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ities of absorption and of radiation are the same if the temperature of the substance is the same in the two cases. While if the temperature of either condition is decreased, so is the intensity of the effect. Thus, if a white- hot solid is placed behind a quantity of cooler gas or vapor, the absorption spectrum is a continuous one from which cer- tain isolated waves are absent ; and these are identical with those which the luminous gas would emit. The gas absorbs certain waves and transmits the others; it also radiates waves of the same wave length as those which it absorbs ; but the intensity of these radiations is so much less than that of those which are transmitted, that the spectrum is practically as if the gas did not radiate. If the gas or vapor is at a higher temperature than the white-hot solid, the spectrum will be that of the luminous gas with a continuous weak background ; i.e. it is a bright- line spectrum. If the gas or vapor and the solid are at the same temperature, the spectrum will be continuous. Solar and Stellar Spectra. — These facts are illustrated in the spectra of the sun and of the stars. The solar spectrum and certain stellar spectra are observed to be absorption 584 LIGHT ones ; while other stars produce bright-line emission spectra. The explanation of the latter is obvious : the stars producing them are surrounded by a luminous gaseous atmosphere, which is hotter than the interior portions. Similarly, in the case of the solar spectrum and other absorption stellar spectra, the explanation is that the interior portions are solid or liquid, and are at a higher temperature than the atmosphere of gases and vapors outside. These vapors are naturally those formed by the evaporation of the interior substances. The absorption spectrum in the case of the sun consists of the Fraunhofer lines ; and they can be identified almost completely with the emission spectra of the vapors of certain substances here on the earth ; and thus the con- stitution of the sun is known. The following are a few of the substances which are in this manner known to be in the sun: calcium, iron, hydrogen, oxygen, sodium, nickel, magnesium, cobalt, silicon, aluminium, carbon, copper, zinc, cadmium, silver, tin, lead, etc. Some of the absorption lines in the solar spectrum are due to* absorption by the atmosphere around the earth. Thus, certain groups of lines known as the " A," " B
," " a " and " B " " bands " are due to absorption by the oxygen in the air, while numerous other lines are due to the presence of water vapor. A method for distinguishing between solar and terrestrial lines will be described presently. Similarly, by a study of the spectra of the stars, either emission or absorption, a great deal may be learned in regard to their constitution, and also motion, as will be shown immediately. The study of these and similar phenomena forms the science of Astrophysics. An excellent book to consult on this subject is Miss Clerke's Problems in Astro- physics, New York, 1903. In speaking of wave motion a certain general property, known as Doppler's principle, was described (see page 345). RADIATION AXD A I: >o /,•/•'/ /o.v sl'WTRA 585 It states that when a source of waves is approaching a point in space, the wave number at this point is increased, while the converse is true if the source is receding. In the case of ether waves that are being dispersed by a glass or quart/, prism or grating, this would be shown by a change in their refrangibility — an increase if the source is approach- ing the earth, a decrease if it is receding from it. There- fore, if a star is emitting certain trains of waves, their corresponding spectrum lines will all be shifted side wise by an amount depending upon the velocity of the star in the line of sight. If these lines, then, all apparently agree exactly with lines observed here on the earth in the labora- tory for any known vapor, except that they are all slightly displaced, the obvious explanation is that the star is moving in the line of sight; and its velocity in this direction may be deduced from the amount of the observed shift. (This statement is not absolutely correct, for shifts of the lines may sometimes be due to anomalous dispersion or to abnor- mal pressures in the atmospheres of the stars.) Similarly, if the image of the sun is focused by a lens upon the slit of a spectroscope, and it is so arranged that first one edge and then the other of the sun's ima^e is on the slit, the lines in the solar spectrum that are due to solar absorption will be shifted slightly, owing to the fact that one edge of tin- sun is receding from the earth while the other is approach- in LT it
, because of the rotation of the sun. Hut those lines in the spectrum due to absorption in the earth's atmosphere will not be so displaced. student should consult Ames, Prismatic and Diffraction Spectra, for Fraunhofer's original memoirs, and Brace, The * of Radiation and Absorption, for the memoirs of Kin-h- hoff :.nd lJunseii. CHAPTER XXXVII EXPLANATION OF COLOR General Discussion. — The color of an object that is self- luminous depends upon the character of the light that it emits. If it radiates all the visible waves with suitable intensities, it will produce in a normal eye the sensation that we call "white." (The case of defective eyes will be considered in the next chapter.) If the intensity of certain waves is abnormally great, the light appears colored, as is shown when "red fire," a "sodium flame," etc., are used. The color of most objects, however, is due to the fact that they are illuminated and either reflect or transmit light to the eye of an observer. It is obvious that the color of the object will depend fundamentally upon that of the illuminat- ing light ; but we are so accustomed to viewing objects in the white light produced by diffused sunlight, that in describ- ing the color of any object it is always assumed that white light is used with which to illuminate it. When we consider the color of an illuminated body, it is evident that it may be due to any one of several causes. It has been explained in the previous chapter that absorption of light may take place in many different ways, and corre- sponding to each of these there will be certain color phe- nomena. Again, we have seen how colors may be produced by any dispersive action, such as that of a prism, a grating, or an interference mechanism. These various cases will now be discussed briefly. 686 EXPLANATION OF COLOR Absorption Colors Body Absorption. — The most familiar kind of absorption is that shown when the incident light is absorbed in the interior of the body and the energy of the absorbed waves is spent in producing heat effects. The light that is trans- mitted appears colored, therefore, owing to the disappear- ance of certain trains of waves. If a single train of waves of wave length I is absorbed, which corresponds, therefore, to a definite color, the transmitted light will
include all the other trains of waves, which will combine in the eye to pro- duce a definite color, called the " complementary color " of that of the waves which were absorbed. If the body absorbs two trains of waves, it may happen that the intensity of the absorption is not the same for both trains ; that is, it may n-.juire a greater thickness of the body to extinguish one color than is required for the other ; and it is thus apparent how such a body may appear of a different color as its thick- ness is varied. It is evident that if the absorbing substance is transparent for those waves which it does not absorb, it cannot itself be seen when viewed from the same end as the incident light, or from one side; but if owing to any cause the body diffuses tin- liirht which it does not absorb, then it will appear of the same color when viewed from any direction. Thus a tank ( -ontaininir colored water will appear practically black, except when the transmitted light is viewed, it there are no minute solid particles in suspension : luit if these are intro- duced, it appears colored from all points of view. two portions of matter having body absorption are so placed that the incident liurht tails upon one, and the trans- mit t«l li'jlit is then incident upon the other, the color of the emerging li^ht is that due to the waves which are left after two absorpti The color of all leaves and flowers, of •us clotlis, of paints, of bricks, etc., is due to body 588 LIGHT absorption.' If two paints are mixed, their color is, as just explained, that due to the absorption by both the paints; there is a double subtraction, as it were, from the incident light. The nature of the light that gives an object its color may be determined in two ways : one is to illuminate the object with white light and analyze by a spectroscope that light which is diffused ; the other is to form a continuous spec- trum on a white wall and move the object along this ; if it appears black for any position, it means that the color cor- responding to this position is absorbed, but if it transmits and so diffuses any particular color of the spectrum, it will in the corresponding position appear of this color. Fluorescence and Phosphorescence. — If the energy of the waves absorbed in the interior of a body is spent
in produc- ing other waves, which are therefore radiated in all direc- tions, the phenomenon is called, as has been said, fluorescence. The fluorescent light consists in general of waves whose wave length is longer than that of the waves whose absorp- tion produces the fluorescence. In this case the color of the transmitted and the diffused light is not the same. It is evident that if the fluorescent body is thick, the waves which cause the fluorescence may be entirely absorbed in that portion of the body which is first traversed by the light; so that the fluorescence will occur in this portion only. In some cases this color is confined to almost the surface layers. If the emission of light continues after the incident light is intercepted, the phenomenon is called, as has been said, phosphorescence. Evidently there is some molecular trans- formation involved in this. Surface Color. — When polished metals and many of the aniline dyes in the solid form (e.g. a dried drop of red ink on paper) are viewed in white light, they have a peculiar appear- ance which is called "metallic lustre." This is due to the EXPLANATION OF COLOR 589 fact that they reflect certain waves much more intensely than others, or, in other words, they have " selective " reflection. This process does not take place in the interior of the sub- stance, as in the case of a colored liquid, but at the surface. If a substance showing this metallic lustre, or surface color, is made in a film which is sufficiently thin, it will transmit certain waves. But the color by reflected light is not the same as by transmitted ; in some cases they are approximately complementary. These substances which exhibit surface color have anoma- lous dispersion and change plane polarized light into ellipti- cally polarized light by reflection. Scattering by Fine Particles. — If the light traverses a region where there are numerous minute particles, it may happen that they are of such a size as to scatter certain trains of waves, and to let pass unaffected all trains of longer wave length. The light so scattered is plane polarized if it is viewed at right angles to the incident beam. This scatter- ing is the explanation of the blue color of the sky, as has i already said, and of the color of sunset clouds, at least in part. The phenomenon also plays a most important part in (h'termining how much radiation (visible
and invisible) reaches the earth from the sun. Dispersion It is not necessary to say anything here in regard to the dispersive action of prisms, gratings, etc., but a few illustra- tions may be given of colors due to it. Prismatic <lis\|>«TM(»n is slmun by rainlmws, halos around the sun and moon, dew- drops, diamonds when mutably cut, etc. Diffraction colors are seen when looking ;l( in,,ili,.r-«.f-p«-arl, at certain line feathers, at corome (the colored rings around tin- mmm ». tli rough fine-ni' ->bcd cl.,tb at a bright light, etc. Int< colors are shown by soap bubbles and other thin films of transparent matt< CHAPTER XXXVIII THE EYE AND COLOR SENSATION A TEXT-BOOK of Physics is not the proper place for a de- tailed description of the structure of the human eye or of the various theories which have been advanced to account for the sensation of color. Some treatise on Physiology or on Physi- ological Optics should be consulted. It is simply necessary to state here a few facts which are of physical importance. The Eye. — From an optical standpoint the eye consists of a converging lens which is provided in front with a diaphragm of adjustable diameter, the " iris," and whose focal length can be changed at will to a cer- tain degree. (This power of accommodation is greatly decreased as one grows old.) This lens exhibits both spheri- cal and chromatic aberration, but not to a noticeable degree in general. The medium on one side the lens is the air, but on the other is a liquid filling the cavity of the eye. At the rear of this is the " retina," upon which a normal eye forms an image of the object viewed. A "near-sighted" eye has its focus in front of the retina; while a "far- sighted" one has its back of it. In the former case, the image may be formed on the retina if a diverging lens is used in front of the eye ; in the latter, if a converging one is substituted. Fio. 801. — The human eye. 590 THE EYE AND COLOR SENSATION 591 Perception of Color. — The retina consists of a structure of minute
parts which are intimately connected with the endings of the optic nerve. The exact mode of excitation of these nerve endings by the incident ether waves is not known. Certain portions of the retina, viz., those remote from its centre, play no part in color sensation ; for, when waves of all wave lengths lying within the limits of the visible spectrum are incident upon them, one is conscious of a sensation of gray only. This is true of all portions of the retina if the light is faint, with the exception of a small area, called the " yellow spot," which gives color sensations only. This spot is slightly off the axis of the eye considered as a lens. There is also a minute area — called the "blind point "-—near the cen- tre of the retina, where the optic nerve enters, at which no sen- sation of light is produced. Over the other central portions of tin: retina, light of all different colors may be perceived. Addition of Colors. — It has been known since the experi- ments of Newton that, in order to produce the sensation kk white," it was not necessary to have all the trains of waves in a continuous spectrum from violet to red. Corresponding to any color there is another such that if these two sensations are produced simultaneously in the eye, white is perceived. These two colors are called, as has been said, complementary. One way of producing these simultaneous sensations is to paint different sectors of a circular piece of cardboard with the two colors, and then to rotate it rapidly while it is illuminated with white light. Thus at consecutive minute intervals of time if one looks at the rotating disk, the eye receives first one impression and then the other; but since, if impressions reach the eye at intervals faster than about thirty or forty a second, a continuous effect is produced, the e\ this case receives two simultaneous impressions. This is what may be called the addition of colors ; and it is evident that the mixing of paints, or the suht rael i"ii of color, has HO connection with it. 592 LIGHT Similarly, a great variety of choices of three colors may be uuule which when added in suitable intensities will produce white light. Taking any three such colors and adding them in different intensities, any other color which is desired may be produced. This proves, then, that in order to account for the perception of colors of all kinds, it is simply necessary to assume that in the eye there are three sets of nerves corresponding
the retina they stimulate the "red," "green," and "blue" sets of nerves to degrees which are proportional to F 1, F 2, and F 3, the phenomena of color sensation have been explained. BOOKS OF REFERENCE ;:. Light for Adranoed Students. London. 1902. An excellent text-hook, contain in.: <!• •-••n\|'tioiis of all the fundamental phenomena and references to all the recent investigations. PftBftTOW. Tin- Th.Miry of Liuht. Loii-lon. iM edition.!*!»:>. Tin- recognized book of reference for all the elementary phenomena of Light OptiOS. (Translation.) \,-w York. 1902. I h. l....st mo. I. M -ii text-book ing the accepted theories and explanations of all optical phenoi LUMMKR. Photographic Optics. (Transit i-. ) LoDdOD. 1000. A text-book on geometrical Optics, with special reference to lenses. PUT8IC8 — 38 MAGNETISM CHAPTER XXXIX PERMANENT AND INDUCED MAGNETIZATION Magnets. — A body which has the property of attracting pieces of iron is called a "magnet" ; that is, if a magnet is brought near a piece of iron there is a force between them which is shown by their approaching each other if either (or both) is free to move. Such bodies occur in nature, for one of the forms of iron ore which is not uncommon, a mix- ture of FeO and Fe2O3, is magnetic. It is, moreover, a simple matter to make any piece of iron or of ordinary steel into a magnet. There are two general methods for doing this : one depends upon a property of an electric current, the other, upon what is called magnetic induction. If an electric current is made to traverse a wire which is wound in the form of a spiral spring, or helix, the apparatus is called a " solenoid " ; and experiments show that, if a piece of iron or steel is placed inside this solenoid, it becomes a magnet. Or, if a piece of iron or steel is brought near, not necessarily in contact with, a magnet, it is made a magnet also. If a piece of iron is magnetized in this manner, ami the magnetizing agency is removed, the iron will
lose its magnetism very easily, if it is jarred or subjected to an increase in temperature; but this is not true of the piece of steel — it remains a magnet under all ordinary conditions. All magnets in ordinary use are made therefore of steel, some kinds of which are much better than others. Much progress in this respect has been made in recent years. ri-:i;MANENT AND IMK' MAC \ l-:i ItATWN 595 Magnets are usually made in the form of bars, rods, or elongated lozenge-shaped "needles." Sometimes the bars or rods are bent into the shape of a U or of a horseshoe; and in this form they are called horseshoe magnets. Experiments show that long magnets are more permanent than short ones Fio. 808. —Horseshoe magnet. and that they remain magnet- ized longer if their ends are joined by a piece of soft iron. Thus an iron bar, called the "arma- ture," is always placed across the ends of a horseshoe magnet when it is not in use. Horseshoe mag- net with soft Iron Bar magnets with armatures. armature. FI.J. Magnetic and Diamagnetic Bodies. — It is found by ex- periment that a magnet can attract other kinds of matter than iron ; such as many forms of steel, nickel, cobalt, man- ganese, etc. These bodies are called " magnetic," and any one of them can be made a magnet by the methods described above for iron or steel. Again, there are many other sub- stam-es which are repelled by a magnet; such as bismuth, antii i\. ami /inc. These bodies are called "diamagnetic." ulay made the most important observation that the • jiit-^tiuii as to whether a body is attracted or repelled by a magnet depends fundamentally upon tin- man-rial medium in winch the magnet an<l tin- body arc innm-rx «1. In the above dcti nit ions of magnetic ami diamagnetic bodies this medium is assumed to be the ordinary atmosphere. Faraday •bowed that, while in OH€ im-dium a l»od\ mi^ht be attracted 1>\ i m.i'jiirt. iii another it might be repelled. Thus tin- 596 MAG* I.T
ISM importance of the medium in the consideration of magnetic phenomena is shown. Poles. — If an iron or steel rod or " needle " is magnetized by means of a long solenoid, and if it is then removed and suspended by a fine thread or 011 a vertical pivot, so that it is free to rotate in a horizontal plane, it will turn and after a number of vibrations gradually come to rest in a direction which is approximately (or exactly) north and south. (This fact in regard to a mag- FIO. sos. -pivoted mag- netized bar or needle has been known for many centuries, and has been made use of by mariners and travelers.) The end which points toward the north is called the " north pole " of the magnet ; the other, the "south pole." The direction in which it points is called "magnetic north and south." If a magnet is suspended as just described, and another is brought near it, it may be shown that there is a force of attraction between a north and a south pole, but one of repul- sion between two north poles or between two south poles. "Unlike poles attract, like ones repel." It is easily proved, further, that the greater the distance apart of the magnets, the less is the force. In order, then, to explain the reason why a magnet when freely suspended points in a north and south direction, all that it is necessary to assume is that the earth itself has the properties of a magnet. The particular magnetic properties that experiments show it to have will be described later in Chapter XLI. Magnetism a Molecular Property. — If a magnet is broken up into smaller pieces, each fragment, however minute, is found to be a magnet, with a north and a south pole. This leads one to believe that magnetism is a molecular property of all magnetic substances ; and all observations are in sup- port of this idea. Every property of a body except its mass and weight is changed when it is magnetized ; and con- \ /:v/ AND L\i>r<h'i> M.\<; \ ETIZATIOX 59 ely, any ehan^e that is known to afi'ect the moleeiii. a body will att'eet tin- magnetism of a magnet. Thus, when an iron rod is magnetized, its length, its volume, its elasticity, etc., are all changed; and when a magnet
is hammered or twisted or heated, its magnetism is altered. as is shown by a change in the force which it exerts upon another magnet or upon a piece of iron at a fixed distance from it. Induction. — We make the assumption, then, that each molecule of a magnetic substance, e.g. of a piece of iron, or of nickel, etc., is a magnet; in other words, that each mole- cule of any one magnetic substance has a certain mass and other mechanical properties and is at the same time a magnet. When the substance is in its natural condition, we can assume that these molecular magnets are not arranged in any order, hut are distributed at random; so that, as far as external actions are concerned, each tiny magnet is neutral- ized by those around it. But if a magnet is brought near such a piece of magnetic sub- stance, each of the r*7vT " becomes a sooth pole. la tter'8 molecular FIG. 806.-Magm-tlo induction: the end A of the Iron bar magnets is acted upon by a force due to the magnet; and the molecules are all turned, more or less completely, in an orderly and regular direction. Thus, if the magnetic substance is a rod or bar, and the magnet is in this form also and is brought near one en<l of the former, so that its north pole is nearest it. the nmlerules will turn so that their mmtli poles are ird the imrth pole <»f the magnet. Therefore the molec- ular magnets no longer neutralize each other; they now have an external a. tion, and. in fact, the bar which they con- stitute is now a magnet \\itl ;h pole toward the north polr of the magnet i/ini: magnet. The change produced in the ;he nioleeular magnets by the magnet is 598 MAGNETISM roughly indicated in the accompanying cut, where each mole- cule is represented by an elongated rectangle whose ends are shaded differently. (Of course, we do not assume that a molecule has actually the shape of a rectangle.) This explains, then, not alone why a piece of magnetic substance is magnetized by the magnet, but also why the two attract each other. The phenomenon is called "magnetic FIG. 807. — Arrangement of molecules In an un magnetized and a magnetized iron bar. • nduction
