A Description of the Unit of Telephone Transmission
Recently Adopted by the Bell System and
A Discussion of the Reasons for its Selection

Research Laboratories of the American Telephone
and Telegraph Company , and the Western
Electric Company , Incorporated.

nection is a question of both technical and
commercial importance. The advances that
have been made in long distance telephony, both
by wire and by radio, are emphasizing the need
of cooperation in Europe in the engineering and
operation of interconnecting systems. The
simplifications in engineering specifications that
would result if the present diversity of units in
Europe could be replaced by a single one are obvi-
ous. At the same time the interchange of in-
formation through the technical press would be
greatly facilitated.

The experience of the engineers of the Bell
System led them, a short time ago, to the con-
clusion that the type of unit discussed in this
paper is the most suitable for present conditions
in the telephone art. This unit is called, for the
present at least, the 11 transmission unit” and
abbreviated T.U. 1 This unit was submitted for
consideration to many of the leading telephone
establishments of the world. The response to
this proposal was favorable, in general, although
there were several exceptions. The American
Telephone and Telegraph Company are adopting
this new unit as standard in the Bell System. 2

The transmission unit is of the same general
nature as the “Mile of Standard Cable at 800

1 For convenience it is intended to dispense with periods
and with s as indicating a number of TV .

2 “The Transmission Unit and Telephone Transmission
Reference System”; VV. II. Martin; Journal of the
A. I. E. E., June, 1924, p. 504.

Cycles” and the (31 unit, both of which it is
intended to replace. It is used to measure the
same quantities as are now measured in those
units. At the same time it is defined in such a
way as to facilitate the extension of its applica-
tion to meet the needs of the newer develop-
ments in the communication art. Its magni-
tude is very nearly the same as that of the 800
cycle mile. It is, however, so chosen as to
make the use of common or Briggs’ logarithms
convenient in transmission computations. The
number of 800 cycle miles corresponding to a
condition wherein the currents under com-
parison are i\ and /*> is given by

from which it follows that the TU is a loga-
rithmic measure of power ratio and is numer-
ically equal to log 10 01 .

The use of powers rather than currents is
connected with the breadth of application
already referred to, and will be discussed in
more detail later. In case the currents associ-
ated with the powers under comparison are

The reasons for selecting this particular unit
rather than some other will probably not be
obvious at first sight. They should, however,
become apparent as we run over what the re-
quirements for such a unit are, and in what
respects the various possible units may differ
from one another.

The “mile of standard cable” as originally
used gave a means of comparing the loudness of
the sound emitted by a receiver under any two
conditions in terms of the number of miles of
actual physical cable that had to be inserted
under one of the conditions to make the two of
equal loudness. In practice, of course, ad-
justable artificial cables were used. The defini-
tion of the unit then was in terms of the con-
stants per mile of the cable chosen as standard.
Unfortunately two slightly different cables have
become standard. That used in America has a
loop resistance of 88 ohms and a capacity of
.054 microfarads per mile. Some of the other
countries use a cable of the same resistance
and capacity which has in addition an induc-
tance of 1 milhenry and a conductance of 1
micromho per mile.

The effect on the output of the receiver of
inserting such a cable is much greater at high
frequencies than at low; that is, it distorts the
speech at the same time that it attenuates it.
Moreover, the distortion increases with the
length of the cable used. This distortion was
rather a desirable property so long as the use of
the unit was confined to talking comparisons of
lines having roughly the same distortion as the
standard cable. This condition no longer exists,
however. Many of the circuits now in use have
much less distortion than has a length of stand-
ard cable having the same attenuation. Also
the unit is used to express the effect of inserting
pieces of apparatus whose frequency character-
istic bears no resemblance to that of the cable.
In America at least the use of voice testing in
the plant has been practically replaced by
methods employing sine wave currents and
electric measuring instruments. As these tests
may be made with currents of various fre-
quencies, it is important that the results be
expressed in units which are independent of the
frequency.

As this need arose it was natural to adapt the
existing unit to meet it. Thus the effect of the
circuit under test for a current of any particular
frequency came to be compared with that of the
standard cable for a current of one standard
frequency; namely, 796 cycles per second, for
which 27r/=5000. In this way a new unit was
introduced which came to be called the “800
Cycle Mile.” It has, of course, two slightly
different values corresponding to the two speci-
fications for the standard cable. So far as our
further discussion goes we may eliminate the
original mile of standard cable as a possible
unit on the ground that it fails to meet the
fundamental requirement of being independent
of frequency.

