmitting  end  all  of  the  amplification  re-
quired for  delivering  this  volume  of  transmission  to  the  receiving  end
thru  the  combination  circuit,  the  kilowatts  required  would  be  measured
by  a  twenty-nine  place  figure,  an  amount  of  power  unavailable  in
the  world.  The  importance  of  correctly  distributing  the  amplifica-
tion along  the  system  is  well  illustrated  by  this  figure  by  comparing
it  with  the  signaling  power  actually  represented  in  the  system,  which
sums  up  to  something  less  than  1  kilowatt.  The  difference  is  simply
a  question  of  the  transmission  level  at  which  the  amplification  is
worked.

Fig.  7  gives  a  view  of  the  interior  of  one  of  these  radio  telephone
stations  of  the  American  Telephone  and  Telegraph  Company  and
Western  Electric  Company.    It  is  located  at  Deal  Beach,  New  Jersey.

In  the  foreground  is  the  switchboard  for  enabling  the  operator  to
control  the  radio-wire  circuit  at  the  connecting  point.  In  the  back-
ground are  the  transmitter  units — four  of  them.  These,  together
with  the  four  antennas  with  which  the  station  is  equipped,  "multiplex"
the  ether,  in  effect,  and  permit  four  channels  to  be  established  to  as
many  distant  stations.  It  is  intended  that  three  of  these  be  tele-
phone talking  channels  and  the  fourth  a  signaling  or  a  reserve  talking
channel.  The  receiving  station  is  located  at  another  point.  It  is
not  desired  to  describe  this  station  in  any  detail  but  merely  to  illus-
trate it  as  an  example  of  a  radio  repeating  station  functioning  to

connect  the  wire  system  with  ships  at  sea  and  capable  of  effecting
simultaneously  three  different  connections.  It  is  hoped  that  this
ship-to-shore  development  may  be  itself  the  subject  of  an  Institute
paper.

The  transcontinental  line  with  radio  extensions  as  shown  in  Fig.  6
is  a  good  illustration  of  the  use  of  intermediate  repeaters  generally.
Two  types  of  repeaters  are  represented,  the  straight  wire  telephone

repeaters  and  the  shore  radio  stations  which  are  in  effect  huge  re-
peaters rehaying  between  the  land  line  and  the  radio  circuits.

Because  of  the  moderate  attenuation  obtaining  in  the  wire  trans-
mission system,  we  can  work  with  fairly  long  repeater  spacings,  about
300  miles  in  this  case,  and  with  moderate  amounts  of  power  and  yet
keep   the   transmission  levels  at   the  receiving  end   relatively   much

TRANSMISSION  LEVEL  DIAGRAM
Wire  Transmission f=l  K.C
Rad  lolransmission  f  ■- 1000  K  C

higher  than  is  usual  in  radio  systems.  Due  to  the  large  attenuations
obtaining  over  the  radio  extensions,  the  radio  repeaters  must  put  out  a
high  transmission  level,  making  them  costly,  and  even  with  this  rela-
tively high  output,  the  level  drops  to  very  low  values  at  the  receiving

end.  This  falling  off  occurs  largely  in  the  get-away  loss  at  the  trans-
mitting end  of  the  radio  circuit,  as  the  diagram  indicates.

Fig.  8  depicts  an  all-radio  system  provided  with  intermediate
repeaters  and  compares  for  illustration  purposes  the  transmission
levels  obtaining  therein  with  those  for  a  wire  system.  The  solid
lines  are  for  radio  and  the  dash  for  wire.  It  will  be  seen  that  the
radio  system  courses  thru  wide  transmission  level  variations  as  com-
pared to  the  ordinary  wire  system  due  to  the  large  attenuations
obtaining  and  particularly  to  the  large  step-off  loss  near  the  sending
station.

The  figure  illustrates  the  same  spacing  for  both  radio  and  wire
repeating  and  gives  a  measure  of  the  difference  in  amplification
required  in  the  two  cases.  Altho  in  the  radio  repeaters  the  level
can  be  permitted  to  drop  to  low  values,  nevertheless  a  large  part  of
the  total  amplification  has  to  be  supplied  at  relatively  high  power
levels  and  it  is  this  fact,  together  with  the  antenna  structures  required
at  each  point  to  "get  into"  the  ether  transmission  medium  anew,
that  militates  against  the  economics  of  radio  repeaters  as  compared
with  straight-away  radio  transmission.  The  tendency  will  be  to
"stretch  out"  the  straight-away  transmission  due  to  the  fact  that
for  the  longer  distances  the  transmission  loss  increases  relatively
slowly.  While  we  may  look  for  some  important  uses  of  radio  re-
peaters in  special  cases,  we  should  not,  in  general,  expect  them  to  be
as  important  to  the  radio  art  as  are  wire  repeaters  in  wire  operation.

In  dealing  with  the  subject  of  power  levels  in  radio  transmission,
it  is  important  to  recognize  that  a  modulated  radio  telephone  wave
consists  of  two  components,  one,  the  carrier  frequency  itself  and  the
other,  the  so-called  side  bands,  which  are  the  actual  modulated
components.  This  resolution  of  the  modulated  carrier  into  two
or,  rather,  three  components,  the  carrier  and  two  side-bands,  has
been  given  mathematically  a  number  of  times  and  need  not  be  re-
peated. It  is  physically  analogous  to  the  resolution  of  the  uni-
directional current  of  a  microphone  transmitter  into  direct  current
and  alternating  current  components,  the  direct  current  corresponding
to  the  carrier  and  the  alternating  current  to  the  modulated  components.

Now,  the  important  thing  about  this  matter  of  side  bands  and  the
unmodulated  carrier  component,  with  reference  to  transmission
considerations,  is  this,  that  it  is  the  side  bands  alone,  and  not  the
carrier,  which  convey  the  actual  intelligence.     The  function  of  the

carrier  comes  in  merely  at  the  rerei\inp:  end,  in  the  detector,  as  a
means  for  translating  the  side  band  from  radio  frequency  back  to
audio  frequency.