"; or the former is said to be magnetized by "in- duction." Strictly speaking, these names apply to the phe- nomenon only so long as the magnetizing magnet is kept in its position near the magnetic substance ; when the two are separated, the latter remains a magnet, although a weaker one, for a greater or less time, as described above ; but its magnetism is now spoken of not as induced, but as " intrinsic " or "permanent." Similarly, when a rod is magnetized by the action of a solenoid, the magnetism is said to be induced ; etc. The reason why a long thin magnet is more permanent than a short one is clear, because in the latter the two ends are closer together and the molecular magnets at one end may disturb the direction of those at the other, and so produce demagnetization. The action of the armature of a PXSMANMNT AM) i\i>r< I;D MA<;.\ /•;///. I y/o.v 599 horseshoe magnet is also easily explained : it keeps the molecular magnets at the ends from changing their positions. It is evident that, \vh«-n a bar or rod is magnetized by the action of a magnet at one end, the molecular magnets in the former will be arranged in an orderly manner at the end near the magnet; but at its other end FIG. 80S. — Magnetization of an iron bar by induction. these minute magnets will not be so systematically distributed. Tha magnetizing of the bar or rod may be made more complete if two mag- nets are used, one at each end of the rod, and turned in opposite direc- tions as shown in the cut. The action may be made still more complete if the two magnets are plan •«! on top of the rod at its middle point — oj >\| "»ite poles being in contact — and are slightly inrlinrd to it, as shown in tin- cut (and if then the two magnets are <lra\\ti otf the bar lengthwise in opposite The process should be re- Fio.aw. — Processor mapneti/ peated several limes. If during any of these processes the rod is ham- mered or Jan..1. tin; magnetization is increased. Experience shows that it is impossible to magnetize a ba» more than up to
of Rn and Rt measured along the magnet, and if this special bar magnet is made of the length Z, it might replace the former so far as action at a considerable distance is concerned. The forces on the two ends of the latter magnet due to the distant one are then equal in amount but opposite in direction. We are therefore led to make the assumption that each molecular magnet has two centres of forces, a minute distance apart, which are equal in amount but opposite in kind ; that is-, if one centre exerts a force of attraction on one end of any distant -Forces magnet, the other exerts on it a force of repul- between two small sion. Thus, if JV^ and N^S2 are ^wo molec- ular magnets, there are four forces acting on each, as shown, arid if S2 is at the same distance from both N! and Sr the two forces acting on it are equal in amount but are in nearly opposite directions. All observed facts in regard to magnetization are in accord with this assumption. We say that each molecular magnet has two poles whose " strengths " are equal but opposite ; or that they have equal but opposite " quantities of magnetism " or " magnetic charges." The same statement in regard to magnetic charges must then be true of any magnet, however large or compli- cated, because it is made upof magnetic molecules, and therefore contains as much south as north magnetism. It is impossible to separate a north pole from an equal south pole and obtain them distinct from each other, because, when a magnetic mole- cule is decomposed into simpler parts, it ceases to be a magnet, and equal amounts of north and south magnetism vanish. Magnetic Field and Lines of Force. — When a small mag- net is placed near a large one, it is acted on by certain forces; I'Ki;MA\i:\T AM) 1XDUCED MAGNETIZATION 603 and, in general, a region in which a small magnet experiences forces is called u " magnetic field." A simple mode of study- ing and describing the properties of such a field is to draw what are called "lines of force." These are continuous lines such that any one indicates by its tangent at any point the direction in which a north pole would move if placed there. Thus, if P is any point on a line of force AB, a north pole, if placed there, would move in the direction of
Lines of force do not, of course, have a physical existence ; and the above statements are simply descriptions of the appearance of their geometrical curves. By means of these ideas it is often possible to give simple descriptions of com- FIG. 317 a. — Bar of soft iron placed in a uniform magnetic field. plicated cases of magnetic forces. CHAPTER XL MAGNETIC FORCE AND INDUCTION Quantity of Magnetic Charge ; Law of Force. — If the art inn of several magnets upon one which is pivoted is observed, it is seen that the intensity of this action, as measured by the deflection of the magnet from a north and smith line, depends upon many things. It is different if the magnets are inclined at different directions to the pivoted one; and so for purposes of comparison \|/>N of different magnets we ft may place them, in turn, Fio. 819.-Force actlnc upon a small S I east and west (magnetic- east or west of it. ally) of the pivoted mag- t, s • pivoted iniiLMirt l.y a bar magnet placed net in a hori/.ontal plane, with their north poles pointed toward the latin. As a result, the latter will be deflected and will come to rest, making a definite angle with its origi- nal north and smith position, which will vary with the dis- tance of the magnet from it, and also, in general, with different magnets when placed in the same position. This indicates that the magnetic forces between poles vary with their distance apart and with different magnets. Let us assume, as an ideal case, that the magnets have all magnetic charges at their ends (see page 602), and let us assume that we can assign a numerical value to this mag- netic charge, so that the forces it exerts are proportional to it. Thus, if /// is the magnetic charge of the north pole, — 9ii is that of the south pole; and the forces which each 607 608 MAG. \KTISM exerts are proportional to m. Then, if there is another magnet which under similar conditions exerts different forces, its poles must have different magnetic charges, which may be written ml and — mr Therefore, if these two mag- nets are acting on each other, the force of the north poles on each other is proportional to the product mmr Experiments show that this force varies with their distance apart, being less for
a great than for a small distance. Coulomb made the assumption that, so far as distance was concerned, the force varied inversely as its square. So calling this distance r, the law of action of two poles is assumed to be that the force between them is proportional to — ^> This is known as Coulomb's Law, and it was verified by him (1785) so far as was possible with the instruments at his command. It was verified also by Gauss, and to a greater degree of accu- racy ; but our main reason for believing that the law is exact is that all of its consequences are found to be in accord with the varied facts of electrical engineering, into which enter so many questions connected with magnets and magnetic fields. In order to assign a number to the magnetic charge of any magnet, it is necessary to define a unit charge ; and in doing this it must be remembered that magnetic forces are different in different media. (See page 595.) Making use of the C. G. S. system of units, a " unit magnetic charge " is defined to be such a charge that, if placed at a distance of 1 cm. in air from another equal charge, the force between them is 1 dyne. Then, if a charge equal to m of these units is placed at a distance r cm. from a charge m1 in air, the force between them expressed in dynes is given by the equation f=—^- In any other medium the force is proportional to this, and therefore, following the accepted system of symbols and writing as a factor of proportionality -, the force in any f* MAGNETIC FORCE AND INDUCTION 609 medium is/ = From what has just been said, the value of fj, for air is one on the C. G. S. system of units and using as a unit magnetic charge that defined above; natu- rally, if another unit charge were adopted, the value of this constant for air would be different. The factor /A is a quan- tity which is characteristic of any medium — it is not, how- ever, necessarily a constant. It is called the " permeability," for reasons which will appear later. Intensity of Magnetic Field ; Magnetic Moment. — When a magnet is placed in a magnetic field, it is acted on by two forces, one at each pole, they being the resultants of all the forces acting over the surface, as explained on page 601. Let
us assume the simplest case, viz., that the charges are entirely at the ends ; then, if the magnet is short, the forces at the two ends are equal in amount, although opposite in direction, because the two ends are at almost the same point in the field. The "intensity" of the field at any point is defined to be the value of the force which would be exerted (»n a unit north charge if placed at that point. Therefore if the inten- sity of the field is R, and if m is the (1 large on either pole of a short ni;i'_rn«-t which is placed in the field, there is a force Rm acting on each pole. If I is the length of the magnet and if it is in such a posi- ti"M that it makes an angle N with the direction of the field, the per- pendicular distance between the Fio. MO.— Moment acting on a tor magnet when placed In a field of intensity R. two i'"ives is I sin N i so the strength of the couple acting on the nii_rii.t is Rml sin N. If the magnet is pivoted AMES'S PHYSICS— 89 f>10 MAGNETISM around an axis perpendicular to a plane which includes the magnet and the line of force at its middle point, it will turn under the action of this couple toward the direction of the field ; so the moment of this couple should be written — Rml sin N. The product ml is evidently a property of the magnet itself, and it has received the name " magnetic moment of the magnet." In the general case of any kind of magnet, the magnetic moment around any axis is defined to be the maximum value of the moment of the forces acting on the magnet when it is placed in a field whose inten- sity is one, with this axis at right angles to the field. If a magnet is broken up into parts, these are found, as a rule, to have different magnetic moments ; and the value of the "intensity of magnetization" at any point of the magnet is defined to be that of the magnetic moment per unit volume around that point. Thus, if M is the magnetic moment of a portion whose volume is V, the ratio — in the limit, as Vis taken smaller and smaller, is the value of the intensity of magnetization. If the magnetic charges are entirely at the ends, the intensity is the same throughout the magnet ;
- m m 2 m/r But if r is very great in comparison with Z, /=— ::ir-, 2 m/r 2 A/ Consequently, substituting in the formula for tan JV, M r* tan N Various precautions and modifications for this experiment are explained in laboratory manuals, but it is evident that * = — 2— both r and N can be measured ; and so — may be determined. R Measurement of R or M. — By a combination of the two formula' for RM and — -, it is seen that R B>= »«V r«r»tanJV* and so both R and M may be measured. It /! i> known fur any one fu-ld, it has been explained how its value for any other field may be determined by means of a \ ilir.it in-_r magnet whose period can be measured. Magnetic Tubes. - If one refers to the illustrations of lines of force given on page 604, it is evident that these lines are most crowded together at those places where the intensity of the tirlil is the greatest, and are the farthest apart at those »'.U MAGNETISM points where the intensity is the least. This suggests a systematic mode of drawing lines of force. We can describe a small closed curve at some point near the magnet, and can imagine lines of force drawn through each point of this curve ; these lines, if continued, will of course be found to start from a north pole of a magnet and end on a south pole ; so they thus form a hollow tube leading from one pole to the other, whose cross section is small near each end, but greater at a distance. If the initial small curve is taken of exactly the proper size, this tube will inclose at its two ends a unit magnetic charge. Such a tube is called a "unit tube"; and, if the magnet has a charge m at each end, tnere are m tubes leaving the north pole and returning to the south pole. It is evident that where the cross section of a tube is least, 'the intensity of the field is greatest ; and vice versa. Similarly, if A is the area of any small surface in the field at right angles to the force, and if there are JV tubes passing through this surface, the intensity of the field at that point is pro- portional to the limiting value of the ratio —, as A is taken -ZV A smaller and smaller. In
words, the intensity of the field at any point is proportional to the number of tubes per unit area at that point. Magnetic Induction. — As was explained on page 605, and as is apparent from the cuts on that page, the effect of intro- ducing a piece of iron or other magnetic material into a field of force in air is to cause the lines of force to change their direction and enter the iron. If the iron is in the form of a rod, and if its cross section is A, more tubes pass through it than did through the same area of air before the iron was substituted for it. If the original field of force in the air is uniform, so that the intensity is the same at all points, the lines of force are all parallel, and the tubes are all of the same cross section. If the intensity of the field is 72, the number of tubes per unit area is proportional to this. If, MA<; \KTH- FOWK AM) IMK'CTION 615 now, a long iron rod is introduced parallel to the field, the number of tubes per unit area of its cross section is greatly increased; and it may be proved by methods of the infinitesi- mal calculus that the ratio of this number to the previous one equals the value of the quantity ft for iron, as defined on page 608. It is for this reason that- p is called the permea- bility. (For different kinds of iron, and for different con- ditions. p may have values as great as 2000.) It is thus seen that for any magnetic substance /A is greater than for air. The number of tubes per unit area in the iron (or other magnetic substance), when in a field of intensity 72, is, then, proportional to the product pR ; and this quantity has re- ceived the name of the "magnetic induction" at the point where Ii is the intensity of the field and p is the permeability. The fact that the tubes do not simply end on the iron rod, l>ut must be considered as passing through it, may be proved by certain phenomena of electric currents which will be dis- cussed in a later chapter, and also by the simple experiment of cutting the rod into two pieces by a transverse section and separating tin-in slightly ; the field of force in the crevasse is found to be much more intense than in the original fit-Id. When the magnet causing the field of
; and so we are led to believe that the energy is MAGNETIC FORCE AND INDUCTION 617 located in the surrounding medium where the magnetic field exists. It follows from the formula that / is small if //. is huL,re, or, in words, the forces are small if the permeability of the medium is large ; and consequently in such a medium the energy per unit volume is also small, since small amounts of work are involved in any changes, other things being equal. (Magnetic forces can be felt through a vacuum, and so the energy of a magnetic field is, in the case of any material medium, both in the ether and in the matter.) Attraction and Repulsion. — Therefore, if a piece of iron — for which ft is greater than for air — is introduced into a field of force in air near a magnet, the energy in the space occu- pied by the iron is less than when it was occupied by air; and the decrease in the energy is greater if the field of force is intense than if it is feeble. In other words, if a piece of iron is moved up gradually toward a magnet, the potential energy of the field becomes less and less ; therefore, if a mag- net and a piece of iron are left to themselves, there is a force of attraction between them, and they will approach each other. Similarly, a magnet will attract a piece of any magnetic sub- stance in air. Conversely, and for obvious reasons, a magnet will repel a piece of any diamagnetic substance in air. In general, if /z for any substance is greater than for the sur- rounding medium, it is attracted by a magnet; while, if it is less than for the medium, there is repulsion. The obser- vations described on page 595 are therefore explained. An exactly analogous phenomenon in mechanics is afforded by the motions of a block of stone and a block of wood wln-n immersed in a tank of water: the fonwr will be attracted by the earth and will sink; tin- latt.-r will be repelled and will rise. The explanation in both canes is that the motion takes place in such a direction as to make the potential energy of the system less. The stone sinks because it is heavier than the water; and therefore by replacing an equal volume of water closer to the earth, the potential energy of gravitation is decreased. The wood rises because it is lighter than the water; ami
. th<-i<!•»•. it it moves up iin.l \\at.-r rrj.Isu-."* it. tin- potential energy is again decreased. CHAPTER XLI MAGNETISM OF THE EARTH Magnetic Elements. — The fact that there is a magnetic field of force on the surface of the earth is proved by the ob- servations on the motion of a suspended magnet, which were referred to on page 596. If a bar magnet or a magnetic needle is suspended in such a manner that it can turn freely in all direc- tions, it will finally come to rest in a position such that its axis is inclined with reference to a horizontal plane and lies in a vertical plane which nearly, if not quite, coincides with the geographical meridian at the point of suspension. This vertical plane is called 'the " magnetic meridian " at the point ; and the angle it makes with the geographical meridian is called the " magnetic declina- tion " or the " variation." The angle which the axis of the needle makes with the hori- zontal plane is called the "magnetic inclina- tion " or udip." The earth's magnetic field at any point is then completely denned by its intensity, the declination and the inclination. These three quantities are called the "magnetic elements." FIG. 324. — A mag- netic needle suspended free to turn in any di- rection. The dip can be measured by observing the angle which the needle makes with the horizontal plane. The variation is most easily determined by mounting the needle so that it is free to turn about a vertical pivot, and noting the angle it makes with a true north-and-south line, which may be 618 MAVXETISM OF THE AM/,' 777 619 1 orated by astronomical methods. It is convenient for most purposes of measurement to consider the earth's magnetic force as resolved into two com- ponents, one horizontal, the other vertical. Thus, if OD is the direc- tion of the field of force at 0, and if OA and OB are horizontal and vertical lines through 0 in the same plane as 0/>, the angle (AOD) is the dip ; and calling it N and the intensity of the force R, the horizontal com- ponent is R cos N, and the vertical one R sin N. The former can be meas- ured with great accuracy by the method described
on pages 610-613. Therefore, since the angle of dip, N, can be measured directly, the value of R may be deduced. Further, if the ratio of the horizontal and vertical components can be meas- ured, the dip may be calculated ; for, calling these H and V* "26. — Diagram rep- resenting the horizontal and vertical components of the earth's magnetic force. \, A dip circl.-. Y=-~. Variations in the Elements. — Observations show that the values of all three of these elements at any one point are con- tinually (hanging. So far as is known, these changes are pei i(,di(, that is, for instance, the dip makes a pendulum-like oscillation during the twenty-four hours, increasing slowly, t hen decreasing, etc. ; further, the mean value for any one day iges slightly the next day, and so on, having an oscilla- tion whose period is a year; and, again, the mean value for any one year is not the same for the next year, but changes slightly; but the period of this change is not known, for 620 MAGNETISM since regular observations began to be taken — about the year 1540 — this oscillation in the mean annual value of the dip has not been completed. Similar statements may be made in regard to the other two magnetic elements ; there are daily, yearly, and secular changes, so called. (There are other periodic changes than these, but they are the most important.) It often happens that there FIG. 827. — Chart showing secular change In IG.. — r w cr cg. -, •, j the earth's magnetism, from observations made 1S a Sudden and Unexpected at London ; the black line indicates both the in- disturbance of the magnetic clination and the declination. elements of a magnitude far greater than the regular changes ; this constitutes a " mag- netic storm." The explanation of such phenomena is not known ; but observations have shown that they occur most frequently when the spots on the sun and when aurorse in our atmosphere are most numerous. „.,,.. Magnetic Maps. — The magnetic field over the earth's sur- face may best be described by drawing on a map of the earth certain lines which indicate the values of the elements at any one epoch. Thus lines can be drawn such that at each point of the earth's surface,
through whose position on the map any one line passes, the value of the declination (or variation) is the same. Such lines are called "isog- onals," and are of the greatest possible assistance to mariners and surveyors. They are shown in the cut for the year 1900, and each one is marked with a certain number, e.g. 5°, which indicates the value of the variation for all points on that line. These lines run approximately north and south ; and it should be observed that for two lines the variation is zero, i.e. at points on them a mag- netic needle points true north and south: they are called "agonic" lines. One of these is approximately a great MAGNETISM OF THE EARTH 621 circle of the earth ; the other lies in northern Asia, and is called the "Siberian oval." Again, lines can be drawn which indicate in a similar man- ner the inclination or dip ; they are called " isoclinals," and are approximately parallels of latitude. The line of zero dip is called an "aclinic" line, or the "magnetic equator." There are two points in the earth's surface where the dip is 90°; these are often called the "magnetic poles." The lines for the year 1900 are shown in the cut. Other lines, giving other information, may also be drawn ; but they need not be described here. Conclusion. — The explanation of the magnetic action of the earth is not known. It has been proved, however, that it is due almost entirely to causes which are within the earth itself. Certain of the periodic changes are occasioned, how- ever, by external causes, such as electric currents in the atmosphere. Historical Sketch of Magnetism The property which the lodestone possesses, of attracting iron, was known centuries before the beginning of the Christian Era, because it is mentioned by Thales, who lived from the year 640 to M»; i..<. The Greeks and the Unmans were acquainted with the fact that the intervention of other bodies, like brass, does not destroy magnetic effects. That like poles repel and unlike attract, and that a lodestone possesses the power to eniniminicate polarity to inert iron, were known at least as rarly as the twelfth century. The compass was in daily use in Kumpo also as early as this, l>ut the disenvrries nf magnetic declination and its
variation t'mm place to place were made by Columbus in Hart man is reputed to have di.senvn-ed the dip in 1644. He obtained a value of 9° when- he should have obtained 624 MAGNETISM 70°. This fact was not published, and Norman, in 1576, independently discovered it in London, obtaining a value of 71° 50'. Norman was probably the first to suggest that the source of attraction is in the earth, and not in the heavens as gen- erally supposed. He also showed that the earth's field is simply directive and produces no motion of translation, by floating a needle on water. The variations in the magnetism of the earth were discovered by Gellibrand in 1636. The first systematic treatise on magnetism was William Gilbert's De Magnete. It was published in 1600, and con- tains a complete account of what was known as magnetism up to that time, as well as a great number of new ideas and experiments which are due to Gilbert himself. Gilbert was the first to recognize the difference between temporary and permanent magnets ; to detect the effect of a change in temperature ; to show that the fragments of a magnet are themselves magnets; to observe the effect of hammering, etc. ; to make use of the idea of lines of force, although in an imperfect manner. The fact that iron was not the only magnetic substance was shown by Brandt, who proved in 1733 that cobalt was magnetic. The diamagnetism of bis- muth was recognized by Brugmans in 1778, but the first systematic study of the subject was made by Faraday in 1845. It was he also who made the great discovery that the forces of attraction and repulsion depend fundamentally upon the surrounding medium. ELECTROSTATICS CHAPTER XLII 1 IXDA.MKNTAL PIIKNOMEXA Introduction. — It is observed if a piece of silk is rubbed against a glass rod and is then separated from it that both now have the power of attracting small fragments of paper, of metal foil, of thread, etc., toward those portions of their surfaces which had been in contact, and that, further, if either one of them is suspended so as to be free to move, it may be attracted by the other. The silk and the glass are said to be " electrified," to have on them " electrical charges " or " charges of electricity," or, more simply, to be u charged."