Before proceeding, however, let us look more
carefully at what was involved in the transition

to the 800 cycle mile. The artificial cable box
has been replaced in substitution measurements
by an artificial line calibrated in 800 cycle miles,
which is made up of resistances only and so has
the same effect on all frequencies. This fact
tends to suggest that the 800 cycle mile, like the
mile of standard cable, has, or may have, an
actual physical existence. This, however, is not
the case. The 800 cycle mile is a purely theo-
retical unit based on certain mathematical
relationships. This is evident from the fact that
the specifications to be met in designing a “re-
sistance line” are that the overall effect shall
vary with the length in the prescribed fashion,
whereas the magnitude of the resistances used
and their particular arrangement in the circuit is
immaterial. The theoretical nature of the unit
is still more evident when it is used for expressing
the transmission of a system as determined by
the ratio of two electric quantities such as
currents, which may have been either measured
or computed without making use of any artificial
line.

The relation which defines the unit is that
which connects the number of miles of standard
cable with the effect which it produces at 800
cycles. The particular effect which came to be
most commonly taken as a criterion was the ratio
of the received current before and after the
insertion of a length of standard cable. To
avoid ambiguity due to terminal conditions, the
line was assumed long enough so that the effect
of the inserted cable is independent of the im-
pedances at the ends of the cable in which it
is inserted. The ratio of the currents under
these conditions is identical with that of the
currents at two points in an infinite line separ-
ated by a length equal to the number of miles

inserted. This ratio j is an exponential func-
tion of the distance x y which, because of the

occurrence of the naperian base e in line theory,
is ordinarily expressed in the form

where a is a constant depending on the cable
and the frequency. It should be noted, however,
that the use of e is purely arbitrary, as the rela-
tion can be completely expressed with a single
constant as,

The arbitrary introduction of this unneces-
sary constant e is only justifiable if it simplifies
the treatment of the whole problem. Since, as
will be brought out more fully later, it is uniquely
related to only a small part of transmission
engineering, its inclusion at this point tends
rather to confuse than clarify the situation.

Expressing the number of units x as an ex-
plicit function of the current ratio gives

From this expression we may deduce the
nature and magnitude of the 800 cycle mile as a
unit. If we wish to find the number of seconds
in any interval of time we divide the length of
the interval by the length of the second. If we
want the number of hours we divide by the
length of the hour. Here the quantity which the

unit expresses is the logarithm of a current
ratio. The number of units x is the logarithm
of the ratio being measured divided by the unit,
which is log b. Thus the nature of the unit is
the logarithm of a current ratio. Its magnitude
is the logarithm of that particular current ratio
b which is chosen for defining it; in this case
1.115. It should be noted that (11) is true
regardless of the base of the system of loga-
rithms used. The numerical value of the unit
will , of course , vary with the base chosen , but the
number of units corresponding to the particular
current ratio will not.

The fit unit is of the same nature as the 800
cycle mile, and differs from it only in its magni-
tude, which has been selected to facilitate the
computation of the transmission of a long line
from its primary constants. Its theoretical
basis is more obvious than in the case of the
mile, although its evolution from the theory of
line transmission has tended to associate it more
closely with long lines than is perhaps justified
in view of the other uses to which it is now put.
Thus while the idea of its being the product of a
length by an attenuation per unit length is
retained in the symbol 0l } for practical purposes
a single letter would be equally useful.

The 01 unit, like the 800 cycle mile, is the
logarithm of a current ratio. The number of
units is given directly by the natural logarithm
of the current ratio in question. Thus in (7) a
is unity. This means that in (11) b is equal
to €, and so the unit itself is log e. When
expressed in natural logarithms the absolute
value of the unit is therefore unity, as would be
expected.

The TU is like the other two units in that it is
defined theoretically and measures the loga-
rithm of a ratio. The fact that the ratio meas-
ured is that of powers rather than currents is a
separate question from that of its meeting the
fundamental requirement of being the logarithm

of a ratio. 3 The magnitude of the transmission
unit is readily deducible from the relation given
in (3). Dropping subscripts, this may be written

Following the same reasoning as was applied
to (11) with reference to the 800 cycle mile, we
see that the TU is a unit for expressing the
logarithm of the ratio of two amounts of power,
and that it is numerically equal to the logarithm
of a power ratio of 10 0 ’ 1 . When common
logarithms are used its value is 0.1 and the
number of units corresponding to any power
ratio is ten times the common logarithm of the
ratio.