This  will  be  made  clearer  by  reference  to  Fig.  9.  At  the  bottom
of  the  figure  is  shown  schematically  a  one-way  radio  system.  Above
it  is  depicted  the  voice-frequency  band,  showing  the  manner  in  which
it  is  shifted  by  modulation  up  to  the  carrier  frequency  range,  and  at
the  receiving  end,  by  detection,  back  to  the  voice  frequency  range.
The  voice  frequency  band,  as  it  comes  out  of  the  ordinary  telephone
transmitter,  is  shown  at  (61)  at  its  normal  telephone-frequency  posi-

tion.  Upon  modulation  with  the  carrier  the  reference  point  of  the
voice  frequency  band  is  shifted  from  zero  frequency  (direct  current)
up  to  the  carrier  frequency  as  shown  at  b^  where  the  two  side  bands
appear.  The  effect  of  modulation  is,  therefore,  simply  to  shift  the
band  of  signaling  frequencies  upward  in  the  frequency  range  and
refer  it  in  a  double  relation  to  the  carrier  frequency.

Located  between  the  upper  and  lower  side  band  in  the  figure,
there  is  indicated  the  unmodulated  component  of  the  carrier.  The
fact  that  this  component  is  unnecessary  so  far  as  the  actual  intelli-
gence-carrying energy  is  concerned,  is  proven  by  the  fact  that  it
need  not  be  transmitted  to  the  receiver.     The  carrier  may  be  sup-

pressed  as  shown  at  63.  A  means  for  doing  this  is  the  Carson  balanced
tube  modulator  circuit  illustrated  below  in  the  figure.

A  reduction  of  the  total  band  can  be  effected  by  filtering  out  one
of  them  as  shown  at  ^4-  The  remaining  single  band  is  the  simplest
component  of  the  modulation  process  with  which  intelligence  can
be  transmitted  to  the  distant  end.  Upon  arriving  at  the  receiving
end  at  b^,  this  side  band  is  fed  into  the  detector  along  with  a  carrier
of  the  same  frequency  as  that  employed  at  the  sending  end;  these
two  components  demodulate  one  another,  with  the  result  that  the
side  band  is  shifted  down  to  its  original  audio-frequency  position  in
the  scale,  as  indicated  at  be,.

Actually  this  general  method  of  transmission,  involving  both
carrier  suppression  and  side  band  elimination,  is  being  employed  in
wire  carrier  systems  in  the  Bell  Telephone  Plant. ^  It  is  briefly  ex-
plained here  because  it  represents  a  valuable  improvement  in  wire
transmission  which  should  have  important  application  in  radio.

From  the  standpoint  of  transmission  levels  its  application  is  in
showing  that  the  real  intelligence-carrying  component  of  a  radio  wave
is  the  side-band  and  not  the  carrier  itself.  In  considering  transmission
levels  accurately  care  should  be  taken,  therefore,  to  deal  in  terms  of
the  level  or  wave-intensity  of  the  side-band  component  and  not  the
carrier.  It  is  because  of  this  that  as  nearly  complete  modulation
as  possible  is  desired  at  the  transmitting  station.

It  follows  that  the  power  resident  in  the  carrier  is  a  pure  waste  in
so  far  as  overcoming  interference  is  concerned.  An  important  power
saving  can  be  effected  in  the  transmitting  station  by  providing  some
such  means  as  is  illustrated  whereby  the  carrier  power  is  held  back
in  the  circuit.  The  two  side-bands  together  can  never  be  greater  in
current  and  voltage  value  than  the  carrier,  and  each  side-band  alone
cannot  be  greater  than  half  the  carrier.  The  power  of  the  carrier  is
therefore  always  at  least  four  times  the  power  of  one  side-band  or
twice  that  of  both  together.  Thus  by  "  holding-back  "  the  carrier
at  the  transmitter  we  can  transmit  with  but  one-third  the  power
ordinarily  required.  Actually  the  power  saving  is  much  greater
than  this  because  of  the  necessity  of  normally  working  with  larger
ratios  between  carrier  and  side-band  in  order  to  accommodate  the
peaks  of  the  telephone  waves  and  thereby  preserve  the  quality  of
transmission.  The  power  saving  is,  of  course,  especially  important
in  long  distance  work.

•"Carrier  Current  Telephony  and  Telegraphy,"  by  Colpitis  and  Blackwell,
Journal  of  the  American  Institute  of  Electrical  Engineers,  February  16-18,  1921.

band  required  for  transmission  and  would  double  the  message-carrying
capacity  of  the  ether  were  no  frequency  range  required  to  space  the
channels  apart.  This  advantage  of  the  present  method  is  likewise  of
special  importance  in  long-distance-long-wave  transmission.

We  have  spoken  above  of  factors  concerned  with  the  volume  of
transmission  and  only  incidentally  of  that  other  requisite  of  trans-
mission, namely,  good  quality.  Without  going  into  this  matter  in
much  detail,  it  will  be  well  to  make  note  of  the  several  factors  in-
volved in  obtaining  good  quality,  as  follows:

1.  It  is  important  that  a  substantial  band  of  voice  frequencies  be
transmitted.  Of  course,  distorted  talk  can  be  transmitted  on  a
relatively  narrow  band,  but  commercial  transmission  has  been  found
to  require  a  single  side-band  width  of  the  order  of  2,000  or  more
cycles,  the  band  width  increasing  with  the  quality  desired,  up  to
about  5,000  cycles.

2.  It  is  necessary  that  the  distortion  which  is  due  to  non-linearity
of  transmission  with  respect  to  amplitude,  be  avoided.  This  is
equivalent  to  saying  that  there  should  not  be  permitted  to  take  place
self-modulation  between  the  components  of  the  side-band,  nor  the
too  close  cutting-ofT  of  the  peaks  of  the  telephone  waves  due  to  satura-
tion effects.

3.  The  transmission  must  be  kept  free  from  interfering  noises.
The  ratio  between  interfering  noise  current  and  voice  currents  of  the
order  of  0.1  is  regarded  as  large  in  wire  practice.  While  this  amount  of
interfering  current  will  not  prohibit  service,  it  does  seriously  impair  the
effectiveness  of  transmission  and  annoys  the  listener.  In  radio  the
ratio  of  static  noise  to  signal  strength  is  very  often  much  greater  than
this  value.  As  the  radio  art  progresses  it  will  be  necessary  to  work
toward  standards  more  nearly  in  keeping  with  those  which  have  been
found  necessary  for  wire  service.

The  writer  wishes  to  express  his  indebtedness  to  the  following  of
his  associates  for  helpful  suggestions  and  assistance — Messrs.  J.  R.  Car-
son, Ralph  Bown,  and  D.  K.  Martin.