The same phenomena may be observed with any two por- tions.)f different kinds of matter; but with certain kinds the forces of attraction are manifested, not alone by those portions of the surface where they were in contact with the other body, but also over all their surface. This is true of metals, for instance. So, if one end of a long metal wire is charged, the forces are evident over all its length; the wire is said to "conduct" the charge, and it and similar bodies are called "conductors." l'»\ suitable means the charges on the other end of the wire may be removed; but, if the charge on the first end is continually renewed, charges will appear again at the former one, etc. This may be called, then, an electric "current," and while it is going on, many interesting phenomena occur both in the wire and ide it. We are thus led to divide the subject of Elec- AMBS'S PHYSICS — 40 ''25 626 ELECTROSTA TICS tricity into two parts : one deals with electrical phenomena when the charges are at rest, it is called " Electrostatics " ; the other with the phenomena of electric currents, it is called " Electrodynamics." We shall begin with the former. Electrical Charges. — As said above, when two portions of different kinds of matter are rubbed together and then separated, they are charged, and can produce forces which they could not when in an uncharged or neutral condition. The act of friction is not essential ; all that is necessary is that the two pieces of matter should be brought closely in contact. We distinguish, too, as stated above, between "conductors" and " non-conductors." The following bodies are the commonest illustrations of conductors : all metals, either solid or liquid; water containing in solution almost any salt or acid ; the human body ; the earth. The follow- ing are illustrations of non-conductors : glass, silk, paper, cloths, dry wood, porcelain, rubber, sulphur. In order to produce any appreciable charge, therefore, in a conductor, it must not come in contact with the hand, but must be " insulated " by holding it in a piece of paper or cloth. Energy of Charges. — The fact that forces are exhibited near charged bodies and that therefore work can be done by producing motion, proves that there must be energy associ- ated with charges. This is evident also
, because, as stated above, when two bodies are charged by rubbing them against each other and then separating them, one attracts the other, and this proves that in order to separate them work was required. In other words, work is necessary in order to have electrical charges. This energy which is associated with charges is not in the bodies themselves: it is in the medium which surrounds them wherever the electrical forces may be felt, that is, throughout the "electric field." This fact is proved by the phenomena of electric sparks. It is known to every one that if the electric charges are too intense, sparks take place in the medium (e.g. ordinary / •'[ • \ DA M /•; \ T. 1 /. I'll h'\<>M i:\. 1 627 all(l these are due to the breaking down of the material structure of the medium. It' a spark passes through a sheet of paper or a pane of glass, a hole is made in it : it the spark is in air, the molecules of its gases are broken into parts. This proves that the medium must have been greatly >t rained just before the sparks passed ; and, if it was strained, it must have possessed potential energy. Electric forces may be shown in a vacuum; and therefore the seat of the energy of electric charges is in both the surrounding ether and the material medium immersed in it. The importance of the nature of this medium in all electrical phenomena is thus established. r Positive and Negative Charges. — If two rods of the same kind of L,rlass are charged by means of a piece of silk, and if • >nr is suspended horizontally in a paper sling so that it is free t<» turn, it may be seen, "ii bringing the charged por- tion of the other rod near it, that one repels the other. Whereas, if the piece of silk \vhieh was used to charge the glass rods is brought near, there is attraction. Simi- larly, if other charged bodies are brought near the sus- P'-nded glass rod, some repel it and the others attract it. All those charged bodi« •> whieh repel it are said to be " positively " charged ; while those which attract it are said to be "negatively' d. Thil unonntfl definition of positive cr plus ( 4- ) and negative or minus ( — ) ehurijes. Thus the experiim-
nt s jn that 628 ELECTROSTATICS glass rubbed with silk is charged positively ; and that the silk is charged negatively. Similarly, in all cases, experi- ments show that when any two bodies are brought in con- tact and then separated, they are charged oppositely. If different charged bodies are suspended in turn, it is observed that it is a general law that a positive charge attracts a negative one but repels another positive charge, and that a negative charge repels another negative one. "Like charges repel; unlike ones attract." It is found, further, that the force becomes less as the distance apart of the charges which are acting is increased. A body which is charged positively when rubbed with some definite body may be charged negatively when rubbed with another one. And, further, the character of the charge received by a body often depends upon the condition of its surface, whether it is smooth or scratched, etc. Thus, glass is charged positively by a piece of silk, but negatively by a piece of flannel ; and smooth glass may be charged positively, while, if it is rough, it may be charged negatively. By a careful study of the character of the charges produced on different bodies when rubbed with other ones, it is found that it is possible to arrange all bodies in a series, A, B, (7, etc., such that if B is rubbed with A it is negatively charged, whereas if it is rubbed with C it is charged positively. Such an arrangement is called the "electrostatic series." A few of its terms are : cat's fur, flannel, glass, cotton, silk, wood, the metals, rubber, sealing wax, resin, sulphur. Conductors. — We say that a body is charged at any point if electrical forces are exhibited when a small piece of matter is brought near that point. If the charged body is a con- ductor, there are no forces shown in its interior ; if it is a hollow solid, — like a hollow ball, — there are no forces in the interior region ; in other words, if a conducting body is charged, the charge is entirely on its surface. This phenomenon may be considered as due to the repul- l--l-\l>.\Ml-:\TAL PHENOMENA 629 sion of a charge by a similar charge ; the charges distribute themselves as far apart as possible, and, since a conductor allows charges to flow, they will all be on the
surface. (This is true only after the charges have come to rest ; it does not hold when there are currents.) This fact may be proved by direct experiment in many ways. Faraday made a metal box large enough to allow him to enter it and carry with him his instruments ; and he showed that, however the box was charged, there were no effects inside after the charges came to rest. (Similarly, he showed that whatever electrical charges or changes he produced inside, there was no elec- trical force outside. The explanation of this will be given later.) Lines of Force. — The region around charged bodies in which electrical forces may be shown is called the " electric field " ; and a " line of electric force " is a line in the field such that at each of its points its tangent is the direction in which a minute body charged positively would move if left to itself. (A negatively charged body would, of course, move in the opposite direction.) If a line of force is con- tinued, it will be found, therefore, to start from a positive charge and to end on a negative one. Two lines of force < iiiniot cross, for that would mean that at the point of inter- section a charged body would move in two directions. 'I 'here are no lines of force inside a conducting body; they all end at its surface. In I i^. :>:51, lines of force are drawn for several special cases. It is seen that the phenomena of attraction and re- pulsion and the distribution of the lines themselves may be described by saying that lines in the same direction repel each other, and that there is a tension in the lines tending to m.ike them contract. It may not be unnecessary to state the obvious fact that these lines have no physical existence, but are merely geometrical constructions. The lines of force may be mapped by a method exactly 030 ELECTROSTA TICS Two unlike charges, the positive one four times Two similar charges, one four tiim.« as great as the negative one. as great as the other. FIG. 381. — Lines of electrostatic force. FUNDAMI-:M.\L ni I:\OMENA 631 similar to that described for a magnetic field. It will be shown in the next paragraph that when any piece of matter is put in an electric field it becomes electrically charged, some portions with plus electricity, others with minus. If it is an elongated body
sitely on its two ends or faces, as described above. There is an essential difference, however, between this case and that of a piece of non-conductor, owing to the fact that lines of force do not pass through a conductor and, there- fore, end on its surface, while they can and do pass through a non-conductor. This difference will be explained more fully in the next chapter. These induced charges on a conductor are caused by the attraction of the charge on the charged body for an unlike charge and its repulsion of a similar charge ; it being borne in mind that these forces are due to the fact that when unlike charges approach each other, or when like charges recede from each other, the potential energy in the medium becomes less. Thus, if a conductor is joined to the earth by a con- PIG. 884. — Charging a conductor by induction. ducting wire, and if a positively charged body is brought near it, a positive charge is repelled to the earth and the rr.\i>.\Mi-;\ i AL 633 conductor itself has a negative charge ; if now the conduct- ing wire is removed, the conductor retains its charge. The distribution of the lines of force is shown in the cut. This process of charging a conductor is known as "charging by induction." Fio. 884 a. — Charging a conductor by induction. Experiments show that, if a charged body has points on its sur- face, the electric force in the air is greatest near them ; and, in fact, if such a charged conductor is carried into a darkened room, faint sparks will be seen at the points. The charges are passing off to the particles of dust and to other small portions of matter in the surrounding air. These thus become charged with the same kind of electricity as that on the body, and are, there- fore, repelled by the latter, forming a current in the air, or a wind. This is often sufficient to be felt by the hand or to blow out a candle flame. If, then, a pointed conductor is brought near a « haiLced body, so that its points are to wanl the latter, which may be either a conductor or a_ non-conductor, t In- latter will induce charges on the for- mer ; and those on the points turned toward the charged body will escape, Fw. 886. -Action of,K,int» by induction.
be drawn to the latter, and "discharge " it by neutrali/in^ the charges on it; the other induced charges, which are like tlmse on the body originally charged, will remain on the eondiu -tor. The final action, therefore, is as if the obi 634 ELECTRO 8T A TICS were bodily transferred to the pointed conductor. This action of such a pointed conductor, or a "comb," is made use of in many electrical machines. (Its importance was first recognized by Benjamin Franklin (1747). It is the reason why lightning rods are always made with sharp points.) Electroscopes. — It may be well to explain at this point one or two simple instruments which are used in the study of electric phenomena. One of the most useful of these is the "gold-leaf electroscope," which consists essentially of two vertical slender strips of thin gold foil connected at their upper ends to a metal rod which is attached to a metal plate or ball. The gold leaves are, as a rule, inclosed in a glass bottle so as to prevent any action of draughts of air. If the plate or ball is given a charge, this will spread over the leaves, and since they are now charged alike, they will repel each other, and will diverge. The angle of divergence will vary with the intensity of the force of repul- sion. Further, if a charged body is simply brought near the plate (or ball), charges will FIG. 886.— Gold-leaf electroscope. be induced on the leaves and they will diverge. In most gold-leaf electroscopes there are thin strips of tin foil fastened to the walls of the glass vessel and attached to the metal base of the instrument, so that if the gold leaves are diverged too far they will not communicate their charge to the non-conducting glass walls, but to the conducting strip, which will carry the charges to the outside of the instrument. Another simple instrument is the "pith-ball electroscope." It consists of a small pith ball covered with a thin layer of metal foil and supported from a vertical metal rod by a fine wire or other conductor. If the rod is charged, it will trans- fer some of its charge to the pith ball, which will be repelled. The angle its supporting wire makes with the rod is a meas- FUMtAM K.\TAL I'll K.\< >M KNA (J
35 urc of the force. It is obvious that a single gold leaf could be used in place of the pith hall, or that two pith halls could be used in place of the two gold leaves in the former instrument. Electrical Machines. — As we have seen, electrical charges may be produced by two independent methods: by friction or contact between two different bodies, and by induc- tion on a conductor. Corresponding to these are two types of machines for producing (barges continuously. a. Friction Machine. — There are various forms of these so-called friction machines ; but a description of the one shown in the cut will apply to all. There is a large glass plate pivoted on an axle, which is clasped at one point by two metal clips lined with leather; so that. as the wheel is turned, the glass becomes charged positively and the clamps negatively. The charges are removed from Fi... M, the latter by joining them to the earth, and from the former by the use of a point. -d conductor or "comb." A positive 036 ELECTROSTATICS charge is thus accumulated on the large conductor which is joined to the comb. b. Induction Machine. — The simplest form of instrument for producing charges by induction is the so-called "elec- trophorus," which was invented by Volta about 1775. It consists of a thick plate A, of some non-conducting sub- stance such as glass or hard rubber, which rests in a metal base B ; and of a loose metal cap (7, provided with an insu- lating handle D. In using the instrument, the cap is removed and the upper surface of A is charged by friction with a piece of -flan- nel or cat's fur ; let it be assumed that it is thus charged negatively. This charge will induce a plus charge on the upper surface of the metal base B, and the induced minus charge flows off to the earth. (The function of this in- duced charge on B is by its attraction for the charge on A to prevent the latter from escaping or leaking.) The metal cap 0 is now lowered on A. Actually, it touches it at the most in only a few points and so does not receive any appreciable charge from A directly. But the charge on A induces a positive charge on the lower side of C and a nega- tive one on the upper side. This cover 0 is now touched with the finger
or otherwise connected to the earth ; so the negative charge is removed, and only the positive one re- mains. Connection with the earth is now broken, and if the cap is lifted by its handle, it will carry with it its positive charge. This charge may be transferred to some conductor ; and the cap being discharged may be replaced on the plate A, which still retains its charge. So the process may be repeated indefinitely. FIG. 889.— Electrophorus. Machines have been made by which these various steps are M i-;.\ i. i L /'// I-:.\»M I:.\A 037 carried out automatically. One of these is shown in the cut. The explanation of its action is simple, but is so long that it need not be given here. It may be found in almost Fio. 840. —Induction electrical machine. any special treatise on Electricity, such as dimming, Elec- tricity ; Perkins, J5Y«///W/v <tu<l Magnetism; S. P. Thomp- son, Elementary Lessons in Electricity and Magnetism, etc. CHAPTER XLIII ELECTRIC FORCE; MEASUREMENT OF ELECTRIC QUANTITIES Quantities of Electricity. — The fact that an electric charge is a quantity to which a numerical value may be assigned is suggested by many experiments. If a hollow metal vessel, like a can, is placed on top of a gold-leaf electro- scope, and if a charged body is lowered into it by means of a silk fibre (or other non-conductor), the leaves diverge owing to induction ; but the amount of the divergence is found to depend upon the charge lowered, not upon its position inside the vessel. Further, if another similar charge is lowered into the vessel, the leaves diverge still more, but the amount of this does not change if the two charged bodies are brought in contact, or even if they touch the walls of the vessel. We are thus led to speak of the "quantity" or "amount" of charge, or of electricity. It should be noted that the last experiment described shows that the total quantity of electric- ity on two or more conductors is the same before and after they touch. Thus we speak of the " Conservation of Elec- tricity." Equal Quantities of + and -- always produced. — If two uncharged bodies are lowered into the vessel, e.g. a piece of
silk and a piece of glass, the leaves do not diverge, even when these two bodies are touched or rubbed together and then separated. But, if one of them is now removed, the leaves do diverge, showing that the two bodies were charged, but with exactly equal amounts of opposite kinds of electric- ity. Similarly, if an insulated conductor is lowered into 638 ELECTRIC FORCE the can in which there is already a charged body, there is no change in the di\ er^vnce of tlie leaves, thus proving that the two induced charges are of exactly equal amounts of opposite kind. Thus it can be stated as a general law that whenever a charge of any kind is produced, an equal charge of the opposite kind also appears. Faraday's "Ice-pail Experiment. " Dielectrics. — An in- teresting experiment in this connection is one due to Faraday. If a charged body is lowered by means of a silk cord into the interior of a nearly closed hollow conducting v< which is joined by a wire to an electroscope, the leaves of the latter will diverge ; but, as said above, the amount of the divergence does not change as the charged body is moved about inside the vessel, or even if the two touch. aday in his original experiment used a metal "ice-pail " as the vessel.) If the. charged body is a conduc- tor, it will lose its cha when it touches the metal vessel, because the charge will all go to the outside of the hollow conductor. (See page 628.) Hut since the divergence of the leaves is not affected, there can hare been no change in the cep11 ep6r"nent charge on this ronihietor. The explanation is that when the charged body is lowered into the hollow vessel, it induces an equal amount of electricity on the inner wall of the vessel of a kind opposite to its own — and therefore also an equal amount of the same kind as its o\\-n on the outside of the wall of the vessel; so, when the charged conductor touches the inner wall of the vessel, equal amounts of plus and minus charges pass to the outer surface, and there is con- sequently no change in the external conditions. It is "I, 640 ELECT If <> T. I TICS served, further, that when the charged body is lowered into the hollow vessel, the divergence of the gold leaves, is the
same whatever non-conducting medium is used to fill the vessel or is present in it: air, oil, sulphur, etc. Thus, electri- cal effects are transmitted through these various substances; and for that reason Faraday called them "dielectrics." (Actually there is a distinction between the idea of a dielectric and that of a non-conductor or insulator, but it need not be emphasized here.) Law of Force. — The force between two charged bodies is found to depend upon the amounts of their charges, their distance apart, and the nature of the surrounding medium or dielectric. So far as distance is concerned, Cavendish proposed the relation that the force varied inversely as the square of the distance. He showed by most ingenious mathe- matical reasoning that, if this were true, the charge on a spherical conductor must be entirely on its outer surface, even if there were bodies in its interior which were joined with it ; and he then proved by direct experiment that the charge was entirely on the outer surface. (This was pre- vious to 1773.) This same suggestion as to the law of force was made independently by Coulomb (1785) ; and he verified it by direct experiment, placing charges at different distances apart. A unit electrical charge may be defined in a manner simi- lar to that used for a magnetic charge. On the C. G. S. system of units a unit charge is defined to be such a one that, if it is at a distance of 1 cm. in air from an equal '•- charge, the force is 1 dyne. This is called the "C. G. S. Electrostatic Unit." Then, if a charge whose value is e is at a distance of r cm. from - a charge e^ in air, the force in dynes between them is —• But it is found that the force depends upon the surrounding medium ; and this is expressed by writing the value of the force in ELECTRIC FORCE 641 dynes as /= *,. where K is a quantity which is character- istic (and constant) for any one dielectric. It is called the '•dielectric constant." Using the system of units defined ahove, the value of ITfor air is one. Its value for all other dielectrics (with the exception of a few gases) is greater than for air, as may be proved by directly measuring forces in different media. Tubes of
Induction. — The "intensity" of an electric field of force at any point is defined to be the value of the force \vhieh would act on a unit positive charge if placed at that point. Kxactly as in the case of a magnetic field, too, tubes hounded by lines of electric force can be drawn; and if they are of the proper size they will end on unit plus and minus charges. They are called " tubes of induction." Since there is no force inside a closed conductor, even if it is charged, these tubes must end on its surface, not traverse it. They do, however, pass through a dielectric, as is shown by i day's experiment described on page 639. In this the tubes all start fn>ni either the charge which is introduced or from the inner wall of the vessel, and end on the other charge. We can, in fact, define a real charge as one which origi- nates tubes of induction. Thus, in the cases of induction described on page 6tfl tin- tubes from the charged body pass into and through the dielectric bodyj'but they end on the iiictiiiLT on,-, and an e.jual number leave the other end. Thus, the charges on the latter body are /v/// ; while in the former case they are only <//'/»//v///, the forces manifested bein'_r di; iv be sliown by methods of the inlinitcsimal calculus, to the fact that the tubes are passing from one dielectric into another. The number of unit tubes per square centimetre at ri^ht angles to the Held at any point is, as in the case of magnet- — 41 ism, prop.M-ii.mal to the intensity of the field at that point. 642 ELECTROSTATICS Explanation of Attraction and Repulsion. — The explanation of electric attraction and repulsion may be given in terms of energy exactly as was done for mag- netic forces ; the constant K taking the place of /*. Since K is less for air than for all other dielectrics, a small piece of any such dielectric is more permeable for tubes than is air, and is attracted by a charged body if air is the surrounding medium. Further, since there is no force and therefore ™ energy inside a conducting body, a small piece of a conductor is attracted even more than a piece
of non-conductor. The action of charges on each other has already been discussed. Electric Potential. — The properties of electric charges and the condition for their being in equilibrium may be expressed in a different manner. When a charge is moved in an elec- tric field, work is done, either at the expense of the energy of the field or against the forces of the field. Thus, if a plus charge moves in the direction of the field of force (or a minus charge in the opposite direction), the field loses energy and the charged body gains kinetic energy as it moves ; if a plus charge is moved against a field of force (or a minus charge in the opposite direction), work is done by some outside agency i and the energy of the field is increased. We have a mechanical analogy in moving a body toward or away from the earth ; if it is raised, work is done against gravitational forces and the potential energy is increased ; if it falls, it gains kinetic energy at the expense of the potential energy. We may define the potential energy of a body of unit mass with reference to the earth when placed at any point as the " potential at that point," or we may say that the potential at a point is the work required to raise a body of unit masft from the earth to it ; and we may describe /;/./,' ntic FORCE 643 the gravitational forces in terms of this quantity. The potential is evidently constant at all points of any horizontal plane; and the higher the plane is from the earth, so much the greater is the potential. Such a surface of constant potential is called an " equipotential " one. Evidently there is no change in energy as a body moves along such a surface ; but the change as a body of unit mass is moved from a point Pl in an equipo- tential surface, the -£ V, potential of whose points is Vv to a point P2 in a second equipotential sur- face whose potential I.2 - J r and FIQ m _ p. and F> ^ two horlzonul planes is entirely independ- ent of the path of the motion. (See page 108.) The line of action of the force at any point is perpendicular to the equipotential surface through that point ; because, if it were inclined to it, there would be a component force in the surface, and work would be required to move a body against it, \\hich is contrary to tin- idea <>t'