Before discussing the reasons for proposing
a unit based on power rather than current ratio
some misunderstanding may be prevented by
pointing out that the power ratio as here used
is not to be confused with the ratio commonly
used for expressing the efficiency of electrical or
other machinery, it is not necessarily the
ratio of the power delivered by a device to
that entering it, but may be the ratio of any
two amounts of power whatsoever. Just what
powers are to be taken in any case will be de-

3 Units of this general type are not confined to trans-
mission, hut have come into use for expressing various
ratios. Thus the octave and the musical tone are units
of different magnitudes for expressing the logarithm of
a frequency ratio. The stellar magnitude is one for ex-
pressing the logarithm of the ratios of the light received
from the stars. They all are aimed at substituting addi-
tion for multiplication in combining ratios.

termined by what quantity is being measured
in transmission units and how that quantity
is defined. It may, for example, be the efficiency
of a system as compared with some reference
system, the crosstalk between two lines, or
the relative power at two points in a system.

No attempt will be made here to define
these quantities beyond pointing out that it
can be done more generally in terms of powers
than currents. As the general includes the
special, such a definition need not interfere
with the practical use of currents under those
conditions where this gives satisfactory results.
That there are, however, conditions under
which this is not the case is evidenced by the
fact that in certain branches of transmission
engineering the “800 cycle mile” has already
come to be used as a unit defined on a power
basis. In laying out a circuit containing a
number of repeaters it is customary to construct
what is called a transmission level chart. 4
Corresponding to each point along the circuit
is plotted the “level” at that point relative to
some point, usually the entrance to the long
distance line, which is taken as a reference level.
The level at any point is determined by the ratio
of the power passing that point to that passing
the point of reference. The purpose of such a
chart is to indicate on the one hand what power
the various repeater tubes will be called upon to
handle, since they are limited in this respect,
and, on the other hand, what is the ratio of the
power of the voice currents to that of the inter-
fering currents. This ratio is important because
it determines the detrimental effect of the inter-
ference when it reaches the listener. These
relative levels are most conveniently plotted
in logarithmic units, so it was natural to use
800 cycle miles. Since, however, the impedances

4 Telephone Transmission over Long Cable Circuits:
A. B. Clark; 'Frans. A. I. E. E. Vol. XXXVIII, Part 2, p.
1 287, Electrical- Communication , Vol. I, No. 3. Feb., 1923.

of the various line sections and of the apparatus
including vacuum tubes vary over a wide range,
a very misleading picture would be obtained if
the ratios of the currents at the various points
to that at the reference point were used directly
in calculating the levels. To avoid this diffi-
culty and still permit the use of formulae based
on the mile as defined in terms of current ratio,
the square root of the power at the various
points has come to be used as a soft of fictitious
equivalent current. Had the impedance been
the same at all points, the use of the currents
directly would have given a correct picture.

This example serves to illustrate the arguments
in favor of the power ratio unit. It brings out
the fact that the really important quantity in
transmission is the power. So long as the
powers under comparison are associated with
equal impedances, the corresponding currents
give a correct measure of relative powers. In the
earlier stages of the art very few of the com-
parisons were between powers in unequal im-
pedances, and so a current unit was satisfactory.
The more recent developments, particularly
those associated with the use of vacuum tubes,
have introduced an increasing proportion of
cases in which the impedances are unequal, and
hence an increasing demand for a unit which
expresses power ratio regardless of the associated
impedances. Such an extension of the unit in no
way interferes with the use of current ratios in
cases involving equal impedances, such as the
computation of specific equivalents of lines, or
the determination of transmission loss by ob-
serving the change in current in a fixed receiving
instrument. All that is necessary here is to use
twice as large a constant in the formula when
computing units from the current ratio as is
used for power ratios. Thus the number of TU
is twenty times the common logarithm of the
current ratio.

Some other illustrations of cases where a
current ratio unit is inadequate may be men-
tioned.

Receivers are often compared by determining
the ratio of the currents which must be passed
through them to secure the same loudness of
sound from both. Such a comparison means
very little unless the impedances of the two
happen to be the same. A high impedance
receiver appears at a distinct advantage in such
a test, owing to the fact that it receives more
power for the same current flowing through it.
For such a test to give a true picture, correc-
tion must be made for the difference in im-
pedance in a manner which is equivalent to
reducing the comparison to a power basis.