As  regards  antenna  resistance  we  assume  symmetry  as  between
the  two  ends,  and  that  the  external  (radiation)  resistance  of  the  an-
tenna equals  the  resistance  within  the  antenna  (which  resistance
would  be  internal  apparatus  resistance  in  the  case  of  a  perfect  an-
tenna). This  makes  R^  (radiation  resistance)  =  i?,-  (ohmic  resistance) ;
and  R  of  (1)  becomes  =  R^  -^  Ri  where:

Expressing  in  terms  of  current  ratio  and  substituting  values  of  R,
equation  (1)  becomes,

In  order  to  plot  this  equation  on  the  same  basis  as  we  usually  plot
wire  attenuation,  the  logarithm  of  the  ratio  is  used,  thus;

The  ratio  of  the  currents  in  the  two  antennas  is  in  this  case  a  true
measure  of  the  transmission  because  they  are  in  circuits  of  equal  im-
pedances, by  the  assumption  of  antenna  symmetry.

For  number  8  Birmingham  wire  gauge  open  wire  (diam.  =  0.165
in.  =  4.19mm.  wire  spacing  =  12  in.  =  30.5  cm.  40  poles  per  mile)
dry  weather,  the  constants  per  mile  are;

Synopsis:  A  sensitive  cathode  ray  oscillograph  is  described  which
operates  at  the  low  potential  of  from  300  to  400  volts.  The  electron  stream
comes  from  a  thermionic  cathode  and  is  focused  by  the  action  of  ionized
gas  in  the  tube.  This  gas,  at  a  pressure  of  a  few  thousandths  of  a  milli-
meter, serves  to  reduce  to  1mm.  diameter  a  spot  which  would  be  1  cm.
across  in  a  high  vacuum  tube.  The  sensitivity  of  the  tube  is  such  that
the  deflection  of  the  spot  is  about  1  mm.  per  volt  applied  between  deflector
plates.  When  using  magnetic  deflection,  a  pair  of  coils  4  cm.  in  diameter,
placed  on  the  sides  of  the  tube  produces  a  deflection  of  approximately  1  mm.
per  ampere-turn  of  the  coils. — Editor.

In  the  older  types  of  Braun  tubes  the  electron  stream  is  produced
by  a  high  voltage  discharge  through  the  residual  gas  in  the  tube.
This  requires  a  source  of  steady  potential  of  from  10,000  to  50,000
volts,  an  installation  which  is  expensive,  non-portable,  and  dangerous.
In  the  new  type  of  tube  the  low  voltage  operation  has  been  obtained
by  the  use  of  a  Wehnelt  cathode  as  the  source  of  electrons,  so  that  the
lower  limit  of  voltage  is  set  by  the  effect  of  the  electrons  on  the  fluores-
cent screen  and  not  by  the  voltage  needed  to  obtain  the  electrons.
At  300  volts  the  electrons  produce  quite  bright  fluorescence  on  the
screen  and  the  tubes  are  therefore  designed  to  operate  at  300  to  400
volts.

The  external  appearance  of  the  tube  is  shown  in  Fig.  1.  The
electrodes  are  located  at  one  end  of  the  pear-shaped  bulb,  and  the
fluorescent  material  is  deposited  on  the  inside  of  the  larger,  flattened
end.  The  tube  is  provided  with  a  base  which  fits  into  a  bayonet
socket  such  as  is  used  for  vacuum  tubes,  and  all  the  connections  are
made  through  the  base.  There  are  two  orthogonal  pairs  of  deflector
plates  inside  the  tube  for  electrostatic  deflection,  while  magnetic
deflection  is  produced  by  applying  a  field  from  the  outside.

'Also  published  in  the"  Journal  of  the  Optical  Society  of  America  and  Review  oj
Scientific  Instruments,  September,  1922.
*Phys.  Rev.  (2),  Vol.  17,  p.  420,  1921.

In  some  forms  of  Braun  tube  a  sharp  spot  has  been  secured  by  using
a  very  high  voltage,  and  therefore  high  electron  velocity,  so  that
after  the  electrons  have  passed  through  one  or  two  fine  apertures
to  make  the  beam  parallel  there  is  not  time  enough  for  the  mutual
repulsion  to  spread  the  beam  again  appreciably  before  the  electrons
strike  the  screen.  With  other  tubes  an  external  "striction"  coil  has
been  used  which  maintains  a  strong  longitudinal  magnetic  field  in  the
region  between  the  anode  and  the  cathode  and  which  brings  the
electrons  to  a  focus  on  the  screen.  In  the  low  voltage  tube  the  spread-
ing of  the  electron  stream  is  greater  than  in  high  voltage  tubes  because
of  the  greater  time  during  which  the  mutual  repulsion  of  the  electrons

acts,  so  that  some  means  of  focusing  must  be  used.  The  electrons
can  be  brought  to  a  focus  by  a  longitudinal  magnetic  field  so  adjusted
that  each  divergent  electron  makes  very  nearly  one  complete  turn  of
a  spiral  and  in  travelling  the  length  of  the  tube  returns  to  the  axis  at
the  screen.  In  this  way  a  very  sharp  spot  can  be  produced,  but  the
sensitivity  of  the  beam  to  deflection  is  reduced  very  much  by  the
directing  magnetic  field.

The  method  of  focusing  that  is  used  in  the  present  tubes  grew  out
of  the  suggestion  by  Dr.  H.  J.  van  der  Bijl,  that  a  small  amount  of
gas  be  introduced  into  the  tube.  This  gas,  at  a  pressure  of  a  few
thousandths  of  a  millimeter  of  mercury,  serves  to  reduce  to  1  mm.
diameter  a  spot  which  would  be  1  cm.  across  in  a  high  vacuum  tube.
The  sharpness  of  the  spot  depends  also  upon  the  current  in  the  electron
stream  so  that  the  focus  may  be  controlled  by  the  cathode  temper-
ature.    The  mechanism  of  this  focusing  action  will  be  explained  later.

The  presence  of  this  slightly  ionized  gas  also  serves  the  purpose  of
preventing  the  accumulation  of  charges  on  the  glass,  and  it  provides

for  the  discharging  of  the  fluorescent  screen  so  that  the  electrons  can
drift  back  to  the  metallic  circuit.

With  gas  present  in  the  tube,  steps  have  to  be  taken  to  guard  against
arcing  and  the  injurious  effects  of  positive  ion  bombardment  on  the
cathode.  This  is  done  by  making  the  volume  of  gas  surrounding  the
electrodes  very  small.  For  this  purpose  the  cathode  and  anode,
themselves  small,  are  sealed  into  a  short  and  narrow  glass  tube  so
that  the  volume  exposed  to  both  electrodes  in  common  is  less  than
1  cu.  cm.  All  paths  between  the  electrodes  are  then  so  short  that  at
this  low  pressure  there  is  not  sufficient  ionization  to  build  up  an  arc.