an equipotential surface. The direction of the force is, obviously, from points of high to those of low potential. Similarly, in the case of electrical phenomena, we may >se the earth as our standard body, since it is a con- ductor, and is so large that its electrical condition ma\ In- regarded as permanent, and may define the "electric pot en - tial " at any point in an electric field as the work required to a unit plus charge from the earth to that point. I not necessary to specify any particular point on tin- earth, because tin- potentials of all points of a conducting body are the same, if tin' charges are at rest. If this were not so, it would require work to carry a charge from one point to another in the conductor; this would presuppose that there was an elec- 644 EL EC TROSTA TICS trical force in a conductor ; and, as we know, this is not true. So, since the earth may be regarded on the whole as a con- ductor, all points of its surface are at the same potential, whose numerical value is zero in accordance with the definition of potential given above. (This does not imply a zero amount of anything; for potential is not a quantity which can be measured. See page 11. We give it a number, just as we give temperature a number. 0° temperature does not mean a zero amount of anything, but indicates a temperature which serves as the starting point of a thermometer scale. So the potential of the earth is 0, because the earth is the body of reference. Actually the earth is not a good conductor, and there may be local differences of potential.) Similarly, the potential at any point far removed from the electric charges, that is, at " infinity," is zero, because no work would be re- quired to move a unit charge from such point to one on the farther side of the earth, where by definition the potential is zero. We can draw equipotential sur- faces in the field of force ; the lines of force are at right angles to them ; and the direction of the lines is from high to low potential. Thus, if the field is due to a charged spherical conductor, whose complementary charge is at a great no. 844. -Lines of force and equi- distance, everything is symmet- potenttal surfaces around a charged rical with reference to its Centl'6 ; spherical
conductor. „ the equipotential surfaces are con- centric spheres, and the lines of force are portions of radii starting from the spherical conductor. If the charge on the conductor is plus, the potential at points near it is higher than that at those more distant ; if the charge is negative, just the reverse is true. Thus, if a plus charge is put at any point, the potential of all points near ELECTRIC FORCE 1>\ is raised ; while the contrary is the case if the charge is negative. Induction. — We can thus explain the appearance of in- duced charges on a conductor. Let a positively charged body be brought near an insulated uncharged conductor AB. All points of this must be at the same potential since it is a conductor ; but if tlu' conductor were absent, the potential at a point A near the charged body would be higher than at a point B which is more remote ; consequently, if the poten- tials at A and B are to be the same, a negative charge must appear at A so as to lower its potential, and a positive charge at 5 so as to raise its potential. Or, again, since when the conductor is absent, the potential at A is greater than at B^ the electric force is in the direction from A to B\ and, when the conductor is introduced, a plus charge moves in tin- direction of the force toward B, and a negative charge moves in the opposite direction toward A. T I A FIG. 845. -Electrostatic Induction. Further, if the conductor is joined to the earth by a wire, its potential must be zero; but 'under the influence of the FIG. 846.- Effect upon line* of force and c.\|ii1poti>ntUt Mirftrr,,f introducing a uphoric! dttctor in the field and HIM. joining It to the earth. charged body alone it would be some positive amount ; there- fore, in order to lower it to zero, a negative charge must appear on it. (The same explanation can be given of the inducing action of a negative charge.) Distribution of Charges. — The fact that the potentials at all points of a conductor on which the charges are at rest are the same is a consequence, as was shown above, of the fact that there are no forces in a closed conductor. This may be expressed in a different manner : the charges on a conductor are all on the surface
, and they are so distributed that the inten- sity at any point inside is zero, or, what is the same thing, that the potential at all points is the same. Thus, consider a closed FI«. 347. -Diagram illustrating the conductor of any shape, and let P fact that the force inside a closed con- be any point in its interior and Qv ductor is zero. r\ r\ i • ± f • L Qv Qp etc., be any points of its surface. The charge at Ql is at the distance rl from P ; that at Qy at the distance rv etc. So, if Av A2, Ay etc., are small areas at Qv Qv $3, etc. ; and if dv d%, c?8, etc., are the values of the surface density of the charges at these points, i.e. the charge per unit area, the intensity at P, or the force acting on a unit plus charge, if placed there, is the geomet- rical sum of 1 21, 2 22, 3 23, etc. This sum must be zero. ri rz rz By considerations of this kind it may be proved that the sur- face density at a point is greater than over a plane surface. (See page 633.) Sparks. — One of the commonest phenomena associated with electric charges is that of sparks. They are occasioned, as has been explained, by the mechanical rupture of the mate- rial medium in an electric field ; and they prove the existence of a great strain due to the electric forces. The intensity of the field at any point may be expressed in terms of the poten- ELECTIUC FORCE 047 tiul. If F"and V + AF"are the potentials at two neighboring points at a distance apart Aa?, the electric force is in the direction from the second point to the first ; and if R is its numerical value R&x = &V, because each member of the equation expresses the work required to move a unit charge from one point to the other. Since R is actually in tin* direction in which V decreases, the exact formula is R&x = AF — AF; or 72=——. Consequently, if the intensity is great, there must be a great fall of potential in a small dis- tance. Thus, if the difference of potential between two con- ductors is high, there is danger of a
spark passing between them, and a connection may be found by experiment between the potential difference and the spark length in any dielectric under definite conditions. A limit is therefore fixed by the electric properties or " strength " of the air for the value to which the potential of a conductor may be raised; for, if it is exceeded, a spark will pass to the earth or to particles of foreign matter in the air. When a spark passes between two conductors, its path through the air is an excellent conductor ; and therefore both bodies are brought to the same potential. The pot. n- tial of one is raised by the passage to it of a certain amount of positive electricity, or by the \\ ithdrawal from it of a cer- tain amount of negative electricity; and that of the other is lowered by the opposite process. (See Electric Current. page 663.) The luminous character of a spark or dischar^1 in any gas is due to the luminosity produced by the electrical changes \\-hich accompany the disruption of the molecules and the conduct ion of the current. Capacity of a Conductor. — If we consider an insulated eondiirt.ir 1.;. i ii space, it is eviden t that if it is charged pnMt ivdv. it \\,11 itself liave a posit ivi- potent ial. and that if it ( -hai-irc is increased, so is its potential, because a greater amount of \\«.ik would be required to bring up to the 648 ELECT HOST A TICS conductor a unit charge from the earth. If the charge is doubled, so is this amount of work, and therefore so is the potential, etc. We may express this fact in a formula, writing e for the charge, V for the potential of the con- ductor, and 0 as a factor of proportionality, viz., e = OV. This quantity O is called the " capacity " of the isolated conductor ; it may be defined, as is seen from the formula, as equal in value to that charge which would raise the poten- tial of the conductor by a unit amount. It is evident from general considerations that 0 must depend upon the shape and dimensions of the conductor, and upon the dielectric constant of the surrounding dielectric. If air is the dielectric and if the conductor is charged with a quantity, e, the potential VA is, by definition, the work required
to carry to it a unit plus charge from the earth; while if the dielectric has the value jfiT, the forces are dimin- ished JT-fold (since the electric forces vary inversely as 7f ), and the potential of the conductor, F^, or the work now re- quired to bring up a unit plus charge, is less than VA in the ratio 1 : K\ or, VA=KVK. So if CA and CK are the capaci- ties in the two cases, e = CAVA=CKVK\ and hence OK=KQA. In words, the capacity of a conductor varies directly as the dielectric constant of the surrounding medium. The connection between the capacity of a conductor and its shape and size may be deduced in certain simple cases by means of the infinitesimal calculus. Thus, it is known for a sphere, an ellipsoid, a cylinder, etc. The capacity of a sphere of radius a in air is numerically equal to a ; and, there- fore, in any other medium it is Ka. If a charge is distributed over two spherical conductors of radii rl and r2, which are in contact, their potentials are the same, but their charges are different. If the dielectric is air, we have, writing el and e2 for the charges and V for the common potential, e\ = r\V, e2 =?'2F; and the surface densities of the charges on the two spheres are. * a and 2 2> (/" we assume the distribution over each to be uniform. Calling these d\ and ELECTRIC FORCE 649 rfj = F orrf,:rf,= I:I. This in- 4?rr2 rt r2 dicates that if n > r2, </i < </2- So, if the curvature is great, the surface density is great. A point on the surface of a sphere may be compared roughly with a small sphere attached to it ; and so we see why the sur- face density of the charge on a point is so great. Energy of a Charge. — The energy of a charged conductor is located in the surrounding dielectric ; but its numerical value can be expressed in terms of the charge, e, and the potential, F, of the conductor itself. We can imagine the conductor as being originally uncharged, and the process of charging as consisting
in the bringing up to it from the earth a series of minute charges. In this manner the charge grad- ually increases from 0 to its final value, e ; and the potential rises from 0 to F". Since the potential at an instant varies directly as the charge at that moment, the mean value of the potential during the process is \V\ that is, the work done in charging the conductor is the same as if the whole charge, «, were brought up against this potential of JF", in- stead of the small amounts having been brought up against the continually increasing potential. By definition, the po- tential is the work required to move a unit plus charge from the earth up to the conductor, and so tin- work required to move the charge e is the product of e and the potential. In the present case, then, the \\.uk don.- is the product of e and JFi or \eV. This is the value of the energy of the field. It should!M» noted that in this mode of considering the charg- ing of the conductor, an equal charge, — e, of the opposite kind, is left on the earth, whose potential is /ero. Similarly, the energy due to a charge — e whose potential -%cV. (This does not mean that there is such a thing as negative energy ; for if a charge — e is by itself in space, its potential T has a negative value. » S... in general, if there are two conductors with equal and opposite eharges, + e and — e, at potentials /'..and \'r the energy in the di- electric surrounding them I'., l\i 650 ELECTROSTATICS The energy of an isolated conductor can be expressed in another form, which is often useful. Calling it W, the formula is W = \eV\ but e = CV, so we may write W- \?- or W= J C V\ The capacity is a constant C for a given conductor in a given dielectric, and is independent of the charge or its potential ; so these formulae show that the energy is inde- pendent of the sign of the charge, depending simply upon its numerical value. Mechanical and Thermal Analogies. — An analogy may be drawn between electrostatic potential and fluid pressure, which is useful. A fluid, either gas or liquid, always flows from points of high to those of low pressure : a positive ele
c- tric charge moves from points of high to those of low poten- tial. When a gas is compressed by a pump into a vessel of any kind, the pressure continues to increase until a point is reached at which the vessel breaks or the gas leaks, and this maximum pressure does not depend upon the size of the vessel, but upon its strength, etc. ; when the charge of a conductor is increased, the potential rises, and a condition is finally reached when a spark passes or the charge leaks off, but this maximum potential is determined by the " strength " of the surrounding dielectric, not by the size or capacity of the conductor. Similarly, heat energy always flows from bodies at high temperature to those at low ; and, if a small flame is main- tained at as high a temperature as a large one, it is just as useful. Condensers ; Capacity. — Owing to the liability of a charged conductor to lose its charge if its potential is high, a method has been devised by which the conductor may keep its charge unaltered, but may have its potential lowered. When this is done, its charge may be increased before there is again danger of its escaping. The apparatus is called a "con- denser." The general principle, then, is to make use of any processes which will decrease the potential of a charged conductor. ELECTRIC FORCE 651 If the conductor is a plate and is charged positively, the charge will he distributed the same on its two sides, if it is isolated; but if, as shown in the second figure in the cut, another conducting plate is brought near it, minus and plus charges will be induced on this, and an additional amount of the plus charge on the first plate will be attracted around to the face opposite the second one. As a result, the poten- tial of the first plate is lowered ; because if a unit plus charge is brought up to it from the earth, less work is required than before, owing to the action of the induced negative charge on the second plate. The induced plus charge on this plate serves to keep the potential hi<_rh ; and if it is removed by join- in- the plate to the earth, the potential is lowered still more. This potential is now the work required to carry a unit plus charge across from the second plate, whose potential is zero, to the first one; and it may be decreased n if a dielectric, such as glass, is substituted for the
air between the plates; for if K is increased, the force required to move a charge is decreased. Therefore, in the end practically all the charge on the first plate is on the face toward the second one, and there is an equal amount ot electricity of the opposite kind on that lace of the second plate which is toward the first one; and the potential of the iir>t plate is greatly below that which it was originally. Fio. 848. — Different steps in the construction of a condenser. "EARTH If the connection with the earth is removed, and the whole apparatus is moved elsewhere, possibly near some other charged bodies, the potentials of the two plates will change, but f/i.-ir difference remains constant, because it equals the \\ork re.\|niivd to move a unit positive charge from one plate 652 ELECTROSTATICS to the other; and we may assume that the two plates are so close together that this work depends simply upon the charges on them. If, then, -f- e and — e are the charges on the two plates, and V^ and Vl are their potentials, F^ — V\ is a constant so long as e does not change. If it varies, so does V<i — V\\ and one is proportional to the other. We may therefore write e — G(V^— Fi), where 0 is called the "capacity of the condenser." It is evident that this quantity is a constant for a given combination of two conductors of definite size and shape separated by a definite dielectric of a definite thickness ; and it has, of course, no connection with the similar constant for a single isolated conductor. The numerical value of the capacity may be calculated for many simple cases. A condenser consists essentially of two similarly shaped conductors placed close together and sepa- rated by a dielectric, such as glass, mica, etc. The com- monest forms are those in which the conducting plates, or "armatures," are parallel plates, concentric spheres, or coaxial cylinders. A few facts in regard to the capacity of these condensers are evident from the formula of definition : The capacity must vary directly as the dielec- tric constant of the two dielectrics, because for a given value of e, V^ — V\ varies inversely as K\ the capacity must vary directly as the area of the armatures, because for a given "value
seillat ion jirudiicus waves. Kxperim- lia\i-.sliown that ihe^- waves tra\«-l in air with the vel<> of li^lit ami that thev are t rans\ ers.-. I IP ean In- relli-j-ted, • ;:>• ; ELECTROSTA TICS refracted, diffracted, polarized, etc. Their wave lengths can be measured, and waves as short as a small fraction of a cen- timetre have been obtained; as a rule, however, they are much longer. These waves may be detected by means which will be described later. One method may, however, be men- tioned here ; if they fall upon two conductors which are close together, they will — under suitable precautions — cause minute sparks to pass between them. These " electro-magnetic " waves, so called, were first in- vestigated by Joseph Henry, in 1842, but were rediscovered many years later by Hertz. They serve a commercial pur- pose in the various systems of wireless telegraphy which are now in daily use. Since the waves travel in air with the velocity of light, it is proved that they are ether waves. One would not expect them to travel in solid dielectrics such as glass with the same velocity as does light, because their wave lengths are so different, and it has been shown in Chapter XXX that the velocity of waves varies greatly with the wave length in all solid or liquid media. The medium, then, which serves as the means by which magnetic and electric forces are manifested, which is the " carrier" of the tubes of induction, is the luminiferous ether. This fact was first suspected by Faraday, but was proved by Maxwell by an indirect method. Condensers (continued). — The energy of a charged con- denser is, from what was proved above, Je(F^ — Fj). This may be written \^ or £tf(F2- F^2. Since the field of force is confined almost entirely to the space between the two armatures, as is shown in the cut for a parallel plate con- denser, the energy is located there also. Condensers are often joined together so as to increase their action. There are two general methods of doing this. Let the two plates of the first condenser be called Pl and §1 ; ELECTRIC FOR
CE 657 those of the second, P2 and Qv etc.; and let them be always charged in such a manner that Pp Pa, etc., are positive, and Qv Qv etc., are nega- tive Then, if Px, Pv p,. f. P. 1 r. p3( etc., are connected by wires, and (>r 0* etc., are also connected, the FIG. 858. — Three condensers joined in parallel. condensers are said to be "in parallel." Whereas, if Ql is joined to P2, #2 to P8, etc., they are said to be "in series." Let the condensers all have the same capacity and all be charged alike before they are connected ; then their differ- ences in potential are all equal, but the potentials of any two plates, e.g. Pl the be and P, need same. the potentials of P1 and Qv V, and U2 those of P2 and Qr etc. Then in all cases not be and •I.— Three condensers joined in series. Let FJ- tf1= F2- Z72 = etc.'1 1 the condensers are joined in parallel, Vl = V^ = Fg = etc., and Ul = U^ = Us= etc. ; so, it is exactly as if the condenser were made up of two large plates, one, Pv Pv P8, etc., the other, Qv Q2, Qy etc. The difference of potential 2, is Fj — Ur and the total charge on either " plate " is ne^ \\ here n is the number of condensers connected and e is the charge on each plate; so the capacity is increased n tim« •>. Thus, joining in parallel gives an increased quantity^ but does not change the difference in potential. 1 1 the condensers are joi m-d in series, J7j = Vv U^ = V# etc. ; t there are n condensers, V± — Un^n(Vl— U-^). Thus if P! and Qn are connected so as to discharge the condenser, the difference of potential is increased n-fold; but the quantity of electricity discharged is the same as for a single con- d. Miser. Since the distance between two conductors at which a spark will lak«- place is increased
if their difference AMES1* PHT81C8 - 42 658 ELECT It OSTA TIC 8 of potential is incrt-usi'd, joining condensers in series in- creases their sparking distance. (When two or more con- densers are joined in series, the minus charge on Ql does not combine with the equal plus charge on P2, etc., until Pl is joined to Qn. Before this, the minus charge on Ql is held in place by the attraction of the plus charge on Pv etc.) Electrometers. — Before we can explain how the various electric quantities are measured, it is necessary to describe an instrument which enables us to measure differences in Principle of quadrant electrometer. potential. Such an instrument is called an "electrometer." There are many forms which may be used to measure the ratio of two differ- ences in potential; so that, if one is known, the other may be calcu- lated. The best of these is the Km. 856. — Thomson's quadrant -l-'tP.meter; one of the quadrants is removed so as to show the " needle." " quadrant electrometer," which was invented by Lord Kelvin, then William Thomson. It consists, as shown in the drawing, of a cylindrical metal box which is divided by two trans- verse cuts into four " quadrants," and of a horizontal metal " needle " shaped like a solid figure eight, which is sus- pended by a fibre. The pairs of diagonally opposite quad- ELECTRIC FORCE 659 rants are connected by wires, and the needle is raised to a high potential by some electrical machine. If the difference of potential of two plates of a condenser is to be measured, each is joined to a pair of quadrants ; and the needle, which takes a symmetrical position with reference to the quadrants when they are not at different potentials, will now move so as to enter one pair, until it is brought to rest by the torsion in the fibre. The needle forms with the two plates of a quadrant a condenser, and the motion takes place in such a direction as to make as small as possible the energy of the i ondeiisers it makes with the four quadrants. It may be pn»ved by methods of the infinitesimal calculus that the angle through which the needle turns varies directly as the di Hen- nee
of potential of its two sets of quadrants. Thus, two differences of potential may be compared by measuring the corresponding deflections of the needle. In order, however, to measure any one difference of poten- tial, a different instrument must be used. This is the "absolute electrometer," which was also invented by Lord Kelvin. As shown in the cut, it consists of a paral- lel plate condenser, with a disc cut out of the upper plate as described on page 653. In practice this is suspended from one arm of ilance. The two phltCS of the condenser are joined tO the tWO OOndUOtOn WHOM Fl<1 **• -Thomson' original form of n1 difference of potential d.-sired: the plates are ihns charge. 1 with opposite kinds of electricity, and the!'<.!•.•<•,,f attraction on the movable disc may he n. putting vreightfl in the balance pan. It the area of this i the distance.ip.u-t of the plates, d, the difference of potential, f^_ V^ the dielectric con- 660 ELECTROSTATICS stant, JT, the force of attraction on the disc is given by the formula (V.-V^AK B««P zL If the plates are, as usual, in air, K= 1, and ( F^— F1)2=— F, rf, and A can all be measured ; and so V^—V^ is known. Measurement of Electric Quantities. — The four electrical quantities that have to be measured are quantity, potential, capacity, and dielectric constant. We have just shown how differences in potential may be measured ; and, if the poten- tial of a conductor is to be measured, it may be joined to one plate of an electrometer, while the other plate is connected with the earth. The capacity of a sphere or of a simple form of condenser may be calculated from a knowledge of its dimensions, as explained on page 652. But there is a simple method, due to Cavendish, for determining when the capacity of two con- densers is the same ; and so, if the capacity of any condenser is desired, it may be compared by this method with a con- denser whose capacity may the capacities of two condensers. B