In computing the transmission efficiency of a
line involving inserted apparatus a type of
quantity which has been found cpiite useful is
the so-called loss at a junction. This includes
reflexion, transition and other similar losses.
These can be expressed independently of the
rest of the circuit in the form of the ratio of the
power actually transferred across the junction
to what would be transferred if the circuit re-
ceiving the energy were replaced by one having
an impedance, as measured from the junction,
bearing some prescribed relation to that of the
circuit supplying the energy. Such a loss is
expressible directly in terms of the power ratio
used, whereas the application of a current ratio
unit to such a case is forced, to say the least.

Again, in the application of line transmission
methods to radio telephony 5 level diagrams
similar to those on long lines are useful. Here
we may wish to compare power in the form of
ether waves with that in the form of currents in
wires. Just what currents would here be used
is not obvious.

5 Application to Radio of Wire Transmission Engineer-
ing: L. Espenschied; Inst, of Radio Eng., Oct., 1922, p.
344.

In the treatment of the mechanically vibrating
parts of a telephone system, such as a receiver,
there is a tendency in the direction of consider-
ing the electrical and mechanical parts as a
continuous transmission system. In such an
arrangement the comparison of electric and
mechanical power at two points would be
natural in terms of a power ratio unit, whereas
the analog of a current ratio would be the ratio
of current to mechanical velocity.

It might be argued that the use of a power
ratio would be undesirable because there is no
instrument available which measures power
directly. This difficulty is, however, more ap-
parent than real. Power is commonly measured
in telephony by measuring a current (or voltage)
in an impedance which is known either by
measurement or by computation. The use of
current ratios as a measure of transmission is all
based on an implied knowledge of the impedances
involved, or at least of their relative values.
Where this knowledge is available no more
measurements are required to give the neces-
sary information about the powers than about
the currents. Where it is not available the
same steps as are involved in measuring powers
must be taken before a knowledge of the cur-
rents can have any significance as a measure of
transmission. The desire to measure power
arises from its own importance in engineering,
and not from any arbitrary selection of a unit.
That it cannot be measured directly may per-
haps be considered unfortunate, but it would
be more unfortunate still if, having measured
it by indirect methods, no units were available
for expressing the result.

Nor does a definition in terms of power ratio
do any violence to the concept of the unit as
being derived from the standard cable or the
so-called “unit line,” which is sometimes asso-
ciated with the 0/ unit. It will be remembered
that in tracing the evolution of the S00 cycle

mile there was found a point at which it was
necessary in fixing the unit to choose some
criterion of the effect of the cable on the wave
transmitted over it. While its effect on the
current has been most commonly chosen, there
can be no logical reason other than usefulness
for choosing this rather than any one of the
other quantities which are affected, such as
voltage or power. Since, however, experience
is showing power to be the most useful quantity
it is obvious that if the 800 cycle mile continued
in use its natural evolution would be to a power
basis. The same is true of the 0/ unit. It would
seem foolish, therefore, to set up a new unit on
anything but a power basis.

The question of power ratio is really one of
making the definition of any unit of the type
under consideration broad enough to meet the
needs of the art. All of the proposed units
may be so defined without restricting their
usefulness in other directions. Assuming that
this is 'done, the choice between them is then
to be based on other considerations.

Units which are independent of frequency and
measure the logarithm of a power ratio may
differ only in the magnitude of the unit; that is,
in the ratio corresponding to one unit. Here
two factors are important: the order of magni-
tude of the unit and its relation to the systems
of logarithms in common use. Obviously the
simplest units from the latter standpoint would
be the logarithms of power ratios of 10 and e.
Their values would then be unity in the com-
mon and natural systems, respectively. How-
ever, if some other order of magnitude is more
desirable it may be approximated with either
system by taking a multiple or sub-multiple,
just as the kilometer and centimeter are derived
from the meter. The TU is such a sub-multiple
of the simplest unit employing the base 10.

Let us consider then the approximate size
of the unit regardless of the logarithmic base.
This question is complicated by the fact that
two quite different sizes are already in use.
Those familiar with each have acquired a sense
of the practical significance of any particular
number of the units to which they are accus-
tomed. Also measuring apparatus and data
adapted to each unit have been accumulated.
The adoption of any universal unit must there-
fore involve a considerable readjustment of ideas,
and some expense in conversion of equipment
and data. The aim then should be to make this
readjustment as small as is consistent with
making the most of the rare opportunity of
selecting the intrinsically best size of unit.