The  structure  of  this  unit,  or  "electron  gun"  is  shown  in  Fig.  2.
The  cathode,  /,  is  an  oxide  coated  platinum  ribbon  of  the  same  kind

as  the  filament  in  our  audion  tubes.  The  anode,  a,  is  a  thin  platinum
tube  1  cm.  long  and  1  mm.  in  diameter,  one  end  of  which  is  about
1  mm.  from  the  top  of  the  filament  loop,  the  other  end  opening  into
the  main  tube  towards  the  fluorescent  screen.  Between  the  cathode
and  the  anode  and  connected  to  the  cathode  is  a  metal  shield,  s,  with
a  small  aperture  through  which  the  electrons  must  pass  in  going  to  the
anode.  Nearly  all  of  the  electrons  must  then  go  to  the  inside  of  the
tubular  anode,  and  a  small  fraction  of  them  pass  through  the  whole

length  of  the  anode  and  form  the  beam  in  the  main  part  of  the  tube.
The  deflector  plates,  p,  are  also  mounted  rigidly  on  this  unit.  In
order  to  avoid  large  differences  of  potential  in  the  tube,  one  plate  from
each  pair  is  permanently  connected  to  the  anode,  the  variable  poten-
tials being  applied  to  the  other  plates.  The  complete  unit  is  mounted
at  the  small  end  of  the  tube  with  the  anode  and  deflector  plates  toward
the  fluorescent  screen.

In  some  earl>'  forms  the  filament  was  bent  into  a  simple  hair  pin
loop  which  was  placed  close  to  the  aperture  in  the  shield.  It  was  then
found  that  the  positive  ions  striking  the  filament  from  the  direction
of  the  anode  soon  destroyed  the  oxide  coating  and  left  the  filament
inactive.  This  trouble  was  largely  overcome  by  placing  the  filament
out  of  the  direct  path  of  the  positive  ions.  The  flat  filament  is  now
shaped  into  a  ring  as  shown  in  P'ig.  3,  slightly  larger  in  diameter  than

the  aperture  in  the  shield  and  is  placed  coaxial  with  the  anode.  The
momentum  of  the  positive  ions  then  carries  them  past  the  active
part  of  the  filament  and  they  strike  where  little  damage  can  be  done.
The  length  of  service  of  the  tube  is  still  limited  by  the  filament  life,
but  this  has  been  increased  by  the  above  artifice  so  that  the  tube  now
gives  around  200  hours  of  actual  operation.

The  deflector  plates  are  made  of  German  silver,  which  is  non-
magnetic and  which  has  a  high  specific  resistance  that  diminishes  the
effect  of  eddy  currents  when  magnetic  deflection  is  used.  The  plates
are  13.7  mm.  long  in  the  direction  of  the  tube  axis  and  the  separation
between  them  is  4.7  mm.

The  sensitivity  of  the  tube  is  such  that  the  deflection  of  the  spot
is  about  one  mm.  per  volt  applied  between  the  deflector  plates.    When

using  magnetic  deflection,  a  pair  of  coils  4  cm.  in  diameter  placed  on
the  sides  of  the  tube  at  the  level  of  the  deflector  plates  produces  a
deflection  of  approximately  1  mm.  per  ampere-turn  flowing  in  the  coils.
The  electrons  striking  the  screen  drift  back  to  the  anode  structure,
and  most  of  them  are  collected  by  the  deflector  plates.  There  is  also
a  small  ionization  current  flowing  to  the  plates.  The  tube  is  therefore
not  strictly  an  electrostatic  device,  and  this  must  be  kept  in  mind
when  using  it.  Fig.  4  shows  the  current  flowing  to  the  two  free  plates
at  various  voltages  with  respect  to  the  anode.     With  the  large  posi-

tive  values  of  plate  voltage  the  current  to  the  plates  is  practically
equal  to  the  current  in  the  electron  stream  and  consists  largely  of  the
returning  electrons.  The  small  current  in  the  other  direction  when
the  plate  voltage  is  negative  is  a  measure  of  the  ionization  in  the  tube.

The  screen  is  spread  on  the  inner  surface  of  the  large  end  of  the
tube,  using  pure  water  glass  for  binder.  The  active  material  consists
of  equal  parts  of  calcium  tungstate  and  zinc  silicate,  both  specially
prepared  for  fluorescence.  This  mixture  produces  a  generally  more
useful  screen  than  either  constituent  alone.  The  pure  tungstate
gives  a  deep  blue  light  which  is  about  30  times  as  active  on  the  photo-
graphic plate  as  the  yellow-green  light  of  the  silicate,  while  the  silicate
gives  a  light  which  is  many  times  brighter  visually  than  that  from  the
tungstate.  By  mixing  the  two  materials  in  equal  parts  a  screen  is
produced  which  is  more  than  half  as  bright  visually  as  pure  zinc
silicate  and  more  than  half  as  active  photographically  as  pure  calcium
tungstate.

For  mechanical  strength  the  end  of  the  bulb  which  carries  the  screen
is  rounded  outwards  so  that  the  screen  is  not  a  plane  surface.  This
introduces  a  distortion  of  the  fluorescent  pattern  which  in  most  in-
stances is  negligible.  If  the  pattern  is  recorded  by  a  camera  whose
lens  is  D  cm.  from  the  end  of  the  tube,  then  the  apparent  reduction
of  the  deflection  produced  by  the  curvature  of  the  bulb  is  given  in
terms  of  the  deflection  y  approximately  by