, known, e.g. a parallel plate FIO. 867.— cavendish's method of comparing condenser the distance apart of whose plates can be varied. The method is as follows : let Av B1 and Av J?2 be the two condensers ; charge them by joining A1 and A% to some electrical machine, while Bl and B% are joined to the earth ; then disconnect B2 from the earth, and A1 and A2 from the machine and from each other ; join Bl to A2 by a conductor, and A1 to the earth (or to B^). If the capacities are equal, an electroscope in contact with the wire joining Bl to A2 will show no effect when Al is earthed ; for let O1 and (72 be the two capacities, and let V be the potential given Al and Az by the machine ; the charge on Al is then + 01 V, on Bl is — Ol F, on A2 is + C2 V, and on B is ELECTRIC FORCE 661 - C'2 r. \VlKMi Bl and A2 are joined, the two charges, — 6\T and -f-(72F, do not combine until Al is joined to the earth. Then they do, and the final charge, which is distributed over Bv AT and the wire joining them, is V^C^— C^)\ and this will utYi'L-t an electroscope unless Ol=Cy This method also permits one to measure K for any di- electric, and was so used by Cavendish. The capacity of the second condenser may be measured when air is the dielectric and again when glass, or sulphur, etc., is substituted. The ratio of the latter capacity to the former is the value of K. In order to measure a charge, the accepted method is to place it on a condenser whose capacity is known and to meas- ure the resulting potential. Then, since e = C ( V^ — Fi), the value of e is known. There may be a difficulty in making the charge pass to the condenser, but the method described on page 639 may always be used. This is to put the charge inside a conducting vessel which is nearly closed; an equal charge will appear on the outside and this may be measuivd. An ingenious method was devised by Lord Kelvin for the measurement of the potential at any point in the atmosphere. Let A be
the point of a conductor which is joined to an electrometer, and let some means be adopted to have a continuous current of small conducting particles leave it. Let B be such a particle. Then if the potential of A is higher than that of points in the air near it, a plus charge will he induced on B and a minus one on A ; B will carry this charge off as it moves away; and the process is repeated as the stream of particles is maintained. Finally, the potential of A will be lowered by this accumulation of negative charges until it is the same as that of the surround- ing air. Similarly, if the potential of A is lower than that of the air near by, it will be raised until it is the same. There- fore, when the potential of A ceases to change, it gives the potential <>! tin- air at that point, and may be measured by the electrometer. One means of causing a pointed conductor to t ; 1 5 '2 ELECTROS! A TICS oil particles is to use a small flame, because a burning gas is a good conductor. Another method is to have as the conductor A a vessel of water ending below in a small fun- ik-1, so that drops of water are continually forming and break- ing away. In this manner many interesting facts in regard to atmospheric electricity have been learned; one at least should be noted ; the potential of the lower layers of air is as a rule always higher than that of the earth, and its value is continually changing. Strains Due to Electrification. — The fact that the main phenomenon of electrification consists in a strain of the dielectric is shown, as has been said before, by the formation of sparks, and in many other ways also. One of the most direct proofs is furnished by what is known as the " residual charges " of a glass condenser. If one is charged to a high potential and then discharged, a second discharge may be obtained after the lapse of a short time; then a third may be obtained, etc., each one being feebler than the preceding one. These are said to be due to residual charges. They depend upon the fact that glass is non-homogeneous ; for they cannot be obtained with a homogeneous dielectric. Their explanation is as follows : When the condenser is first charged, the glass is mechanically strained, and when it is discharged, certain parts of the glass lose their strain and, owing to inertia, are strained again
in the opposite manner, while other portions of the glass do not relax completely; these two portions, however, balance each other for the moment, and there is no resultant strain ; as time goes on, however, these strains, not being maintained by any force, gradually relax, but not to the same degree, so there is again a resultant strain ; this causes the second discharge when the armatures are joined, etc. If it is remembered that there is no field of force inside a conductor, so that such a body cannot maintain a strain, all the phenomena of induction, etc., may be at once explained. ELECTRODYNAMICS CHAPTER XLIV PRODUCTION OF ELECTRIC CURRENTS Definition of Terms. — The simplest case of an electric current is furnished by the steady discharge of a condenser. (See page 647.) In this, two plates having a difference of potential are joined by a conducting wire; and, as a result of the change, the charges of the two plates disappear. It is noticed further that the temperature of the wire is raised, and certain magnetic effects are produced in the region around the wire. All these phenomena constitute the elec- tric current. \Ve speak of the current as beni- in the wire; Imt this is only a mode of speaking. As the discharge begins, the plus charge on the plate of higher potential decreases, and so does the minus charge on the plate of lower potential : if by some means these charges may be maintained constant by adding continually the nec- essary <\|iiantitics of plus and minus charges, the potentials of the plates will remain unchanged: and the current i> said to be "steady." The phenomenon in the Conducting wire, which constitutes the current, consists, as will be shown in the next chapter, of a motion of a stream of positively charged particles in the direction from hi^h to low potential in the wire, and of a stream of negatively charged particles in the opposite direction. lly •/•_///////"// the former direction is called that of the current. If t\ is the cjuantity of plus elec- tricity that passes through the cross section of the wire at 688 664 ELECTRODYNAMICS any point in a unit of time, and i2 is the quantity of minus electricity that passes at the same time in the opposite direction, the quantity i\ + e'2 is called the " strength of the current" or
, more often, "the current." If the current is steady, the quantities ij and izt pass in an interval of time t ; and (tj + iz)t is called the " quantity of the current." If the current is not steady, and if in any interval of time the quan- tities of plus and minus charges that pass are e1 and ez, the quantity of current is (^ 4-02). (Thus, in the discharge of the condenser whose plates are charged with + e and — e, the quantity of the current is e, because the plates will be dis- charged if e± + 02 = e. If H- e passes from one plate to the other ; or if — e passes in the reverse way ; or if 4- ^ e and — $ e pass in opposite ways ; etc., the plates are discharged.) In order, then, to produce a current in a conducting wire it is necessary to have a difference in potential between any two of its points. This difference is called the "electro- motive force" (E.M.F.) between the two points. Work done by a Current. — The passage of a current evi- dently involves the idea of work. If V^ — V\ is the differ- ence of potential between two points in a wire, and if (il + i'2) is the current strength, the quantity of positive electricity il moves from a point of high potential, Vv to one of low, V-p and therefore the electric forces do the amount of work i$y<i— Fi) ; and similarly, owing to the motion of a quan- tity of negative electricity in the opposite direction, the same forces do an amount of work ^'2( V2 — V$. So the total amount of work done in a unit of time by the electric forces is (t'i + *2) (^2— V\) 5 or, calling the current strength i and the difference in potential, E^ it is iE\ and the work done in an interval of time, £, if the current is steady, is iEt. Or, in general, if e is the quantity of current, the work is eE. Ordinarily this work is spent in raising the temperature of the conductor which carries the current ; and the necessary amount of energy is furnished by whatever produces the cur- PRODUCTION OF ELECTRIC CURRENTS
665 rent. (The heat produced in the conductor may be meas- mvil if it is in the form of a wire by coiling it in a calorimeter of water. See chapter XII. If the C.G.S. system of units is used in defining the unit quantity of electricity, the product iEt is a certain number of ergs; and so the heat produced must be expressed in ergs.) Heating Effect of a Current. — This heating effect of a current is, of course, greatest where there is the greatest amount of work done ; that is, where the electromotive force, or drop in potential, is the greatest. This is illustrated in various forms of electric lights, in the electric furnace, in electric heaters, etc. 1 Fw. 868. —The electric arc between two oarb< < The arc light, as used for illuminating purposes, consists of two rurbon rods \\lnrh ;uv connected to some source of a 666 ELECT ROD YNAMICS current, and which are so controlled by automatic mechanism that when no current is flowing they are in contact, and then as soon as the current begins they are slightly separated. The two rods when loosely in contact offer great opposition to the current, so the temperature rises at the points of con- tact ; this makes the surrounding gas a conductor, and now the rods are drawn apart. The current passes off one rod to the gas, and from this to the other rod. There is great resistance to the current passing off or on a solid ; and the temperature of the tips of the rod is raised to a " white heat," if the current is sufficient. This produces the light. Experiments show that more heat is produced at the end of the rod from which the current proceeds to the gas than at the other; this is called the "positive pole." In the ordinary "incandescent light" there is a glass bulb into which enter two platinum wires connected inside by a fine filament of carbonized wood fibre, and from which the gas has been exhausted as completely as possible. A current is made to flow through the filament, and its temperature is raised to white heat. It does not burn up, because there is no oxygen left inside the bulb. Fro. 859.— Incan descent lamp. In the Nernst lamp there is a small filament whose constitution is a commercial secret, which ends in two metal wires ; this filament is not a conductor unless its temperature iy high, and
even then under the action of a current in one direction it decomposes and breaks down. Therefore the process of using the lamp is first to raise the temperature of the filament until it becomes conducting, and then to have it traversed by a current whose direction is reversed at short intervals. If this is done, the filament gives out a brilliant light; and, as it does not oxidize, it may be used in the open air. PRODUCTION OF ELECTRIC CURRENTS 667 In an electric furnace use is made of the high temperature of the arc ; and the carbon rods are inclosed in a space whose walls are non-conductors for heat, and in which the pressure of the i^as may be increased. Direction of Current. — In order to determine by experi- ment the direction of a current it is necessary to ascertain which of the two conductors between which the current flows has the higher potential. The simplest mode of doing this is one invented by Volta. The two conductors 0 whose potentials are F^ and Fi are joined by wires to the two plates of a condenser, A2 and Ar if ra>rr the plate A% becomes A8\|A, charged positively, and Ar negatively ; be- cause lines of force pass across from A% 1 Those Charges Fio. 860. — Method of determining direction of an elt-rtric on the two faces *' current. Volta's condensing electroscope. nearest each other ; but if the wire leading to A l is broken, and the plate A% is then removed, the negative charge on A1 will spread over the whole plate and may be detected and studied. In Volta's arrangement the plate Al was the top plate of a gold-leaf electroscope, and A., was a similar plate coated with a thin layer of shellac and carried by a •_rlass handle. Therefore in this apparatus, after the wire leading to Al is broken and A.2 is then removed, the nega- tive charge will spread over the plate and the, gold leaves, which will then diverge. If now a glass rod which has been rnhhed \\ith silk is brought near the electroscope, it will induce a positive charge on the leaves, which will in part neutralize their negative charges, and so they will collapse. It', on the other hand. J "J, < Fj, the gold leaves will be- come charged positively, and a charged glass rod will
cause ELECTRODYNAMICS them to diverge still farther. In this manner, then, it may be determined whether F2 > Fr or F^< V^\ if the former is the case, and if a wire is made to join the two conductors, the direction of the current is from the one at potential V% to the one at potential Vl ; in the contrary case, the direction of the current is opposite to this. Detection of a Current. — When an electric current is flow- ing in a conductor, its temperature rises, as explained above, owing to the work done by the electrical forces against the molecular forces of the conductor. But this fact does not lead to a simple direct means of ob- serving a current, because with a feeble current the change in tem- perature is small. The magnetic action of a current offers, however, an extremely simple and direct method of detecting and even measuring a current. It was discovered by Oer- Apparatus of Oer- sted> a Danish physicist, in 1819-1820, that a wire carrying a current had a magnetic field around it. We shall take up this question more in detail in a later chapter ; but one or two facts may be stated here. sted for studying the action of an electric current upon a magnet. FIG. 361. If a magnetic needle is pivoted so as to be free to turn about a vertical axis, it will assume a north-and-south posi- tion, and now if a conductor carrying a current is placed parallel to it, but above it, the needle is deflected ; if the current is reversed, so is the deflection. Similarly, if the current is parallel to the needle, but below it, it is deflected ; but the direction Of the deflection is Opposite FlG. 862. -Section of a simple galvanoscope. PRODUCTION OF ELECTRIC CL'RREXT* to what it would be if the current were above the needle. Hence, it follows that if the conductor carrying the current is made in a loop lying in the magnetic meridian and inclos- ing the magnet, the deflection will be increased ; and if many loops are used, forming a flat coil, the deflection will be still greater. This constitutes a "gal- vanoscope." Another mode of increasing the deflection still more, and at the same time of avoiding, to a large extent, any disturbances of the magnet due FIG. 868
. -An astatic combination to other actions than those of the current in the coils, is to attach rigidly to it another magnet of equal magnetic moment, but turned so that its axis is in an opposite direction. Thus, a north pole of one comes opposite to the south pole of the other. If, now, one of -<j magnets is inclosed in the coil and the other is either above or below it, the deflec- tive force of the current is in the same direction on both magnets ; but the action of any other magnetic field is almost entirely prevented. Such a combination of mag- nets as this is called an Fio. 864. —Section of • palvanoscope with MUttc needle. "astatic needle," because if tin -ir magnetic moments were exactly equal, and if their netic axes were exactly parallel, the system would not be under a directive force due to the earth, and would remain stationary in any position. Actually these conditions are not satisfied ; and the earth has an action, but it is extremely small. So, by bnnun,ILr another magnet in-ar the astatic needle, it may be made to take any position that 670 ELECTRODYNAMICS is desired, and the action of the earth may be neutralized as completely as is desired. By thus using a 'control magnet," then, the coils to carry the current may be kept in any position which is convenient, and the astatic needle may be made to lie in their plane, while the field of force due to the earth and the control magnet may be very' small. This last is shown by the period of the magnet becoming very long when it is set in FIG. 866. — Galvanoscope. I £ vibration, for T — ZTT^ — - (see page 611) ; and so, if R is small, T is large. The field of magnetic force near any current may be studied by the use of iron filings or of a small magnetic needle, as* was described on page 603. It is found that the lines of magnetic force form closed curves around the cur- rent; the directions of the current and the lines of force being connected by the right-handed-screw law. Thus, if LINES OF FORCE A'CURRENT Fio. 866. — Diagram Illustrating connection between the direction of a current and that of the lines of magnetic force. AB is any portion of a conductor carrying
a current from A to B, the lines of magnetic force near it are as shown ; or, if the total electric circuit is considered, the lines of force pass through it from one side, and return outside. Thus, a current and any one of its lines of magnetic force form two closed links threading each other, like two links of a chain. If a current, then, is passed through the coil of a PRODUCTION OF ELECTRIC CURRENTS 671 galvanoscope, the magnetic needle will be deflected; and if the current is reversed in direction, so is the deflection of the magnet. If the current in the coil is in the direction of the motion of the hands of a watch as one looks at the coil from one end, the magnetic force is directed away from the observer, so that a north pole is forced away from, and a south pole is forced toward the observer. By means of such an instrument one can determine, then, the direction of a current, and can roughly estimate its strength. Tangent Galvanometer. — If the coil of the galvanoscope is a circular one, that is, if the cylinder on which the wire is wound has a circular cross section, the intensity of the magnetic field at the centre of the coil may be proved (see page 711) to vary directly as the current strength and inversely as the radius of the cylinder referred to. Thus if i is the current strength and the radius, the intensity of the magnetic force is pro- portional to -; it also varies directly with the number of a turns of wire in the coil ; if this is n and if the turns of wire are so close together as practically to coincide, the intensity may be written /= c—, where c is a factor of proportionality. a The numerical value of c depends, of course, on the units chosen for the magnet ie and electric charges. If the coil is placed in tin- magnetic meridian and a current is passed around ic magnet (not an astatic one) sus- pended at its centre is under the action of two opposing couples, one due to the magnetic field of the earth, and the other to that of the current in the coil; and it comes to rest when these balance each other. If M is the magnetic moment of the ma-net. // the l,,,rj- ELECTItOD YNAMICS zontal component of the intensity of the earth's field, and N the angle that the magnet makes with
the magnetic meridian when it comes to rest, the moment due to the earth's force is JIM sin N; and that due to the electric current is /M"cos N. Since these must bal- ance each other, or FIG. 368.— Tangent galvanometer. Therefore the strength of the current is meas- ured by the tangent of the angle of deflection ; that is, the strengths of two currents vary directly as the tangents of the angles of deflection. Such an instrument as this is called a " tangent galvanometer. " Electro-magnetic Unit Current. — The current strength is defined in terms of the quantities of charge which pass a cross section ; but actually these quantities cannot easily be measured directly. So, it is more convenient to define a " unit current " in terms of its magnetic properties, and then from this to deduce the value of a new unit quantity. Thus, a " unit current," or one of unit strength, is defined to be such a current that if flowing in a galvanometer coil of one turn whose radius is 1 cm., the intensity of the magnetic field at its centre equals 2 IT dynes. (The reasons for this choice of unit current will appear later.) Thus, using the same symbols as in the above formula, /= c —, this may be expressed by saying that, when i — 1, n = 1, and a = 1, PRODUCTION OF ELK'TUH' CURRENTS 673 /'= -2 TT : so this < It-tin it ion of a unit current is equivalent to putting c = - TT in the formula. This unit current is called th. ••(.(..S. electro-magnetic" unit, because its definition depends upon the intensity of a magnetic field ; that is, upon the force acting upon a unit magnetic charge. Then in a undent galvanometer the formula becomes.) _^ or, t = H-- tan N. Ha '2 -mi - - is called quantity it (r, i= - - tan N. IT and G may be measured, and the "galvanometer constant " ; TT N observed ; so the strength of a current may be measured. Tin- C. <i. S. electro-magnetic unit quantity of electricity is, then, the quantity carried past any cross section of the conductor in one second by a unit electro-magnetic current. Thru- must, of course
of the magnet, An instrument specially designed to measure quantities of current, as distinguished from current strengths, is called a " ballistic " galvanometer. Measurement of Electro-motive Force. — Since an electro- motive force is a difference of potential, it may be measured by any electrometer. (See page 658.) But, in general, other methods are adopted. One is to join the two points which are at different potentials to a condenser of known capacity, and then to discharge it through a ballistic galva- nometer. If E is the difference of ^potential and 0 the capacity of the condenser, the quantity of current measured will be CE. (The value of 0 on the electro-magnetic system must be used, if E is to be measured; but, if two electro- motive forces are to be compared, it is not necessary to know the value of (7.) PRODI < PlOJi "F l-'.l.KVTRIC CURRENTS 675 Another method of comparing differences of potentials depends upon the fact, which will be discussed more fully later, that in the case of a steady current its strength is directly proportional to the E. M. F. producing it; but, if the E. M. K. is applied at the ends of a long, fine wire, the current is small, while if the wire is short or thick, the current is large. In the former case there is said to be a great " re- sistance"; in the latter, a small one. Thus, if a P — » steady current is flowing through the conductor 0000 PQ, and the value of the R difference Of potential be- FIO.SW.— Diagram Illustrating a method of i tween two points A and B is desired, these points may be connected by wires to a gal- vanometer, #, through coils of wire, R, which are so long and so fine that they offer such an opposition to the passage of a current that practically none flows from A around through Q- to -B, and so no difference is made in the conditions at A and B. If, however, the galvanometer is sufficiently sensi- tive, it will measure this minute current; and its strength is directly proportional to the difference of potential between A and B. Other methods may be found described in labora- tory manuals. Steady Current. — If by any means, mechanical, chemical, thermal,
etc., it is possible to maintain a constant difference of potential between two conductors, a steady current may be produced by connecting these two conductors by a wire or other conductor. There are at least four methods by which this constant diffen -nee in potential may be produced. 1 in electrical machine such as described on page 685 is turn.-.! at a uniform rate, it may be used to furnish a steady current. It' \\\ nt metals, sin-h as y.inr and copper, a re partl\ iniinei ><-d in soiur li.pfid conductor other than a fused metal, Midi as a solution of sulphuric acid in 676 EL ECTROD YNA MICK water, it is found that the rods are at different potentials. If a closed metallic circuit is made by joining several wires of different material in series, and if the junctions of the different wires are at different temperatures, a current is pro- duced in the circuit. Again, if a closed circuit of some wire is moved about in a magnetic field in such a manner that the field of force through the circuit varies, a current arises; and, if this change in the field continues at a uniform rate, the current is steady : this constitutes a " dynamo. " Primary Cells. — Experiments show that, when a solid con- ductor is immersed, partly or completely, in a liquid conductor other than a fused metal, there is a difference of potential between them, which is characteristic of the two conductors. So, if two solid conductors dip in the same liquid, they will be at different potentials ; and, if they are joined outside the liquid by a wire, a current will flow in it. This fact was first observed by Volta (1800), who used zinc, copper, and dilute sulphuric acid in this manner. This is said to be a "Voltaic cell." It is a question of experiment to determine which of the solid conductors has the higher potential. In the case of the voltaic cell, the copper rod is at a higher potential than the acid, and the acid is higher than the zinc ; so the current in the connecting wire outside is from the copper to the zinc. It is observed that, as the current continues to flow, the zinc gradually dissolves away and bubbles of hydrogen gas collect on the copper rod or break loose from it and rise to the surface. It