Other things being equal, there is some ad-
vantage in a unit which bears a unique relation
to the physical quantity which it measures.
The TU, like the “800 cycle mile,” represents
about the least difference in loudness which
can be detected by the ear without special
training. From this standpoint, therefore, it is
preferable to the 0/ unit. From the standpoint
of practical convenience the use of unnecessarily
large or small numbers in expressing commonly
occurring quantities is to be avoided. With a
unit of the size of the TU it is seldom necessary
to use more than two places on either side of the
decimal point. Losses approaching 100 TU
may be encountered in crosstalk considerations,
for example, while the loss of an individual
circuit element such as a transformer may be
expressible in hundredths of a 1 U. Even such
small losses may become important where the
cumulative effect of a large number is involved.

The situation, then, is that the adoption of a
unit of the size of the TU involves a consider-
able readjustment on the part of the users of
the 0/ unit and a comparatively small readjust-
ment by the much greater number of users of
the 800 cycle mile. At the same time, it gives

some advantages which are inherent in a unit
of that general size. The adoption of a unit
of the size oi the pi, on the other hand, would
involve practically no readjustments by those
now using pi, but extensive readjustments by
those using the mile. It would seem then that
the greatest advantage with the least sacrifice
would be given by the smaller unit.

Coming back to the choice between a unit
adapted to the use of common vs. natural loga-
rithms, we may be guided by the general prin-
ciple that in the scientific and engineering world
common logarithms have been shown by their
extended use to be the more convenient except
in cases where some special consideration makes
natural logarithms preferable. Unless, there-
fore, it can be shown that such a special con-
sideration holds in the case of transmission
engineering, it would be going against well
established experience to select anything but
common logarithms.

The occurrence of the base e in formulae for
line attenuation might be advanced as such a
special consideration. While it is true that the
computation of the attenuation of a uniform
line from its primary constants is simplified by
using natural logarithms, the cases where such
an advantage exists form a small and pro-
gressively decreasing part of all the uses of
such a unit.

The practice in certain countries of solving
apparatus problems by reducing them to
equivalent smooth lines tends to give the im-
pression that the natural base is uniquely
related to a larger field of computation than is
actually the case. Most of these problems can
be solved at least as easily by other methods
which do not introduce the natural base. There
are, in fact, two distinct methods of attacking

circuit problems in current use. The one which
is used largely in those countries where the 0 /
unit is employed reduces everything to its
equivalent smooth line. The other, which is
more generally used elsewhere, reduces the part
of the circuit under consideration to a rela-
tively simple network, which may then be
solved by the application of Kirchhoffs Law.
Natural logarithms are doubtless more con-
venient for the first method, and common
logarithms for the second. So far as the theo-
retical man is concerned the choice of unit then
would be based on which of these methods is
preferable. A consideration of this question
seems to indicate that of the problems en-
countered in practical work none are solved
more easily by the first method than the second,
whereas a considerable number are solved more
easily by the second. If this is true, the second
method should ultimately replace the first,
and the demand for the base e, except for
long line computations would then largely
disappear.

The increasing use of interconnected lines of
different types and of terminal equipment,
such as repeaters and carrier current apparatus,
is reducing the relative importance of long line
computations. Also as a reference to the illus-
trations cited under the discussion of power
ratio will show, there is coming to be an increas-
ing need for expressing power ratios which are
measured or else calculated by formulae which
do not involve e. Much of this work is done by
men engaged in the more practical phases of
engineering, to whom the convenience of com-
mon logarithms is very considerable. The fact
that the ordinary slide rule gives the result
directly in such cases is a point of considerable
importance. On the other hand, the cases in
which natural logarithms are of advantage are
handled largely by men of considerable training,
10 whom the conversion to common logarithms

may offer a slight inconvenience in manipula-
tion, hut no theoretical difficulty.

In view of these considerations it does not
appear that transmission engineering is so
different from other branches as to justify a
special type of logarithm.

It was emphasized in the foregoing discussion
that the TU is suitable for expressing a wide
variety of different quantities. Space will not
permit a discussion of all these, but there is one
which deserves attention because of its own
importance and because of the fact that its
measurement involves the use of physical stand-
ards. This is the measurement of the overall
reproduction efficiency of a system for speech as
compared with some reference system, the com-
parison being made by adjusting the “line” in the
reference system so that speech is reproduced
by it with the same loudness as by the system
under test. The number of units in the line is
then taken as the “ equivalent” of the system
relative to the reference system.

Two such reference systems based on the two
types of standard cable are in common use, and
the specifications for their construction are
quite well standardized. No such general agree-
ment exists, however, on a reference system
calibrated in pi units.