The  part  which  the  gas  plays  in  focusing  the  beam  of  electrons
is  an  interesting  phenomenon  which  depends  upon  the  difference  in
the  mobilities  of  electrons  and  positive  ions.  The  electrons  of  the
beam  are  pulled  toward  the  common  axis  by  a  radial  electric  field
produced  by  an  excess  of  positive  electricity  in  the  electron  stream
and  an  excess  of  negative  electricity  in  the  space  outside  the  beam.
This  distribution  is  produced  as  follows:  Some  of  the  electrons  of
the  stream,  in  passing  through  the  gas,  collide  with  gas  molecules
and  ionize  them.  Both  the  colliding  electrons  and  the  secondary
electrons  leave  the  beam  but  the  heavy  positive  ions  receive  very
little  velocity  from  the  impact  and  drift  out  of  the  beam  with  only
their  comparatively  low  thermal  velocity.     Positive  ions,  therefore,

accumulate  down  the  length  of  the  stream  and  may  exceed  in  number
the  negative  charges  passing  along.  At  the  same  time,  electrons  are
moving  at  random  outside  the  stream,  producing  negative  electrifica-
tion. There  is  then  a  field  surrounding  the  stream  which  tends  to
pull  the  electrons  inward.  If  there  were  only  the  mutual  repulsion
between  the  electrons  to  compensate  for,  this  would  be  done  when
the  number  of  positive  ions  in  the  beam  equals  the  number  of  electrons.
There  is  in  addition  an  original  divergence  of  the  beam  which  must  be
overcome.  If  this  divergence  is  assumed  to  be  one  degree  from  the
axis  and  the  electron  current  2  x  10~^  amp.,  then  a  simple  calculation
shows  that  the  radial  field  required  to  pull  the  beam  to  a  focus  at  the
usual  distance  is  about  one  volt  per  cm.  This  field  strength  is  pro-
duced, with  beams  of  the  ordinary  intensity,  if  there  are  four  positive
ions  for  each  electron  in  the  stream,  a  Condition  which  seems  not
unreasonable.

The  number  of  ions  per  electron  in  the  stream  is  probably  constant
as  the  current  in  the  stream  is  varied,  since  the  conditions  of  collision
and  recombination  are  not  altered.  When  the  current  is  increased,
therefore,  the  total  positive  ionization  of  the  beam  increases,  the  field
around  the  beam  becomes  stronger,  and  the  electrons  are  brought  to
a  focus  in  a  shorter  distance.

These  deductions  have  been  confirmed  experimentally.  That  the
focusing  of  the  stream  depends  upon  the  current  flowing  was  one  of
the  earliest  observations  made  in  developing  the  tube  and  this  method
has  been  used  ever  since  to  obtain  a  sharp  spot.  The  point  of  con-
vergence can  be  seen  moving  in  the  manner  expected  when  the  current
is  changed,  and  the  effect  has  been  further  verified  by  using  a  tube  with
a  movable  fluorescent  screen  so  that  the  length  of  the  electron  beam
could  be  varied.  The  presence  of  the  electric  field  around  the  beam
was  shown  by  the  effect  of  two  beams  on  each  other,  in  a  tube  in
which  there  were  two  electron  streams  crossing  each  other  at  right
angles  at  their  mid-points,  each  falling  on  a  fluorescent  screen.  When
one  beam  was  moved  away  from  the  other  by  a  field  between  the
deflector  plates,  the  second  beam  moved  as  if  attracted  by  the  first.
The  directed  electrons  in  each  beam  were  attracted  toward  the  posi-
tive ionization  in  the  other,  and  for  one  particular  adjustment  of  the
tube  the  displacement  was  such  as  would  have  been  caused  by  a
field  ot  about  3  volts  per  cm.,  a  result  not  far  different  from  that
previously  calculated.

Since  the  beam  must  produce  its  own  positive  ionization  some  time
must  elapse  before  it  can  produce  by  collisions  the  required  number
of  positive  ions.     Calculation  shows  this  time  to  be  of  the  order  of

10~*  second.  When  the  beam  moves  it  has  to  build  up  the  ionization
as  it  goes  along,  and  we  should  expect  that  when  deflected  very
rapidly  it  might  no  longer  be  focused,  due  to  lack  of  positive  ions  in
its  path.  A  test  was  made  of  this  by  applying  a  high  frequency
potential  on  the  deflector  plates  so  that  the  spot  described  an  elliptic
pattern.  At  a  frequency  of  10*  cycles  per  second  the  line  was  still
sharp,  but  at  10*  cycles  there  was  a  noticeable  widening  of  the  line
which  is  probably  to  be  ascribed  to  imperfect  focusing  at  this  high
speed .

In  these  experiments  the  evidence  all  points  to  the  view  that  the
focusing  of  the  electrons  is  caused  by  an  excess  of  positive  charge  in
the  beam  itself,  produced  by  ionizing  collisions  of  the  electrons  with
the  gas  molecules.  Further  confirmation  is  found  in  the  fact  that  a
focus  is  much  more  readily  obtained  in  the  heavier  gases  having  slow
molecules,  such  as  nitrogen,  argon  or  mercury  vapor,  than  in  hydrogen
and  helium  where  the  mean  velocity  of  the  molecules  is  greater.  The
tubes  are  therefore  filled  with  argon,  the  heaviest  available  permanent
gas  which  does  not  attack  the  electrodes.  The  best  pressure  for  the
length  of  tube  adopted  and  for  the  current  which  can  be  obtained
in  the  beam  is  5  to  10  microns,  and  this  leaves  considerable  latitude
for  the  adjustment  of  the  electron  current  to  get  a  sharp  focus.

Because  of  the  small  amount  of  auxiliary  apparatus  required  with
this  form  of  Braun  tube  it  has  proved  to  be  a  very  convenient  labora-
tory instrument.  It  has  found  application  in  studying  the  behavior
of  vacuum  tubes  and  amplifier  and  oscillator  circuits,  of  gas  discharge
tubes,  of  relays,  and  of  numerous  other  kinds  of  apparatus,  both  at
low  and  at  high  frequencies.  Some  reproductions  of  photographs  of
various  types  of  curves  are  given  below  to  illustrate  the  kind  of  results
which  are  possible  with  this  oscillograph.

Fig.  5  shows  the  hysteresis  curve  of  a  sample  of  iron  wire.  The
wire  was  placed  in  a  small  solenoid  with  one  end  toward  the  side  of
the  tube.  The  magnetizing  current  passed  through  a  resistance,
the  voltage  drop  of  which  was  applied  to  one  pair  of  deflector  plates
so  as  to  give  a  deflection  proportional  to  the  magnetizing  field.  The
stray  magnetic  field  from  the  iron  itself  produced  the  deflection
proportional  to  the  induction.  Alternating  current  was  used,  and
the  exposure  was  20  seconds  with  lens  opening  /  6.3  and  speed  roll
film.

oscillating  vacuum  tube.     The  axes  were  obtained  by  grounding  one
or  the  other  deflector  element.

been  reduced  to  a  fairly  simple  process  by  means  of  the  cathode  ray
tube.     The    low    frequency    modulating   voltage,    controlled    by    the

voice,  is  applied  to  one  pair  of  deflector  plates,  while  the  radio  fre-
quency output,  with  amplitude  varying  according  to  the  low  frequency
voltage,  is  applied  to  the  other  pair  of  deflector  plates.  The  resulting
pattern  on  the  screen  is  a  quadrilateral  of  solid  fluorescence,  since  the

two  frequencies  are  not  commensurate.  The  two  vertical  sides
indicate  the  greatest  and  the  least  amplitude  of  the  high  frequency,
while  the  other  two  sides  show  the  current-voltage  characteristic  of
the  transmitter.  Fig.  7  shows  such  a  pattern  (retouched) ,  the  edges
being  much  brighter  than  the  centre.  The  exposure  was  two  minutes
using  a  Seed  23  plate  and  /  6.8  lens  opening.