is observed, further, that there is a current also through the dilute acid, and that its direction is from the zinc to the copper. Thus the current flows in a circuit; FIG. 870.— Voltaic cell. PRODUCTION OF ELECTRIC CUliliK\T.< 677 outside the liquid, from copper to zinc ; inside the liquid, from zinc to copper. Since the direction of a current is itl ways from a point of high potential to one of low, it is thus evident that at the boundary separating the zinc and the acid there must be some mechanism which raises the poten- tial: so that the points on the zinc must have the lowest potential in the whole circuit, and contiguous points in the dilute aeid must have the highest potential. This phenom- enon is evidently connected closely with the dissolving of the zinc in the acid. If pieces of zinc are placed in dilute sulphuric acid in a tumbler or beaker, it is noted that the zinc dissolves, that hydrogen gas is evolved, and that the temperature of the acid is raised. This proves that, when zinc dissolves, energy is liberate! 1 : in the simple chemical experiment this energy is spent in producing heat effects; in the voltaic cell it is spent iii raising the potential of points in the acid, and this maintains the current and so heats the conductors, etc. At the surface of the copper, where the current enters it from the acid, work is required to raise the potential of the plus charges from that of the acid to that of the copper, and to lower that of the negative charges which are going in the opposite direction. This difference of potential at the sur- face is due to the evolution there of the hydrogen gas. The mechanism of the current through the acid and at the /ine and copper rods will l»e discussed in the next chapter. The two solid conductors which dip in the liquid are called ••poles"; t he one which 18 at the higher potential is called the positive "ne, while the other is called the negative one. The latter is always dissolving as the current flows; so if it contains any metallic impurities, e.g. if the zinc has particles of iron in it. there will be local currents from the zinc to the acid, th.n to i1, iron, and thence to the zinc, etc. These currents have no external action ; and so should be pre- vented
, it possible, because the zinc consumed in producing 678 them is \\;i>tr<l. This can be done in many cases by rubbing mercury over the xinc rod before it is immersed in the liquid, and thus making a surface of mercury amalgam with the metal, which is practically uniform. As the current flows in a voltaic cell, hydrogen bubbles collect over the copper pole, and thus hinder the action of the cell. Various devices have been invented in order to prevent this. The most successful is due to Daniell. He made a cell, which bears his name, consisting of a porous cup — such as unglazed porcelain — inside a larger vessel ; the cup contains a saturated aqueous solution of copper sul- phate, and the outer vessel, dilute sulphuric acid ; the zinc rod dips in the latter, the copper rod in the former. When the two rods are joined outside by a wire, the current flows from the copper to the zinc. As it flows, the zinc dissolves as before, but now copper is deposited out of the copper sul- phate solution on the copper rod. Consequently there is no change in the nature of the surface of the latter. This cell of Daniell is a typical "two-fluid cell." Other cells, both one and two fluid, can be made by using other metals than zinc and copper, and other liquids than sulphuric acid. They are called " primary cells " in distinc- tion to " secondary " ones, which will be described presently. Cells may be joined "in parallel" or "in series." Thus if Ol and Z1 are the posi- tive and negative poles of one cell, <72 and Z2 those of the second, etc., the cells are said to be in series if Ol and Zv 02 and Zy etc., are con- nected by wires ; while if Ov Cv <73, etc., and Zv Four cells joined tn parallel. 2' 3' Vt0m 87i. nected, the cells are said PRODUCTION OF F/./.r//;/r i 679 t«> he in parallel. If the cells are all of one kind, let E be tin- difference of potential between the two poles of each; then it n cells are joined in series, the difference in potential between C" and Zn is nE. Whereas, if they are joined in parallel, the only effect
is to make what is practically one (dl \viili poles n times as large; this does not affect the difference of potential between the poles. A mechanical analogy of a simple voltaic cell is furnished by a pump or paddle wheel working in a horizontal tube connecting two tall vertical pipes containing some liquid, such as water. If the pump is open, the liquid will stand at the same level in the two vertical pipes; but, when the pump or wheel is set in action, the liquid will be forced through so as to stand higher on one side. A difference of pressure on the two sides of the pump or wheel is thus produced ; and, if sufficient, it will stop the action of the latter. If now a connecting tube between the upper portions of the pipes is opened, the liquid will flow from the one at the foot of \\hich the pressure is the higher over into the other, and a continuous current will be produced. This pij.j- in which tin- pressure against the pump or wheel is the greater corresponds to the o<>pp« -r rod in the voltaic c«-ll ; tin- other pip.- to tin- xinc; and the pump or wheel to the energy furnished by the dissolving zinc. taic cell. Fio. 872.-Model rep- resenting action of vol- Thermoelectricity. — If a closed circuit of linear conduct- ors, like wires, includes at least two different substances, tin-re is in general an electric current produced in the circuit if the junctions nf the.se substances are kept at different temperatures. Thus, if two \vires I and II make up a cir- cuit having junctions at.1 and B, there will be, in general, a current if the temperatures <.f A and //are not the same. The direction and strength,,f the current depend Upon the t \vo substances and upon the difference in temperature. It 'iind by experiment that, beginning with a condition when A and //are at the same temperature, if that of A is 680 EL EC Tit OD YNA MICS kept unchanged and that of B is continuously increased, the current will be in a definite direction and will gradually increase, while if the temperature of B is decreased, the current will be in the opposite direction and will gradually increase ; as the temperature of B is made to differ more and more from that of A in one direction, — in certain cases
when it is higher, in others when it is cuit made up of two con- lower, — there comes a point when the doctors i and //, having current begins to decrease, and finally junctions at A and B. ° J one at which the current ceases; while if the difference in temperature is increased still more, a current is produced, but it is in the opposite direction to that which it was before, and as the change in the tem- perature of B continues, this reverse current increases in strength. If tA is the temperature of A during the experi- ment, and if £/ is that of B at which the current ceases, FIG. 378. -A closed cir- experiments show that their mean A^'r is a constant quan- tity for any two substances : it is known as their " neutral temperature"; and tj is called the "temperature of inver- Zi sion," corresponding to tA. In order to explain these thermocurrents, as they are called, it is necessary to assume that at any cross section in the conductors where two different substances come in con- tact there is a difference of potential. If P and Q are two different substances meeting over a surface, the fundamental experi- ments of electrification show that, when they are separated, one is charged with plus, the other with minus electricity. This proves that when they are in contact there is some electric force — due to the difference in the elec- tric properties of the molecules — acting at the surface of con- FIG. 874. — Junction of two con- ductors P and Q. PRODI < won or I-:LK<-TIUC CURRENTS 681 t.ut, and resulting in a separation of the plus from the minus charges. Let us suppose that P is the substance which is charged positively; then the direction of the force producing this charge must be across the surface of contact from Q to P. As a result of the plus charge on P and the minus charge on Q, the potential of P is higher than that of Q ; so that if P ami Q are conductors, and if they are joined by some wire, a current would tend to flow, owing to this fact, from P through the wire to Q. This difference of potential at the surface of contact would be maintained by the molecular forces. Calling this difference of potential E, we may say that there is a " contact electro
-motive force " E at the boundary. The proof of the existence of this E. M. F. across the surface of contact is afforded if P and Q are conductors, and if an electric current is forced by some source, such as a voltaic cell, across this surface, first in the direction from P to (), then in the opposite direction. It is found that in the former case the temperature of the junction rises; in the latter it falls. If the current i flows for an interval of time t from P to Qi the electricity is passing from high to low potential, and so the external electric forces do the work itE at the junction ; mid this energy appears in the form of heat effects. If, however, the current is in the opposite direction, the elec- tricity is having its potential raised at the junction, and so the work itE must be done on the electric forces at the expense of the energy of the molecules at the junction ; and there- fore its temperature falls. (Or, we may say that in the f on un- case work is done against the molecular forces which produce the electrical M-paraii«>n : \vhih- in the latter, these forces do work themselves in helping on the current.) These forces at tin- surface <•!' miitact of two substances are called "Pel- tier elect i-M-im.tive forces," having been first discovered by him. They can be measured by putting a junction in a rimeter "t water, ;m«l measuring the heat produced, the rui-rent, and the time. Direct experiments prove that they 682 ELECTROJ) Y.\A MICS vary in amount with the temperature. Thus, in the thermo- couple described above there are two such forces, at A and B\ and, if the temperatures at these points are different, these forces are unequal. But there are other similar forces in each conductor between A and B, if the temperatures of these points are different. For, consider either of these conductors, the two ends of which are at different temperatures ; if a section is taken across the wire at any intermediate point, the tempera- tures on its two sides differ slightly, and so the condition of the molecules which are in contact across this section is different on the two sides. Therefore, we might expect an electro-motive force at each point in the conductor. This was proved by Lord Kelvin —
then Sir William Thomson — by the following experiment : let an electric current be forced through a wire of some definite material whose ends are kept at a higher temperature than its middle point, and let the temperatures be noted at two intermediate points, one in each half, which are such that their temperatures are 100o Oo 10Qo the same when no cur- rent flows; it is observed p J^ Q FIG. 875.— Diagram representing Thomson's that, when the Current is flowing, the tempera- ture at one of these points rises, while that at the other falls. Thus if the wire is PQR, let the current be from P to R, and the temperature of P and R be higher than that of Q\ and let A1 and Az be the two points whose temperatures are the same before the current begins. The molecular forces at Al producing the E. M. F. due to the temperature effect just described are either in the direction from Q toward P, i.e. from a cold point to a hot one, or from P toward Q. If the former is true, as the current flows from P to Q, the temperature at Al rises ; while if the latter is true, the temperature at A1 falls. Similarly, the temperature at Az either falls or rises ; but, if the temperature at Al A^ R PROi>r< y/o.v of t-:i.i-:< TR1C CURRENTS G83. if the molecular forces are in the direction from a cold point to a hot one, the current at A1 is in a direction opposite to that of these forces, while at A^ the forces and the current are in the same direction, and so the temperature at A^ falls. These forces in a wire which is homogeneous except for differences in temperature are called "Thomson electro-motive forces." In a simple circuit made up of two w i res there are then these forces at each point of both. The electric current produced in a circuit made up of dif- ferent substances whose junctions are at different tempera- tures is due to the Thomson and Peltier electro-motive forces. These currents were discovered by Seebeck in 1821, but their explanation was not known for muny years. It is evident that, if a sensitive method is known for the detection of an electric current, a means is offered for detecting differences in temperature between two points ; for the junctions of a
thermocouple may be placed at them. The sensitiveness of the instru- ment may be increased by joining in series several pairs of tli«- two conductors, as shown in the cut. If the alternate junctions are kept at one temperature, and the other junctions are kept at a different one, the current will be increased; and so a less difference in temperature mav l»e detected. Such an ins! ruim-nt is called a " thermopile." A cut of an actual in>truuicnt is shown. Fio. 876. — A thermopile. CHAPTER XLV MECHANISM OF THE CURRENT Electrolysis. — It is found by experiment that many liquids are conductors, while others are not. A metal in a liquid condition is a conductor, and its properties are exactly like those of the solid conductor. There are, however, certain liquid conductors such that, when a current is made to traverse them, there is an evolution of matter at the points where the current enters and leaves. The liquid must be held in some vessel and two metal rods or wires connected with some source of electric current — such as a series of cells — must dip into it. The conductor, or "elec- trode," at which the cur- rent enters the liquid is called the "anode"; that at which it leaves, the "cathode." Thus the potential of the former is higher than that of the latter; and the direction of the current in the liquid is from the anode to the cathode. The matter that is liberated at the anode and cathode may bubble off in the form of a gas, it may combine chem- ically with the metal rods themselves, or it may simply form a solid deposit on them. Liquid conductors which have this property are called "electrolytes"; and the process of conduction in them is called " electrolysis." A careful study of the nature of electrolytes has shown that in every case they are solutions, e.g. common salt or sulphuric acid in water; and 684 MECHANISM OF THE CURRENT 685 that the solutions are of the kind which exhibit an abnormal osmotic pressure, an abnormal depression of the freezing point, and an abnormal elevation of the boiling point. (See pages 2(H and -J76.) Faraday's Laws. — A careful study has been made of the character of the
substances which are evolved at the anode and the cathode in different electrolytes. It is found that hydrogen and all metals are liberated at the cathode, while oxygen, chlorine, iodine, etc., are liberated at the anode. Further, the amounts of the substances evolved under dif- ferent conditions were systematically studied by Faraday. As a result of his investigation, he was able to describe all of his observations in two simple laws which bear his name. Before stating these, however, it is necessary to define a chemical term which was used much more commonly in former days than now, and yet which is convenient. Ex- p« i iments have established the fact that a molecule of any chemical compound consists of a certain number of smaller parts, called atoms, the atoms of any element being alike in all respects. Thus, a molecule of steam consists of two atoms of hydrogen and one of oxygen, so its symbol is HaO; a mole- cule of sulphuric acid may be expressed by the symbol H2SO4 ; one of copper sulphate by CuSO4 ; one of hydrochloric acid IIC1; etc. A molecule of hydrogen gas has the symbol II., : "iic of oxygen gas, Oa; etc. The kk molecular weight" iy definite compound has been already defined to be a number which is proportional to the weight of one of its molecules; and a method lias l>een described for the determi- nation of this (piantity in certain cases. Other methods arc kn«.\vn. Similarly, the •• atomic weight " of any element number proportional to the weight of one of its atoms. Thus, the molecular weight of oxygen is 82; so its atomic weight is lr, :. • It is seen from the above illustrations of the com] -.f molecules that in some cases one atom, in others two, of hydrogen are contained in a molecule. Thus, ill hydrogen gas and hydrochloric acid, one atom of hydrogen combines with an atom of hydrogen or one of chlorine respec- tively; in steam and in sulphuric acid, two atoms of hydro- gen combine with one of oxygen or with the " radical " (S()4); etc. The number of hydrogen atoms which is re- quired to form a stable molecule with the atom of a substance or with a certain "radical" (or group of atoms), is called the " valence " of that substance or of
that radical. Thus, the valence of hydrogen and of chlorine is one; that of oxygen and of SO4 is two ; etc. Experiments show that if any molecule is regarded as made up of two parts, the valences of the two parts are the same. Thus, since a mole- cule of copper sulphate is CuSO4, the valence of copper is two, as is shown also by the fact that the saturated oxide of copper is CuO. (An atom may have a different valence in different compounds ; but only one of these is in general a stable mole- cule.) The ratio of the atomic weight of an element, or of the sum of the atomic weights of the atoms in a radical, to its valence is called its " chemical equivalent." We can now state Faraday's two laws : 1. The quantity or mass of a substance liberated from any electrolyte at either the anode or the cathode is directly proportional to the quantity of the current that passes. 2. The masses of different substances liberated at the anode and cathode in any electrolyte by the passage of the same quantity of current are directly proportional to their chemical equivalents. If the current flows through several electrolytes arranged in series, let ml and m^ be the masses of the substances liberated at the anode and the cathode in the first electrolyte, and cl and <?/ their chemical equivalents ; mv w2', <?2, and c2f be similar quantities for the second electrolyte, etc. Fara- day's first law states that any m varies directly as the quan- tity of current ; so, if the current is steady, and if i is its strength, m is directly proportional to the product of i by £, MXCHAX18M <>r THE CURRENT 687 tlu- interval of time taken to liberate law states that m^. //^': wa: mz' : etc. = Voltameters. - - The first law offers a convenient method for the mass m. The second : etc. tin- comparison of the strength of two different currents. An elec- trolyte is placed in series with the two currents in turn, and the (plan titles of matter liberated in < It-finite intervals of time at either anode or cathode are measured. If the strength of one current is called ir and if the mass it liber- - in an interval of time tl is mv r
and suitable precautions are taken to prevent any mechanical currents in the liquid, for it is found that they, for purely chemical reasons, affect slightly the quantity deposited. FIG. 879. — A simple form of silver voltameter. Electro-chemical Equivalent. — By means of Faraday's second law we can calculate the relative amounts of differ- ent substances which are liberated by the same current in the same time. The quantity, i.e. the mass, of any substance which is set free at either anode or cathode as a unit C. G. S. electro-magnetic quantity of electricity passes is called the u electro-chemical equivalent" of that substance. It is a matter of experiment to determine its value for any one substance ; but, being known for this, its value for any other is given at once by the second law. Careful experiments show that the electro-chemical equivalent of any substance apparently varies with the kind of voltameter used ; but the variations are undoubtedly due to secondary reactions or causes. If the voltameter is so constructed as to avoid MECIIAyiSM OF THE CURRENT 689 these, the elect ro-eheniical equivalent of silver is found to be 0.011175 g. The chemical equivalent of silver is 107.93; so calling the electro-chemical equivalent of any other substance M and its chemical equivalent <?, we have the relation <».« ill 175: w = 107.93 :c, _ 0.011175 xc= c Thus, for hydrogen, in = 0.00010354; for copper, m = 107.93 9658* 0.003211:.".!; for zinc, m = 0.0033857 ; etc. Since m is the quantity of any substance liberated by a unit electro-magnetic quantity of electricity, the quantity liberated by 9658 such units is a number of grams equal to c, the chemical equivalent. Ions. — The explanation of electrolysis which was advanced 1 » y Faraday was that in any electrolyte there are present cer- tain charged particles, some with +, others with — charges, and that these particles are driven by the electric force in one direction or the other. Positively charged particles will move in the direction of the force, that is toward the cathode; while those negatively charged will move in the opposite di reet ion, toward the anode. These charged particles Fara- day called
" ions "; and those which move toward the cathode he called "cations," while those which move toward the anode he called "anions." Thus all cations are positively charged; all anions, negatively. The electric current in the electrolyte consists, then, from this point of view, of the passage in opposite directions of these two sets of charged hodies. When they reach the electrodes, they give np their charts and in some manner cause the liberation of uncharged Allies or ordinary matter. Hydrogen and all metals are liberated at the cathode; therefore we must consider a hy- drogen ion or any metallic ion as being positively charged. Similarly, we must consider an oxygen or a ehlorine ion as being negatively charged. \MI *'«. i Hvsics — 44 690 ELECTRODYNAMICS Since the electrolyte itself is not electrically charged, any volume of it must contain as much positive electricity on its cations as negative on its anions. The current consists of the passage across any cross section of the electrolyte of these ions ; if the current strength is i, and if ^ is the positive charge carried on the cations, and z'2 is the negative charge carried on the anions, i = z\ + i2. In the main body of the electrolyte the positively and negatively charged ions balance each other ; but in the immediate neighborhood of the cath- ode, positively charged ions carrying a charge ^ come up in a unit of time, and negatively charged ions carrying a charge iz leave in the same time ; so this space gains in this time cations carrying charges (i^ + i%) which are not balanced by anions ; and these give up their charges to the cathode. Similarly, at the anode, anions carrying a charge i2 come up, and cations carrying a charge i^ leave, thus causing a con- centration, as it were, of anions carrying a charge (^ -h ^'2) which are not balanced by cations. In other words, the current of strength i enters the electrolyte owing to the fact that anions carrying a charge i are liberated at the anode ; and it leaves the electrolyte owing to the fact that cations carrying a charge i are liberated at the cathode. This fact may also be expressed by saying that the same quantity of electricity — not regarding its sign — is carried on that number of ions of any substance, whose mass equals
its electro-chemical equivalent. This may be described differently : When a unit quantity of electricity passes, tj + «2 = 1 ; if ml and m2 are the electro-chemical equivalents of the two sets of ions, m1 and m2 grams are liberated at the two elec- trodes in this interval of time. The liberation of the m1 grams at the cathode is due, as has been shown, in part to the bringing up of the cations carrying the charge il and in part to the withdrawal in the opposite direction of the anions carrying the charge ia ; so the effect is the same as if there were no anions, but only cations, carrying a unit charge. In Ml-:< HAM-.M OF ////,' Cl'RRENT 601 other words, a mass of cations equal to //^ carries a unit elect n '-magnetic charge ; and similarly a mass of anions equal to 7H.2 carries a unit cliarge. 'I'll us, in the case of hydrogen, the electro-chemical equiva- lent equals §3*53; and therefore this number of grams of hydrogen ions carries a unit charge, or one gram of hydrogen ions carries a charge equal to 9658. Similarly, a number of grams of ions of any substance equal to its chemical equivalent carries a charge equal to 9658. (The ratio, then. of the charge carried on a hydrogen ion to its mass equals ^g^, or, approximately, 1 x 10"4.) Faraday showed that both of his experimental laws could be explained if it were assumed that the ions of any one substance were all alike, and that the charge on any ion was proportional to the valence of the substance. For, if these assumptions are true, it is evident that the quantity of elec- tricity carried through the liquid must vary directly as the mass liberated at either electrode ; this is the first law. Further, if the same quantity is being carried by two dif- ferent sets of ions, the masses of these substances liberated, if the charges carried by all the ions are equal, are propor- tional to their atomic weights; whereas, if each ion of one set carries twice the charge carried by each ion of the other set, — that is, if the valence of the former set is twice that of the latter, — only one half as many of the ions of the former are involved in the current as of the latter,
and so the ratio lie mass of the former to that of the latter is equal to that of their chemical equivalents; this is the second law. On this assumption, the charge carried on an ion whose valence is one is the smallest charge involved in electrolysis. It is called an "atom of electricity." Nature of Ions. - The question as to the nature of the ions is a most important one. As was said above, all electrolytes are solutions which show abnormal osmotic pressures, depres- ^ of the free/in^ point, etO.J and it is shown in ; 692 ELECTROD YNAM1CS on Physical Chemistry that these various abnormal phe- nomena can all be explained if it is assumed that in these solutions a certain proportion of the dissolved molecules are dissociated into simpler parts. It is natural to expect that, if a molecule is broken up into parts, they should be electric- ally charged, so that equal amounts of positive and negative electricity are produced. If this is the case, it is seen at once that the charge on any atom or radical is proportional to its valence. Thus, if a molecule of hydrochloric acid, HC1, breaks up into two parts, H and Cl, and if one is charged positively, the other will have an equal amount of negative electricity ; and the valences of hydrogen and chlorine are the same. Similarly, if a molecule of sulphuric acid, H2SO4, dissociates into three parts, H, H, and (SO4), the two hydro- gen atoms will be charged alike, and therefore the radical (SO4) will have an opposite charge equal numerically to twice that on a hydrogen atom ; and the valence of (SO4) is two. We assume, then, that when an electrolytic solution is made, a certain proportion of the dissolved molecules are dissociated into simpler parts, and that these parts are elec- trically charged, some positively, some negatively, so that the total charge is zero. (This condition of dissociation is not to be thought of as a static one, but as dynamic ; mole- cules are constantly dissociating, and others are being formed by combinations of the parts, which are moving about in the solution ; but at any temperature and concentration a certain definite proportion of the molecules are in a state of dissocia- tion.) These charged fragments of molecules form the ions when two electrodes at different potentials are