It should be noted that the use of these refer-
ence systems based on miles gives the results
in miles of standard cable, and not in “800 cycle
miles.” They are, therefore, subject to the
same objections as were raised to the mile of
standard cable as a unit. The transmission of
the system under test is expressed in terms which
depend upon the particular distortion intro-
duced by the standard cable. Furthermore,

owing to the difference in impedance between
the cable and the terminal instruments reflec-
tion effects enter in such a way that when only a
small amount of cable is in the circuit the loud-
ness actually increases with increase of “line”
up to a certain point beyond which it decreases.
As a result certain values of reproduction can be
obtained with two distinct line settings.

That the reference systems now standard are
not suitable for expressing transmission equiva-
lents in TU is obvious. The Bell System has
therefore, undertaken the development of a
transmission reference system designed pri-
marily for use with the new unit. While this is
not fully developed and calibrated, a general
idea may be given of the factors entering into its
design and the form which it is taking.

In line with the fact that the TU is inde-
pendent of frequency, a distortionless reference
system was chosen as the ideal. It might be
argued that such a system would be unsuitable
for comparison with practical systems because
of their distortion. However, the systems in
actual use vary in distortion over a wide range,
from heavy loaded cable circuits on the one
hand to the very high quality systems used for
transmitting and reproducing music and other
entertainment material on the other. 6 It would,
therefore, be impossible to select a reference
system having a distortion typical of operating
conditions in general. Hence it seems prefer-
able to refer all systems finally to a distortion-
less standard, thereby eliminating one variable
factor.

The system which is being constructed to ap-
proximate this ideal has as its adjustable portion
an artificial line of 600 ohms characteristic
impedance made up of resistances and cali-

6 High Quality Transmission and Reproduction of
Speech and Music; W. H. Martin and 11. Fletcher;
Journal of the A. I. E. E. f March, 1924, p. 230; Electri-
cal Communication, Vol. II, No. 4, April, 1924.

brated in TU. At one end is a transmitting
circuit and at the other a receiving circuit.
These are made as nearly distortionless as possi-
ble. Their impedances are GOO ohms pure re-
sistance, so that no reflection effects enter at the
junctions with the line. The transmitter is of
the condenser type, and is connected with a
multi-stage amplifier. The receiving circuit
contains an amplifier and a specially damped
receiver.

These circuits are to be defined by assigning
to them certain conversion ratios between the
acoustic and electric portions of the system. In
order to minimize the readjustment of working
concepts based on the present reference system
it is proposed to make the receiving circuit in
the new system of approximately the same
efficiency as that in the old. The transmitting
efficiency is then to be so chosen that some par-
ticular reproduction efficiency which is repre-
sentative of operating conditions will correspond
to the same equivalent in TU with reference to
the new system as it does in miles with reference
to the old. Efficiencies in the neighborhood of
this will then differ very little on the two
systems.

The practical determination of the trans-
mitting efficiency necessary to satisfy this con-
dition will require a very extended series of
observations, since the error in a single obser-
vation is likely to be large where the distortion
is so different in the two systems. Owing to this
difficulty of comparison it is probable that the
distortionless reference system will be used in
practice only for circuits of relatively high
quality. Such routine talking comparisons as
are made on ordinary commercial circuits will
probably be made against sub-standards each
having distortion typical of a limited class of
commercial circuits. These substandards, will
be calibrated against the transmission reference
system by extended laboratory tests.

In the actual use of the TU , time saving
devices such as tables, curves and approximate
relations are important. Of these the ordinary
slide rule has probably the widest application,
as it permits the conversion between a power
or current ratio and TU to be made by a single
setting. For more accurate results a table of
common logarithms is sufficient. I he curves of

Figure 1 — Transmission Unit Diagram. For power or
current ratios greater than 10, move the decimal point
to the left until the ratio lies between 1 and 10; and for
each place the decimal point is moved, add 10 or 20 to
the figures on the lower or upper scales, respectively.
For power or current ratios less than 0.1, move the decimal
point to the right until the ratio lies between 0.1 and 1;
and for each place the decimal point is moved, add 10
or 20 to the figures on the lower or upper scales, respectively

Figure 1 furnish a simple means of graphical
conversion. For very rough mental estimates
the approximate relations of Table 1 are con-
venient. The error involved in the use of such
approximations is indicated by the more exact
figures given in parenthesis.

Tables 2 and 3 furnish the necessary con-
stants for converting from the TU to other units.

International Western Electric
Company, Inc., Rio de Janeiro
(Rua dos Ourives 91-1)

United Incandescent Lamps and
Electrical Company, Ltd., Ujpest
4 near Budapest

R 00047