George  A.  Campbell,  B.S.,  Massachusetts  Institute  of  Technology,
1891;  A.B.,  Harvard,  1892;  Ph.D.,  1901;  Gottingen,  Vienna  and
Paris,  1893-96.  Mechanical  Department,  American  Bell  Telephone
Company,  1897;  Engineering  Department,  American  Telephone  and
Telegraph  Company,  1903-1919;  Department  of  Development  and
Research,  1919 — ;  Research  Engineer,  1908 — .  Dr.  Campbell  has
published  papers  on  loading  and  the  theory  of  electric  circuits  and  is
also  well-known  to  telephone  engineers  for  his  contributions  to  re-
peater and  substation  circuits.  The  electric  filter  which  is  one  of  his
inventions  plays  a  fundamental  role  in  telephone  repeater,  carrier
current  and  radio  systems.

Ralph  V.  L.  Hartley,  A.B.,  Utah,  1909;  B.A.,  Oxford,  1912;
B.Sc,  1913;  instructor  in  physics,  Nevada,  1909-10;  Engineering
Department,  Western  Electric  Company,  1913 — .  For  some  time
Mr.  Hartley  has  been  closely  connected  with  the  development  of
carrier  current,  telephone  repeater,  and  telegraph  systems.

Thornton  C.  Fry,  A.B.,  Findlay,  1912;  A.M.,  University  of  Wis-
consin, 1913;  Ph.D.,  1920;  instructor  of  mathematics,  Wisconsin,
1912-16;  Engineering  Department,  Western  Electric  Company,
1916 — .  Mr.  Fry  has  written  several  papers  on  the  theory  of  electric
circuits  and  other  subjects  allied  to  telephony.

John  R.  Carson,  B.S.,  Princeton,  1907;  E.E.,  1909;  M.S.,  1912;
Research  Department,  Westinghouse  Electric  and  Manufacturing
Company;  1910-12;  instructor  of  physics  and  electrical  engineering,
Princeton,  1912-14;  American  Telephone  and  Telegraph  Company,
Engineering  Department,  1914-15;  Patent  Department,  1916-17;
Engineering  Department,  1918;  Department  of  Development  and
Research,  1919 — .  Mr.  Carson's  work  has  been  along  theoretical  lines
and  he  has  published  several  papers  on  theory  of  electric  circuits  and
electric  wave  propagation.

R.  L.  Wegel,  A.B.,  Ripon  College,  1910;  assistant  in  physics,
University  of  Wisconsin,  1910-12;  physicist  with  T.  A.  Edison,  1912-
13;  Engineering  Department  of  Western  Electric  Company,  1914 — .
Mr.  Wegel  has  been. closely  associated  with  the  development  of  tele-
phone transmitters  and  receivers,  and  has  made  important  contribu-
tions to  the  theory  of  receivers.

Edward  C.  Molina,  Engineering  Department  of  the  American
Telephone  and  Telegraph  Company,  11)01-19,  as  engineering  assist-
ant; transferred  to  the  Circuits  Design  Department  to  work  on  ma-
chine switching  systems,  1905;  Department  of  Development  and
Research,  1919 — .  Mr.  Molina  has  been  closely  associated  with
the  application  of  the  mathematical  theory  of  probabilities  to  trunking
problems  and  has  taken  out  several  important  patents  relating  to
machine  switching.

William  C.  Helmle,  B.  S.,  University  of  Wisconsin,  1917;  Uni-
versity of  Chicago,  1919-20;  Commercial  Engineer's  Ofifice,  American
Telephone  and  Telegraph  Company  1920 — .

E.  T.  HocH,  B.S.,  in  Electrical  Engineering,  Case  School  of  Ap-
plied Science,  1914;  Western  Electric  Company,  Manufacturing  and
Installation  Departments,  1914-15;  Engineering  Department,  1915 — .

Lloyd  Espenschied,  Pratt  Institute,  1909;  United  Wireless  Tele-
graph Company  as  radio  operator,  summers,  1907-08;  Telefunken
Wireless  Telegraph  Company  of  America  assistant  engineer,  1909-
10;  American  Telephone  and  Telegraph  Company,  Engineering
Department  and  Department  of  Development  and  Research,  1910 — .
Took  part  in  long  distance  radio  telephone  experiments  from  Wash-
ington to  Hawaii  and  Paris,  1915;  since  then  his  work  has  been  con-
nected with  the  development  of  radio  and  carrier  systems.

J.  B.  Johnson,  B.S.,  University  of  North  Dakota,  1913;  M.S.,
1914;  Ph.D.,  Yale,  1917;  Engineering  Department,  Western  Elec-
tric Company,  1917 — .  Since  coming  to  the  Western  Electric  Com-
pany, Mr.  Johnson  has  devoted  much  time  to  high  vacua  and  ioniza-
tion in  gases.

Application  of  Carrier  Telephone  and  Telegraph  in  the  Bell  Sj-stem,  Arthur  F.

Rose,  Vol.  II,  No.  2,  page  41.
Application  to  Radio  of  Wire  Transmission  Engineering,  Lloyd  Espenschicd,  Vol.

I,  No.  2,  page  117.
Arnold,  H.  D.,  Permalloy,  A  New  Magnetic  Material  of  Very  High  Magnetic

Transatlantic  Radio  Telephony,  Vol.  II,  No.  4,  page  116.
Audition,    Physical   Characteristics   of,   R.   L.    Wegel,   Vol.    I,    No.  2,   page   56.
Audition,  Physical  Measurements  of,  Harvey  Fletcher,  Vol.  II,  No.  4,  page  145.