lowered into the solution ; the positively charged ions move toward the cathode during their intervals of existence, before they com- bine with other ions and form electrically neutral molecules ; the negatively charged ones move toward the anode. The fact should be emphasized that the ions are produced in the act of solution, not by any action of the electric current : MECHANISM OF THE CURRENT 693 the current merely liberates the matter at the electrodes. It should also be emphasized that an ion is an electrically charged atom or radical, and is not a molecule ; and that the properties of matter as we observe them, e.g. gases, liquids,. are the properties of molecules or groups of molecules. Tli us, there is no connection between the general properties of a hydrogen ion and those of a hydrogen molecule. Again, as an ion moves through a solution, it is extremely probable that it carries with it a certain number of molecules, and that the number associated with a negative ion is not the same as that associated with a positive ion. If this is true, the effec- tive mass of an ion is much greater than its actual mass, considered merely as a fragment of a molecule. The student should consult Jones, The Modern Theory of Solution, New York, 1899, for the original memoirs of Van't Hoff, Arrhenius, and others. The question as to whether an ion is positive or negative is settled by observing whether it is a cation or an anion. Thus an ion of hydrogen or of any metal is positive ; while one of oxygen, or chlorine, etc., is negative. Again, since the same masses of any substance are liberated by the same quantity of electricity, regardless of the nature of the elec- trolyte, e.g. when hydrogen is liberated from dilute sulphuric acid, or nitric acid, or hydrochloric acid, etc., it is proved that an ion of any one substance always has the same charge in an electrolyte, no matter to what molecule it owes its in. Thus a hydrogen ion in a liquid always has a defi- nite plus charge ; etc. \\V shall now consider in detail one or t wo cases of elec- trolysis. If sulphuric acid, HaSO4, is dissolved in water, let us consider the ions as being II. II where the first two are charged with equal amounts of positive electricity, which we may call + «, and the last has
a charge — 2 e. Under the action of the electrical force the hydrogen ions move in the direction of the cathode, they combine with SO4 894 ions, other molecules dissociate, etc.; but, as the current flows, hydrogen ions continuously come up to the cathode, give up their charges, combine with other hydrogen atoms to form molecules of hydrogen gas which is liberated. The (SO4) ions in a similar manner migrate toward the anode ; but, since a molecule of (SO4) radicals cannot exist under present conditions of temperature, pressure, etc., when these ions reach the anode and give up their charges, there is a reaction with the molecules of the water near the anode, which takes place according to the following formula : S04 + H20 = H2S04 + O. Consequently for each (SO4) radical an oxygen atom appears, and these oxygen atoms form molecules of oxygen gas which may bubble off at the surface of the electrolyte or may act chemically upon the anode and oxidize it. Again, let the electrolyte be a solution of copper sulphate, CuSO4, in water; and let both the electrodes be copper plates. A molecule of copper sulphate dissociates into two ions, Cu and (SO4); the former is charged positively, the latter negatively. When the copper ions reach the cathode, they form molecules and are deposited on it. When the (SO4) ions reach the anode, they react upon the copper mole- cules of the plate in such a manner that the copper goes into solution. Since metal ions are charged positively, the copper dissolves in the form of positive ions ; so the current is carried off the anode by them. These + ions serve, then, to balance the — (SO4) ions which are being continually brought up to the anode. This obviously offers a method for "copper plating" an object. Its surface must be so prepared that it is a conductor and that copper will adhere to it; and it then must be used as a cathode in an electrolytic bath of copper sulphate, the anode being a plate of copper. Similarly, in an aqueous solution of silver nitrate, AgNO3, the ions are Ag and (NO3); the former is the cation, the OF V7//-; < ri;i;i-:.\T 695 latter tin- union. If ;i plate of silver
is the anode, it dis- solves, and silver is deposited on the cathode. This offers a method of silver plating. In tin; last two illustrations it is seen that the mechanism by which tin- current enters the electrolyte from the anode consists in the copper or the silver plates dissolving; this is done by the positively charged ions of copper or of silver leaving the plates and entering the liquid. In the water voltameter, where the anode and cathode are platinum plates, the case is not quite so simple. The negative ions of oxygen are formed at the anode by the reaction of SO4 upon the water molecules ; and in some manner positive charges pass from the anode to certain of these ions, first neutralizing their negative charges and then giving them positive ones ; and, after this takes place, a positive oxygen ion combines with a negative one and forms a molecule of oxygen gas, whieh bubbles off at the surface. At the cathode, the mech- anism is similar. Thus, in the case of copper sulphate, the positive copper ions reach the cathode ; under the electric force negative charges pass from this upon certain of the copper ions, making them negative ; then a negative copper 01 M hinrs with a positive one to form a copper molecule which is deposited on the cathode. Polarization. — If two platinum electrodes dip in a solution of sulphuric arid, and if a \.-ry small elect ro-inotive force is applied to these electrodes, a current will flow, but will i cease. This is owing to the fact that under the aetion of t he electrical force the positively charged hydrogen ions collect at thr rathodr, and t hr negatively charged anioiis at the anode : \|Q that, if theiv is not sullicieiit force to make the ssary charges pass from the electrodes to the ions and then to form the molecules, these charged particles will lower the potential at the anode and raise it at the cathode until the. 1 1 iv electrical force in t IK; electrolyte, and the current stops. As t he applied elect n • mot ive force 696 ELECTRODYNAMICS is gradually increased, a value is reached which will cause the evolution of the gases at the electrodes ; and the current will now continue to flow. The same description applies in general to any case of electrolysis ; a definite E. M. F. must
be applied before electrolysis begins; but its value is dif- ferent for different electrolytes. This may be calculated, however, from a knowledge of the heats of combination of the compounds which are separated by the electrolysis and of their electro-chemical equivalents. Thus, experiments prove that, when 18 g. of water are formed by the combination of 2 g. of hydrogen and 16 g. of oxygen, 68,800 calories of heat energy are evolved; and, therefore, when 18 g. of water are broken up into 2 g. of hydrogen and 16 g. of oxygen, an amount of work equal to the mechanical equivalent of 68,800 calories must be done, i.e. 68,800 x 4.2 x 107 ergs. As a quantity of currents equal to e is passed through the electrolyte consisting of H2SO4, the quantity of hydrogen evolved is me, where m is the electro-chemical equivalent of hydrogen ; and an "equivalent" amount of oxygen is liberated at the anode. Since it requires 68,800 x 4.2 x 107 ergs to liberate 2 g. of hydrogen, that required to liberate me g. is me 68>80° * 4>2 X 1QT. If E is the E. M. F. applied to the electrodes, which just causes the electrolysis, the work required to pass a quantity of electricity e between the electrodes is Ee. Therefore, since this work is spent in liberating the hydrogen and oxygen, — neglecting the work done in heating the electrolyte, and assuming that there is no other source of energy, — we have the equation „ me 68,800 x 4.2 x 107 — -' or E = m 68,800 x 2.1 x 107. For hydrogen, m = 1.035 x 10~4, and therefore E = 688 x 1.036 x 2.1 x 10* = 1.5 x 108 = 1.5 volts. The E. M. F. of a Daniell cell is approxi- mately 1.1 volts; so at least two Daniell cells are required to decompose water. Calculation of the E. M. F. of a Primary Cell. — We may consider the mechanism of a voltaic or of a Daniell cell from this standpoint of ions. In the former, the cause of the current is the solution of the zinc in the acid, that is, the MECHANISM
OF THE CURRENT 697 parsing off of positive zinc ions into the liquid. The chem- ical action is the solution of the zinc in the acid and the evolution of hydrogen at the copper pole ; and experiments have proved that when 65.4 g. of zinc are dissolved in dilute sulphuric acid, 38,066 calories are evolved. The electro- chemical equivalent of zinc is 0.00338. So when a quantity of current e passes off the zinc rod into the acid, the mass of zinc dissolved is 0.00338 e ; and the energy liberated is 38.066 x2x 10' If E is the difference of potential between the copper and the zinc electrodes, it follows that ~,-, _ 38,066 x 4.2 x 107 x 0.00338 or E = 38,066x4.2x107x0.00338 = ^ x 10- = 0.83 volt* 65.4 In this calculation we neglect the loss of energy of heating tin- liquid, and we assume that the only source of energy is that furnished by the solution of the zinc. In a similar manner, when a current is produced by a Daniell cell, /inc dissolves at the zinc plate and copper is deposited at the copper electrode. When 63.6 g. of copper dissolve in sulphuric acid, 12,500 calories are evolved ; and the electro-chemical equivalent of copper is 0.00329. So the E. M. F. of the cell is found by calculation to be 1.1 volts, making the same assumptions as before. Storage Cell. — In certain cases of electrolysis the anode and eith'ide are so modified l>y the passage of the current, and the < >nsequent liberation of matter at them, that they be used afterward t«. form a coll for the production of a current. Therefore, if the battery of cells or the dynamo which was producing the current through the electrolyte is removed, and if the electrodes are joined by a wire, a cur- rent will flow through it. This action does not continue 698 EL ECTI! 0 1) YNA MICS indefinitely, for in producing a current, those modifications which were the result of the electrolysis are reversed, and the electrodes return to an inactive condition. If the bat- tery of cells or the dynamo is again used to send a cur- rent through the electrolyte, the process may be repeated
. Such a combination of elec- trodes and electrolyte is called a "storage cell" or a "secondary cell"; and when it is in a condition to produce a current itself, it is said to be " charged " — but it is evident that this expression has no connec- tion with what has been called a " charge " in pre- vious chapters. FIG. 880. -The ordinary form of storage cell. The commonest form Qf storage cell has dilute sulphuric acid as the electrolyte, and as the anode and cathode two lead grids whose interstices are filled with a paste of lead sulphate. When such a cell is charged, it has an E. M. F. at first of about 2.1 volts; but this falls to about 1.8 volts as the current flows. Conduction of Electricity through Gases. — In speaking in a previous chapter of the passage of sparks through air or any gas, occasion was taken to state that the discharge con- sists in the disruption of molecules into simpler parts, and that the path of a spark is an excellent electric conductor. We are thus led to believe that a gas becomes a conductor owing to the presence in it of small parts of molecules, which we may again call ions, although there is no reason for believing that these ions are the same as those in evi- dence in the electrolysis of a liquid. The charged particles v/.s.u OF nn: < t HHENT 699 may In- the same, hut the in -•>< iciat ed with thiMii are diileivMi ( >ee page 693). All the known facts in regard to condiu -lion through a gas are in support of this idea of tin- ionic nature of the proce The method of determining whether a gas is a conductor or not is, of course, to immerse in it two electrodes, at a small distance apart, and to observe whether a current flows when a difference of potential is produced between these plates by some cell or combination of cells. It is found that a pure dry gas is an extremely poor conductor ; but it may be made conducting by many means. A few will be mentioned. By passing a spark through any portion of the gas, all other neighboring portions have their conductivity increased. In many cases of complex gases, a sufficient rise in temperature makes them conducting. If the ultra-violet waves from a source of light
a dark space from a luminous region, and that this is separated by a second dark space from a luminous striated column extending to the anode, the end of which — if it is a wire — has a bright spot of light. The first dark space near the cathode is called the " Crookes dark space " ; the second one, the " Faraday dark space " ; the region separating them, the " negative glow "; and the striated portion near the anode, the "positive column." As the bulb is more and more exhausted, the Faraday dark space extends farther down '01 or I III-:'URRENT toward the anode, and another phenomenon becomes most prominent. There is a radiation of something from the cathode, proceeding in straight lines perpendicular to its surface, quite independ- ent of the position of the anode. This radia- tion produces a faint luminescence of the traces of gas left in the bulb ; and so the path of the rays through the bulb may be seen. They are called the "cathode rays." Where they strike the walls of the hull), it is made lumin- ous and its temperature a. 6. Fio. 882. — Two forms of vacuum tube discharge: a, moderate vacuum ; b, high vacuum. rises ; the color of the light which is thus produced depends upon the material of the bulb, but ordinary glass emits a greenish yellow light. (If certain other solids are intro- duced in the bulb in the path of the rays, e.g. coral, they emit characteristic colors.) The fact that the rays proceed in straight lines is proved by introducing in the tube solid bodies which are opaque to the rays; for it is observed that they cast sharp shadows on the walls of the tube. The radiation passes directly through metallic films, if sufficiently thin. The path of the rays in the tube is deflected by a strong electric field, provided the vacuum is p< •! feet enough ; and the deflection is in such a direction as to l.-ad one to believe that the radiation OOnifotl of n. -Datively _M-d particles. In fact, all experiments lead to this con- •ItiiT.l t.y r:ith'»lr rny*. 702 ELECTRODYNAMICS elusion. If the rays are made to enter a hollow cylinder which is connected to an electrometer, it is seen that the cylinder
is receiving a negative charge ; and the fact that, when the rays strike a solid its temperature is raised, is ex- plained by assuming that the rays consist of material parti- cles. Again, as will be shown in a few pages, a charged particle in rapid motion has the same action on a magnet as does an electric current ; and, since a wire carrying a current may be made to move under the action of a magnet (which is simply the reverse of the fact that a current can move a magnet), so a particle in rapid motion may have its direction altered if it is charged ; and experiments show that the cath- ode rays may be deflected by a magnet in exactly the man- ner which one would expect if they were negatively charged particles in rapid motion. The velocity of these rays may be measured in many ways ; and it is found to depend upon several conditions : difference of potential between the elec- trodes, pressure of the gas, etc. ; its value is not far from one tenth of the velocity of light. The masses of these particles and their electrical charges may also be measured with a fair degree of accuracy ; and it is believed that the charge of any particle is the same as that on a hydrogen ion in ordinary electrolysis, while its mass is approximately one thousandth of that of a hydrogen atom. So far as experiments can prove, these particles which constitute the cathode rays are the same no matter what gas is put in the tube. If the cathode is in the form of a metal plate with many small openings in it, it is observed that in addition to the cathode rays which are emitted from one side there are rays proceeding in the opposite direction apparently through the holes in the cathode. These are called " canal rays," and have been proved to consist of positively charged particles, moving much more slowly than the cathode rays. Their charges are probably the same as those of the latter rays ; but their masses are comparable with those of an atom. MECHANISM oF THK (Tltl:i-:\T 703 Tin- gas which is traversed by cither the cathmle or the canal rays is ionized; that is, becomes a conductor. This was proved for the former rays by Lenard, who constructed a glass bulb in such a manner that a portion of the wall which was struck by the rays had an opening in it which \\as covered by a thin layer of aluminium. Surrounding this bulb was another which
to canal rays, and "/3 rays," which are negatively charged particles analogous to cathode rays. Radium also emits rays which are like X-rays in many respects; they are called "7 rays." This radiation is accompanied by changes inside the mole- cules of the substances which emit it ; and in some cases the products of the molecular changes are gaseous. Thus, if thorium nitrate is dissolved in water and ammonia is added, a precipitate is formed, which may be separated by filtration. The precipitate is not radioactive at first but gradually becomes so, in fact returning to the same condition as the original thorium nitrate. The filtrate, on the other hand, is 3/AY7M-V/.S.V <>r mi-: CUKRKM 705 mo>t radioactive, but loses this property in time; as it does this, it L,rives off a ^a>emis emanation, which is radioactive. This emanation is at lirst uncharged, but by losing its nega- tive charges it becomes positively charged and may be attracted to any negatively charged body. It undergoes further changes; and during each, radiations are emitted. The emanation of radium finally decomposes into helium gas. During these processes, further, heat energy is evolved, and the temperature is raised several degrees Centigrade. Electrons. — When a gas is ionized, either by the action of X-rays or by the rapid motion of minute positively or nega- tively charged particles through it, all the negative ions are found to be alike in all respects and to be the same as the eathode rays. It is therefore believed that, as such charged particles or as pulses pass through a gas, they break off from its atoms these negative ions. A theory of the constitution of an atom has been based on this idea. An atom is thought to contain within it a great many minute negatively charged particles which are making rapid revolutions — not unlike the constitution of the solar system, the other portions of the atom making up the positive charge. Then ioni/ation would consist in causing one or more of these negative par- ticles to leave the atom. These particles while inside the at oiii — and when outside also, provided they have no other mat. -rial particles elin^in^ to them — are called "electrons." Their vibrations inside the atom irive rise to waves in the ether
. So tar as is known a moving piece of uncharged matter does not affect the ether; but, it' charged. it does; and. if it> motion has a* • //. waves are produced. It is known from theoretical considerations that when a charged particle U in motion, its kinetic energy is greater than it would he if it were not charged; and, therefore, an electric charge in motion by itself — quite apart from matter would have kinetic energy; that is, would have : The (jiiestion thm arisi.1 not the inertia of matter really AMKft'8 PI1T8IC8 — 46 706 ELECTRODYNAMICS due to the motion of electric charges in its minute parts? In other words, is not a moving charge the fundamental fact in nature? This question is fully discussed, and a most in- teresting description of the general properties of electrons is given, in a series of papers in the London Electrician during 1902-1903, by Sir Oliver Lodge. Conduction in a Solid. — It has been proved in what has gone before that conduction in an electrolyte and in a gas consists in the actual motion of charged particles, called ions. In the case of a solid conductor the question as to the mechanism of the conduction of a current is not so simple, owing primarily to the fact that the particles of a solid have so little freedom of motion and can only vibrate. But there is every reason for believing that in a solid also the process of conduction is by means of ions. The existence of free electrons moving about inside the solid conductor from atom to atom may be proved by many experiments ; and the evidence in favor of this explanation of conduction is accumulating continually. Convection Currents. — It was Faraday who first conceived the idea that the essential feature of an electric current was the rapid motion of an electric charge ; but the first to prove by direct experiment that such a charge in motion had the same magnetic action as an ordinary current produced by a voltaic cell was the late Professor Rowland. He charged a circular metallic disc and caused it to rotate rapidly on an axle perpendicular to its faces; he observed that when a magnetic needle was brought near the disc, it was deflected exactly as if electric currents were flowing in circles in the disc. He was able to prove that, within the range of veloc- ities used, a charge e moving with a velocity v is equivalent to a current whose
strength is ev. It is probable that this is true, even if v is very great, much greater than it is possible to attain by any mechanical means. A current due to a moving charge is called a "convection current." CHAPTER XLVI MAGNETIC ACTION OF A CURRENT General Description. — In a previous chapter a general description of the magnetic field due to an electric current was given ; and it was seen that a conductor carrying a cur- rent is surrounded by a field of magnetic force, such that the lines of force form closed curves around the current. The relation between the direction of the current and that of the lines of force is given by the right-handed-screw law. The magnetic field, then, due to a circuit carrying a current is the same as if a great many minute magnets, of the same length and strength, are taken and placed side by side so that their north poles are all turned one way and their south poles in the opposite direetion, thus forming what is called a "magnetic shell." having the same contour as is made by the conductor earn inur the current. For. lines of force would proceed out from the north poles of the slu-11 and all return tn the south poles. We < an thus speak <>f the M north face " (.!' a eiivuit irivnt and of its "south face." Again, if a wire — or other eoiid net «.r — is wound in the form of a helix, and if a current is 708 ELEL'TRODYSAMICS passed through it, thus forming a " solenoid," the magnetic field enters one end and emerges from the other exactly as if it were a bar magnet. Electro-magnets. — If, then, a bar of iron or of any mag- netic substance is inserted in a solenoid, it is magnetized because each little molecular magnet turns and places itself along a line of force. A bar of iron wrapped with a helix of insulated wire is called an "electro-magnet." The bar is FIG. 886. — A powerful electro-magnet arranged to show magnetic or diamagnetic action on suspended sphere. usually made in the shape of a horseshoe, or of the general form shown in the cut. These are used in a countless number of instruments, such as call bells, telegraph instru- ments, etc. The first electro-mag
tte tllf-e. UOD of parallel current. These phenomena of electro-magnetic forces were discov- 1 by Ampere, and lie invented many most beautiful experi- 710 ELECTRODYNAMICS 999.9 - 9999 merits to illustrate them. They may be found described in many text-books. He also proposed a theory of magnetism based upon his observations. He advanced the hypothesis that in each molecule of a magnetic substance there is an electric current, flowing in a fixed chan- nel; and therefore if a bar of sucli a substance is brought into a magnetic field, — due either to a magnet or to a solenoid, — the molecules will all turn so as to include as many tubes of magnetic force as possible. The bar will be saturated magnet. Ampere's theory when the molecules have so arranged themselves that their currents are parallel to each other and to the ends of the bar ; and under these conditions the lines of force due to these currents will emerge at one end and return into the other, exactly like a solenoid. If two parallel wires or rods are placed in a horizontal plane and are joined by a fixed wire BO, containing a cell, and by a movable wire PP', which can roll on the wires, FIG. 888. — South pole of ELECTRO MAGNETIC FORCE Fio. 890. — Relation between directions of current, magnetic Fio. 889. — Electro-magnetic force : magnetic field is upward fleltl> and electro-magnetic force, through circuit. Each is perpendicular to the other two. this movable wire will be set in motion if there is a mag- netic field through the space between the parallel wires, because by so moving a change is made in the number of tubes of force which pass through the circuit (PP1 OB). If MA<.\I-:TI<- ACT1OB or.1 i-rniiKNT 711 the current is in the direction shown in the cut, the upper face is tin- north one; and, if the magnetic field of force is in tin- direction shown, tin- cross wire PP' will move trd the right, so that the circuit incloses more tubes coming out from its north face. This law of force is given by the diagram which describes the connection between t la- directions of the magnetic force, the electric current, and tlu- electro-magnetic