Bateman,  Helene  C,  A  Method  of  Graphical  Analysis,  Vol.  II,  No.  3,  page  77.
Binaural  Location  of  Complex  Sounds,  R.  V.  L.  Hartley  and  Thornton  C.  Fry,
Vol.  I,  No.  2,  page  33.

Cable,  Philadelphia-Pittsburgh  Section  of  the  New  York-Chicago,  J.  J.  Filliod,

Vol.  I,  No.  1,  page  60.
Cable    Circuits,   Telephone   Transmission   Over,   A.   B.    Clark,   Vol.    II,    No.    1,

page.  67.
Cable  Circuits,  Telephone  Equipment  for,  Charles  S.  Demarest,  Vol.  II,  No.  3,

Probability   Curves   Showing    Poisson's   Exponential    Summation,   Vol.    II,
No.  1,  page  95.
Carrier  and  Side  Bands  in  Radio  Transmission,  R.  V.  L.  Hartley,  Vol.  II,  No.  2,

page  90.
Carrier  Telephone  and  Telegraph  in  the  Bell  System,  Practical  Application  of,

Arthur  F.  Rose,  Vol.  II,  No.  2,  page  41.
Carson,  John  R.,  Heaviside  Operational  Calculus,  Vol.  I,  No.  2,  page  43.

Transmission  Characteristics  of  Submarine  Cable,  Vol.  I,  No.  1,  page  88.
Charlesworth,  H.  P.,  Machine  Switching  Telephone  System  for  Large  Metro-
politan Areas,  Vol.  II,  No.  2,  page  53.
Clark,  A.  B.,  Telephone  Transmission  Over  Long  Cable  Circuits,  Vol.  II,  No.  1,
page  67.

Use   of    Public   Address    System   with    Telephone   Lines,    Vol.    II,    No.   2,
page  143.
Complex  Sounds,  the  Binaural  Location  of,  R.  V.  L.  Hartley  and  Thornton  C.

Fry,  Vol.  I.,  No.  2,  page  33.
Craft,    E.    B.,   Machine    Switching  Telephone    System    for   Large    Metropolitan

Areas,  Vol.  II,  No.  2,  page  53.
Crandall,  I.  B.,  Analysis  of  the  Energy  Distribution  in  Speech,  Vol.  I,  No.  1,

page  101.
Demarest,  Charles   S.,  Telephone   Equipment   for  Long  Cable  Circuits,  Vol.   II,

Permeability,  Vol.  II,  No.  3,  page  101.
Energy  Distribution,  Analysis  of   in   Speech,  /.  B.   Crandall  and  D.  Mackenzie,

Vol.  I,  No.  1,  page  116.
Espenschied,   Lloyd,   Application   to   Radio   of   Wire  Transmission   Engineering,
Vol.  I,  No.  2,  page  117.

Transatlantic  Radio  Telephony,  Vol.  II,  No.  4,  page  116.
External  Ear,  Dynamical  Analysis  of,  R.  L.  Wegel,  Vol.  I,  No.  2,  page  56.

Fletcher,  Harvey,  The  Nature  of  Speech  and  Its  Interpretation,  Vol.  I,  No.  1,
page  129.
Physical  Measurements  of  Audition  and  Their  Bearing  on  the  Theory  of
Hearing,  Vol.   II,  No.  4,  page  145.
Fry,  Thornton  C,  The  Binaural  Location  of   Complex  Sounds,  Vol.  I,  No.  2,
page  33.

Gases  Evolved  from  Glasses  of  Knov^^n  Chemical  Composition,  Measurements  of,
J.  E.  Harris  and  E.  E.  Schumacher,  Vol.  II,  No.   1,  page  122.

Gilbert,  J.  J.,  Transmission  Characteristics  of  Submarine  Cable,  Vol.  I,  No.  1,
page  88.

Hartley,  R.  V.  L.,  Relation  of  Carrier  and  Side  Bands  in  Radio  Transmission,
Vol.  II,  No.  2,  page  90.
The  Binaural  Location  of  Complex  Sounds,  Vol.  I,  No.  2,  page  ii.

Harris,  J.  E.,  Measurements  of  the  Gases  Evolved  from  Glasses  of  Known  Chem-
ical Composition,  Vol.  II,  No.  1,  page  122.

Helmle,  W.  C,  The  Relation  Between  Rents  and  Incomes  and  the  Distribution  of
Rental  Values,  Vol.  I,  No.  2,  page  82.

Hoyt,  Ray  S.,  Impedance  of  Smooth  Lines  and  Design  of  Simulating  Networks,
Vol.  II,  No.  2,  page  1.

Impedances  of  Smooth  Lines  and  Design  of  Simulating  Networks,  Ray  S.  Hoyt,
Vol.  II,  No.  2,  page  1.

Inductive  Eflfects  in  Neighboring  Communication  Circuits,  the  Relation  of  Peter-
son System  of  Grounding  Power  Networks  to,  //.  M.  Truchlaod,  Vol.  I,
No.  1,  page  39.

King,  R.  \\'.,  Thermionic  Vacuum  Tubes  and  Their  Uses,  Vol.  II,  No.  4,  page  31.
Kirk,  J.  N.,  Bell  System  Sleet  Storm  Map,  Vol.  II,  No.  1,  page  114.

Specializing  Transportation  Equipment  in  Order  to  Adapt  it  Most  Econom-
ically to  Telephone  Construction  and  Maintenance  Work,  Vol.  II,  No.  1,
page  47.
Use  of  Labor-Saving  Apparatus  in  Outside  Plant  Construction  Work,  Vol.
II,  No.  3,  page  53.

Labor-Saving  Apparatus  in  Outside  Plant  Construction  Work,  /.  A'^.  Kirk,  Vol.
II,  No.  3,  page  53.

Machine  Switching  Telephone  System  for  Large  jMetropolitan  Areas,  E.  B.
Craft,  L.  F.  Morehouse  and  H.  P.  Charlesivorth,  Vol.  II,  No.  2,  page  53.

Martin,  W.  H.,  Use  of  Public  Address  System  with  Telephone  Lines,  Vol.  II,
No.  2,  page  143.

Measurements  of  the  Gases  Evolved  from  Glasses  of  Known  Chemical  Com-
position, /.  E.  Harris  and  E.  E.  Schumacher,  Vol.  II,  No.  1,  page  122.

Molina,  Edward  C,  The  Theory  of  Probabilities  Applied  to  Telephone  Trunking
Problems,  Vol.  I,  No.  2,  page  69.

Morehouse,  L.  F.,  Machine  Switching  Telephone  System  for  Large  Metropolitan
Areas,  Vol.  II,  No.  2,  page  53.

New  York-Chicago  Cable,  Philadelphia-Pittsburgh  Section  of,  /.  /.  Pilliod,  Vol.

Operational  Calculus,  Heaviside,  John  R.  Carson,  Vol.  I,  No.  2,  page  43.
Oscillations,  Transient,  in  Electric  Wave-Filters,  /.  R.  Carson  and  0.  J.  Zohel,

Vol.  II,  No.  3,  page  1.
Oscillograph,  A  Low  Voltage  Cathode  Ray,  J .  B.  Johnson,  Vol.  I,  No.  2,  page

Permalloy,  A  New  Magnetic  Alaterial  of  Very  High  Magnetic  Permeability,  H.
D.  Arnold  and  G.  W.  Elmen,  Vol.  II,  No.  3,  page, 101.

Peterson  System  of  Grounding  Power  Networks,  the  Relation  to  Inductive  Ef-
fects in  Neighboring  Communication  Circuits,  H.  M.  Trueblood,  Vol.  I,
No.  1,  page  39.

Philadelphia-Pittsburgh  Section  of  the  New  York-Chicago  Cable,  /.  /.  Pilliod,
Vol.  I,  No.  1,  page  60.

Physical  Characteristics  of  Audition  and  Dynamical  Analysis  of  the  External
Ear,  R.  L.  Wegel,  Vol.  I,  No.  2,  page  56.

Physical  Measurements  of  Audition  and  Their  Bearing  on  the  Theory  of  Hear-
ing, Harvey  Fletcher,  Vol.  II,  No.  4,  page  145.

Pilliod,  J.  J.,  Philadelphia-Pittsburgh  Section  of  the  New  York-Chicago  Cable,
Vol.  I,  No.  1,  page  60.

Poisson's  Exponential  Summation,  Probability  Curves  Showing,  G.  A.  Campbell,
Vol.  II,  No.  1,  page  95.

Probabilities  Applied  to  Telephone  Trunking  Problems,  The  Theory  of,  Edzvard
C.  Molina,  Vol.  I,  No.  2,  page  69.

Probability  Curves  Showing  Poisson's  Exponential  Summation,  G.  A.  Campbell,
Vol.  II,  No.  1,  page  95.

Public  Address  System,  Use  of.  The  Telephone  Lines,  W.  H.  Martin  and  A.  B.
Clark,  Vol.  II,  No.  2,  page  143.

Radio  Extension  of  the  Telephone  System  to  Ships  at  Sea,  H.  W.  Nichols  and
Lloyd  Espenschied,  Vol.  II,  No.  3,  page  141.

Radio  Telephony,  Transatlantic,  H.  D.  Arnold  and  Lloyd  Espenschied,  Vol.  II,
No.  4,  page  116.

Rents  and  Incomes  and  the  Distribution  of  Rental  Values,  The  Relation  Be-
tween, W.  C.  Hchnlc,  Vol.  I,  No.  2,  page  82.

Rose,  Arthur  P.,  Practical  Application  of  Telephone  and  Telegraph  in  the  Bell
System,  Vol.  II,  No.  2,  page  41.

Chemical  Composition,  Vol.  II,  No.  1,  page  122.
Sleet  Storm  Map,  Bell  System,  /.  A^.  Kirk,  Vol.  II,  No.  1,  page  114.

Some  Con  temporal'  Advances  in  Physics,  A.'.  K.  Darroiv,  Vol.  II,  No.  4,  page  101.
Speech,  Analysis  of  Energy  Distribution  in,  /.  B.  Crandall  and  D.  Mackenzie,

Vol.  I,  No.  1,  page  116.
Speech,  The  Nature  of  and  Its  Interpretation,  H.  Fletcher,  Vol.  I,  No.  1,  page  129.
Submarine  Cable,  Transmission  Characteristics  of,  /.  R.  Carson  and  /.  /.  Gilbert,

No.  3,  page  112.
Theory  and  Design  of  Uniform  and  Composite  Electric  Wave  Filters,  Otto  J.

Zobel,  Vol.  II,  No.  1,  page  1.
Theory,  Electric  Wave  Filter,  G.  A.  Campbell,  Vol.  I,  No.  2,  page  1.
Thermionic  Vacuum  Tubes  and  Their  Uses,  R.  IV.  King,  Vol.  II,  No.  4,  page
Transatlantic  Radio  Telephony,  H.  D.  Arnold  and  Lloyd  Espenschied,  Vol.  II,

No.  4,  page  116.
Transient  Oscillations  in  Electric  Wave-Filters,  /.  R.  Carson  and  0.  /.  Zobel,

Vol.  II,  No.  3,  Page  1.
Transmission  Characteristics  of  the   Submarine  Cable,  /.  R.   Carson  and  /.  /.

Gilbert,  Vol.  I,  No.  1,  page  88.
Transmission  Over  Long  Cable  Circuits,  A.  B.  Clark,  Vol  II,  No.  1,  page  67.
Transportation  Equipment,  Specializing,  In  Order  to  Adapt  It  Most  Economically

1,  page  47.
Trueblood,  H.  M.,  The  Relation  of  the  Peterson  System  of  Grounding  Power

Networks  to  Inductive  Effects  in  Neighboring  Communication  Circuits,  Vol.

I,  No.  1,  page  39.
Trunking  Problems,  The  Theory  of  Probabilities  Applied  to,  Edward  C.  Molina,

Vacuum  Tube,  a  New  Type  of  High-Power,  W.  Wilson,  Vol.  I,  No.  1,  page  4.
Vacuum  Tube,  Thermionic,  R.  W.  King,  Vol.  II,  No.  4,  page  31.

No.  3,  page  1.
Wegel,  R.  L.,  Physical  Characteristics  of  Audition  and  Dynamical  Analysis  of

the  External  Ear,  Vol.  I,  No.  2,  page  56.
Wilson,  W.,  A  New  Type  of  High-Power  Vacuum  Tube,  Vol.  I,  No.  1,  page  4.
Wire  Transmission  Engineering,  Application  to  Radio,  Lloyd  Espenschied,  Vol.

Zobel,  Otto  J.,  Theory  and  Design  of  Uniform  and  Composite  Electric  Wave
Filters,  Vol.  II,  No.  1,  page  1.
Transient  Oscillations  in   Electric  Wave-Filters,  Vol.  II,  No.  3,  page  1.

The Bell System Technical Journal, Volume 1