t, the work done in threading them by a unit pole is, in accordance with the above definition of a unit current, 4 irN x i. So, Rx = 4 TrN x i, or, R = 4 irNi ; a most important formula.. — Magnetic force inside a long solenoid. If there is a rod of iron, of permeability ^, filling the solenoid, the number of tubes of induction per unit area passing through the iron is proportional to pR. (See page 615.) Since p for iron is large, this means that the number of tubes of induction passing through the solenoid is greatly increased by inserting in it a rod of iron. These additional tubes are due to the magnetization of the iron by the current. Since each of these tubes of induction passes N times through a circuit carrying the current i in a unit distance, it is evident that the magnetic action of the solenoid is propor- tional to that of a single turn of wire carrying a current equal to N*i. Energy of a Current. — The fact that, when a current is flowing in a conductor, forces may be experienced in the surrounding medium, proves that there is a certain amount of energy in this medium due to the current. This energy is MAGNETIC ACTION OF A iTRRENT 713 not in the form of a strain — no sparks are observed in the medium, etc. So it is natural to think of the energy as being kinetic- in its nature; and this idea will become more evident in a later chapter. What will be shown is this : as a current is first started, e.g. by joining the two poles of a primary cell, the i urrent does not rise to its full strength instantly, for part of the energy furnished by the source of the current is spent in producing those motions in the surrounding medium which constitute the magnetic field, and it is not until these motions are established that all the energy of the source of the current goes into forcing the current through the con- ductor, and so heating it. Similarly, if the source of the current is suddenly removed, the current does not instantly cease, because the energy in the medium disappears gradu- ally, being spent in maintaining the current for a short time. Compare the case of a railway train starting from rest; it does not In its full speed instantly because the energy furnished by the loco- motive is used in producing kinetic energy ; but, after the desired
around the electro-magnet may be connected to a primary cell or a battery of cells at a distance, with a key in circuit. So, when the key is pressed, a current will flow around the magnet. Even if the current is extremely feeble, the armature will be attracted ; and by means of suitable contact points a sec- ond cell may be closed through any circuit; and thus any elect n> magnetic effect may be produced,. Vi:i\|.l. k.'\.'111.1 -oini.liT. such us rin'_miL,r a bell. etc. NVheii the key is broken, the current ceases, and the armature is drawn Lack from the electro-raagiK'i»iral spring attached to its rear. It* a second eh-- \\itlianannatuivisintroduced in the circuit <>f the second » -ell, the sound made by the 716 ELECTRODYNAMICS armature as it clicks against the electro-magnet may be clearly heard. This is the principle of the ordinary telegraph system, different letters being distinguished by different combinations of " dots and dashes " ; that is, short and long intervals of time between consecutive clicks of the " sounder." Duplex Telegraphy. — In the " Duplex " system of telegra- phy it is possible to receive and send messages from a station at the same time. The instrument consists essentially of a receiving instrument E, such as an electro-magnet or a galvanoscope, around which are wound two coils of wire in opposite directions ; so, if equal currents are passed through both coils, no effect is pro- duced, while, if a current passes through one coil alone, there is an effect. One of these coils is con- nected through the "line wire " to the distant sta- tion, while the other is joined through several coils of wire of adjust- able lengths, R, to the earth. The arrangement of the cell and the key K is as shown in the cut. The coils R are so adjusted that when the key K is pressed and makes connection with the cell jB, equal currents pass around the receiving instrument E, and there is no effect ; but a current passes over the line wire to the distant station. When a current is received over the line wire, it passes to the earth, entirely regardless of the position of the key K, thus affecting the
eshoe magnet, between whose poles a coil 0 is supported by means of a vertical wire. The wire in this coil is continu- ous from A to B, two fixed binding screws. When no current is passing, the coil is held so that its plane is parallel to the line joining the two poles ; but if a current is transmitted through the coil by means of A and B, it will turn so as to include as many of the tubes of force of the magnet as possible. It will be brought to rest by the torsion of the wire ; and so its deflections meas- ure the current strength. PIG. 898. — D'Arsonval galvanometer. Practical Instruments. — In most practical work, such as measuring the electric currents of telegraph systems, lighting systems, dynamos, etc., instruments are used which are porta- ble. They are sometimes called "practical instruments." The principle used in them all is to have a permanent steel horseshoe magnet, between whose poles is supported on pivots a coil of wire through which the current to be measured is passed. This coil turns so as to include as many tubes of force as possible ; but, as it turns, it winds up a flat coiled spring, and so is finally brought to rest. The angle of deflection is measured by a pointer. ACTION OF -l CUBE 719 Radio- micrometer. — This is an instrument invented l»y Pn»fexx,,r P,,.\«, I'm- the detect inn and measure- ment of radiation in the ether. It consists of a thermocouple and a loop of wire, used according bhe principle of the coil in tlu« D'Arsonval galvanometer. A loop of copper wire ends in tine strips of bismuth and antimony, A and B^ which are soldered together. This loop is then suspended by a fibre between the poles of a permanent magnet, with its plane parallel to the line joining them. The junction of the two metals is blackened, and is exposed to the radiation ; as it absorbs energy, its temperature rises, a current flows in the loop; this is then deflected so as to FIG. 899. — Weston's am: t'X). — Boys' ra/llo-nilrroinft.-!-: A and include as many t uhesof ;' OS possible, and it finally to TCSt
OF STEADY CURRENTS Steady Current. — In the foregoing chapters the various properties of electric currents, viz., heating, magnetic, < trolytic, etc., have been discussed and illustrated ; and several methods for the production of currents have been described. A current is called u steady " if these properties remain con- stant, e.<j. if a constant deflection of a galvanometer needle is produced, if heat energy is developed at a constant rate, if matter is liberated in an electrolyte at a constant rate, etc. ; and experiments prove that, if a current satisfies one of these conditions, it satisfies all. A " variable " current is one that is not steady. In order to produce a steady current one may use a source of constant K. M. F., sin -h as a I Smell's cell, or a thermocouple whose junctions are maintained at constant temperatures, or a dynamo — as will be described in the next chapter. Uniformity of Current. — One of the most important properties of a steady current is that its strength is uni- form throughout the circuit ; that is. if the circuit includes conductor* of diflVrent material, of different sizes, etc., the strength of the current is the same in them all. This may!>•• shown by proving that the magnetic or the hea1 • ii of the current is the same for all portions of the lit. A L: i in, if the current were not the same at all points, there would be accumulations of charges at certain points; and, as th.'sr innv.e>c<l, they could be detected; but such is not the case. mlailv. if at an\ point of the circuit, it branches SO as i 721 722 EL ECTItOD YNAM1CS to form two or more parallel conductors, the strength of the current in the single conductor must equal the sum of the strengths of the currents in the branches. This may be expressed in a formula, K,W, x. „„ is the current in any FIG. 402. — A divided circuit. J conductor at a branch point, the direction of the current being called positive if it is toward the point, the summation of all the currents at that point is zero, or, in symbols, 24 = 0. • • °- Ohm's Law. — We have seen that a current flows between
two points of a conductor only if there is a difference in potential between them ; so that we may in a way regard the E. M. F. as the cause of the current, and it is not un- natural, judging from analogy with the flow of heat in a bar owing to difference in temperature between two points, to advance the hypothesis that the current strength in a con- ductor varies directly as the E. M. F. between two points, provided the current is steady. (We are considering the case where there is no cell or other source of E. M. F. introduced in the conductor between the two points.) That is, if A and B are any two points in a circuit in which is flow- ing a steady current of strength i, and if E is the E. M. F. between FIG. 408. — Diagram to illustrate A i T».LI i A i • • 1 1 Ohm's law. A and B, the hypothesis is that E = Ri, where R is a constant depending upon the nature of the conductor between A and B, but not upon the values of E or i. This hypothesis has been found to be true, so far as experiments can decide ; E has been varied by intro- ducing more cells or a dynamo, and the resulting current or STXADT m;i;i-:yT8 723 has been measured. It is called Ohm's law, having been proposed by Georg Ohm in the year 1826. Resistance. — It is evident from the formula that if R is lar^e. / i> >mall, provided E remains constant; while, if // small, i is u'reat. For tliis reason R is called the "resistant. " of the conductor between A and B. This law can also be E 1 H H written i = —- ; and, if for — the symbol 0 is substituted, the formula becomes i = CE. For obvious reasons O is called the u conductanee " of the conductor between A and B. If the conductor between A and B is a uniform wire, it is evident that the K. M. F. between A and B is exactly twice what it is between A and a point halfway to B. Therefore, since the current is uniform, the value of R for the conductor l>et ween.1 and Jt must be twice that for half the length. So, in general. the value
of R for any portion of a uniform con- ductor of constant cross section varies directly as the length of this portion. It, while a constant E. M. F. is maintained between the two points A and B, a second conductor is introduced be- tween them, identical with the first one, each will carry a current i = —, and so the current is doubled or the total E H resistance is halved. The same would be true if, instead of using two conductors, one of twice the cross section were in trod need. So, in general, the resistance of a conductor \aries inversely as its cross section. Direct experiments show that if the same E. M 1 applied at the ends of conductors of the same length and M section, but of different matt rials, the resulting cur- rent is different. This and the two previous statements may be expressed in a formula. p a where R is the i i uniform conductor of length / ~- t i 724 ELECTRO!) YNA AIICS and of constant cross section a, and c is a constant for a con- ductor of any one material, but differs for different ones. This quantity c is called the " specific resistance " of a sub- stance, or its "resistivity." Similarly, the conductance C = — = --, and may be written C = k-, where k = -. This R c I I c constant k is called the " conductivity " of a substance. Illustrations of Ohm's Law. — 1. Con- ductors in series. Let the circuit consist of several conductors in series, and let the resistances of the portions A^AV A2 A^ ^.3^.4, be Rv R2, Rs ; further, let the potentials at the points A^ A2, A%, etc., be Vv Vv V& etc. Then applying Ohm's law to the separate sections, FIG. 404. — Conductors in series. Hence, I = The total resistance between A1 and A± is by definition i = 1 "7 — - ; and it is seen that its value is R1 + R2 + Ry In general, then, the total resistance of a number of conductors in series equals the sum of the resistances of the separate parts. (The fact that R varies as I, the length of a conductor, is a special case of this.) 2. Conductors in parallel.
— Let the circuit branch at any point A into two or more conductors which meet again at B; let the resistance of these branches be Rv R2, R& etc. ; and let the currents FIG. 405.— Conductors in parallel. LAWS «/• STEADY friiliBNTS flowing in each be t\. i.2. iy etc. The total current is / = /! -f /2 4- i3 -I- ••• ; and the total resistance between A and y _ YR B is by definition — —. Applying Ohm's law to the various branches, we have *1 D D'8 D ; etc. and therefore, calling the total resistance R R RZ R This may be expressed more simply in terms of conductances, for 0 = — ; hence, C= C + Ca+ C + — • or. in a branched circuit the total conductance equals the sum of the conductances of the branches. (The fact that R varies inversely as the cross section of a conductor is a special case of this.) It should be noted, further, that the ratio of the currents in any two branches equals the inverse ratio of the resistances of these branches. Thus, 1. 1 3. Wheatstone bridge. — This is a particular arrangement of •onductors ; four form a < iivuit ABCD, and two connect the diagonal points A and <\ and B an<l />. This network of con- ductors is used in many experi- mental methods ; l.ut only one will be descrihe.1 here. In this a cell is introduced in one of the diagonal branches, say AC. and 726 ELECTRODYNAMICS a galvanoscope in the other. If the arrangement is such that A is joined to the positive pole of the cell, the potential of A is higher than that of (7; and the potentials of B and D are both less than that of A and greater than that of C. So it must be possible to find a point D in the branch ADC whose potential equals that of any given point B in the branch ABC. If this is the case in the actual arrangement, no current will flow across from B to D, and the current flowing from A to B will equal that from B to C ; and that flowing from A to D will equal that from D to C. Call the poten- tials, at A,
adopt the resistance of this conductor as the unit. Thus, the ohm i d. -lined to he t ipial to the resistance of a column of mereui\ 730 KlJX'TltoDY \AMirs at 0° C., of uniform cross section, of length 106.3 cm. and having the mass 14.4521 g. (This column, then, has a cross section of almost exactly 1 sq. mm., accepting the usual value for the density of mercury at 0° C.) The resistance of this column of mercury is equal to 109 C. (i. S. electro-magnetic units, to within the limits of accuracy of our present experimental methods. The volt is defined to be the E. M. F. which, steadily applied to a conductor whose resistance is 1 ohm, will pro- duce a current of 1 ampere. It is therefore practically equiv- alent to 108 C. G. S. electro-magnetic units. The E. M. F. of a certain cell, known as the " Clark cell," which can be made in a definite manner, is found by careful experiments to be 1.4322 volts at 15° C. The E. M. F. of the " cadmium cell," which is another standard cell, is found to be 1.0186 at 20° C. (The E. M. F. of the latter cell changes with the temperature much less than that of the former.) Heating Effect. — It was shown on page 664 that the heat energy developed in a conductor carrying a current of strength i in a period of time t was Hit, where E is the dif- ference of potential at the ends of the conductor considered. As was also noted, the number expressing this quantity -of heat is in ergs, if the C. G. S. electro-magnetic system is used. If the current is steady, this quantity may be expressed in other ways, for E — iR. So, writing W '= Eit, we have W= izRt = —~. It is seen, then, that the heating effect R is independent of the direction of the current, because tin- square of the current enters the formula, and it has the samr value for either a plus or a minus sign. If the current is z\ amperes and the resistance is R1 ohms, i = ^, and R
a conductor with change in temperature offers at once a method of making a "resistance thermometer " ; and, in fact, a " platinum thermometer " con- sisting of a coil of platinum wire whose resistance can be measured is at the present time the most satisfactory ther- mometer in use for accurate work. Similarly, the same phenomenon is made use of in the " bolometer," an instru- ment for the detection and the measurement of radiation in the form of ether waves. A strip of platinum is covered with lampblack, so that it absorbs as completely as possible all radiation that falls upon it, and is made to form one arm of a Wheatstone bridge. As ether waves are incident upon it, its resistance changes, and the amount of the change measures the intensity of the radiation. CHAPTER XLVIII INDUCED CURRENTS Tin: discovery by Oersted of the fact that an electric current produced a magnetic field, and the subsequent dis- covery of methods for making a bar of iron a magnet by means of a current, led many investigators to seek for means « »t' producing an electric current by means of a magnet. The method of doing this was discovered independently by Joseph Hi-nryin America and Michael Faraday in England about 1831. Experiments of Henry. — Henry's experiments were the • •arlier. H« observed that, if a circuit in which there was a UUUUUUi Fio. 411. -A solenoid, Ultutntlog Henry'* fl«t «p«rtm«ot rv «.f rells was lu«.k m at any point, there was a f spark; and, further, if the l>n-ak was made by means of the 788 734 EL ECTR ()1)Y. \A.M /r.s hands, so that the circuit was completed by the arms and body, a shock was felt. He noticed, too, that both the effects were increased by increasing the length of the conductor and by coiling it up into a helix. There is thus an " extra- current " on breaking a circuit, in addition to the one due to the battery; and Henry's experiments prove that this cur- rent varies as the magnetic field of the original current ; for, if the conductor forms a helix, the magnetic field is much greater than if the conductor forms simply an approximately circular circuit. A few years later
Henry observed that if a wire were wound around the soft iron armature of a horseshoe electro-magnet and if the current were suddenly broken, or if the armature were suddenly removed from the magnet, a shock would be felt, if the two ends of the wire were held in the hands ; or, if these ends were joined to a galvanometer, a sudden deflection of the needle would be produced, but the needle would return to its original posi- tion. The same effects are produced if LJI V FIG. 412.— Diagram rep- resenting Henry's second the current is again made or if the arma- ture, when separated from the magnet, is brought close to the magnet, but the current in the galva- nometer is in the opposite direction. The quantity of the current in the galvanometer, or the shock received by the arm, varies with the number of turns of wire on the arma- ture ; and the shock varies with the suddenness of the motion of the armature ; the current also varies with the material of the conductor, while the shock does not. It is evident that these "induced" currents, as they are called, are due to the change in the number of tubes of magnetic induc- tion which pass through the coil of wire wound on the armature. INDUCED CUi;i;i 73f> Experiments of Faraday. — Faraday's experiments were somewhat different, lie had two separate coils of \\irc wound on the same iron ring, one coil being joined to a cell, the other to a galvanometer ; and he observed that, if he broke the current or made it again, there was a sudden fling of the needle, but that the current was only a transient one. Here, again, the induced current is due evidently to the change in the number of tubes of magnetic induction through the circuit which is GAIVANOMFTCT joined to the galva- nometer. Faraday then showed by a series of most brilliant experi- ments that if the num- ber of tubes of magnetic induction inclosed by any closed conducting circuit is varied in any manner, e.g. by bring- ing up or removing a magnet or another cir- cuit carrying a current, there is an induced cur- ivnt, whose strength varies directly as the change in the number of tubes of magnetic induction and as the r.ite of this change, and also depends upon the material of
the cir- cuit. If iron is inside the circuit, it is magnetized bv the current ; and thus the induction is changed. (It \\a>, in Fio. 418. - Faraday '» double coll in his first experiment. iiUr to this Study of induced currents that Farada\ Was h-d to his Conception of tubes of induction and to the id.-. i of these tubes being continuous through a magnet. See page 61 M.in\ years later Faraday rediaoovered tin- phenomena,,f the e\t ra current on I,: i^'ed his apparatus as sho\\ n in Fi^. II I, where K i^ a cell, C is a helix 736 ELECTRODYNAMICS or electro-magnet, and A and B are the two ends of a broken wire in parallel with the helix. He observed that, if A and £ are held in the hands and the electrical current is broken at E^ a shock is felt. Similarly, if A and B are joined to a gal- vanometer, there is a sudden fling of the needle when the circuit is broken. Just before the current is broken, there is a magnetic field through the helix ; but, when the circuit is broken at E, there is still a closed circuit around the helix and through ^ 5 'dnd the magnetic field in thi» ^W de- creases, since the cell is out of circuit, and so there is no E. M. F. to maintain the current. Owing to the change in the number of tubes of induction in this cir- cuit there is the extra current. Law of Induced E. M. F. — All of the facts discovered by Henry and Faraday in regard to the strength of induced currents may be expressed by saying that, when the number of tubes of magnetic induction inclosed by a closed conduct- ing circuit is varied, there is an induced E. M. F. in this circuit whose value is proportional directly to the change in this number, and inversely to the time taken for the change. If there are n turns of the wire, as in a helix or coil, the tubes pass through each, and the induced E. M. F. is n times as great as if there was but one turn. Thus, calling the change in the number of tubes of magnetic induction A^V, and the time taken for this change A£,
a decrease in the number «.f t ul».-s. the induced current h a direction as to incre<i*> tin- number. In general. then, the induced em-rent produced by any change in the magnetic field throu-h i h a direction as to tend to neutralize this change. ( If this \\.-re n..t true, an increase in AMBS'8 FIIT«ICfl — 47 738 ELECTRODYNAMICS the magnetic field would induce a current in such a direction as to increase the field still more ; this second increase would produce a second induced current in the same direction, etc. ; so conditions would be unstable.) If there is already a cur- rent flowing in the circuit, the induced current is superim- posed upon it, either increasing or decreasing it. Special Cases. — A few simple cases will be considered ; if a current is flowing in a circuit, and if a bar magnet is made to approach it or to recede from it, the direction of the induced current may be at once predicted. If the north pole of the magnet is nearest the south face of the circuit, some tubes due to the magnet pass out of the north face of the circuit. So, if the magnet is brought nearer the current, more tubes will pass through it, and the induced current will be in such a direction as to oppose this change; i.e. it will be in a direction opposite to that of the original current. Thus the current in the circuit is decreased as long as the magnet is approaching. This means, expressed in other lan- FIG. 415. — Diagram to illustrate induced guage, that WOrk is required to move the magnet, and since this is done by the current, only part of the energy of the cell is available for forcing the current around the circuit. Con- versely, if the magnet is withdrawn, the field of force through the circuit is decreased, and the induced current is in the same direction as is the original current. This means that work is being done by whatever agency moves the magnet ; and this work appears as an increased current. The case when the bar magnet is turned with its south face toward the south face of the circuit may be treated in a similar manner. Earth Inductor. — If a coil of wire is arranged so as to turn on an axis parallel to its plane faces, it may be so placed < r ///;/:. \ ro 739 that this axis
(These currents produced in a solid core are called "eddy," or Foucault currents.) A condenser is always in- troduced in the battery circuit in parallel with the " primary " coil A. One of its chief functions is to prevent sparking FIG. 418. — Diagram of induction coil. at the points where the circuit is broken ; it does this by diverting the extra current in the primary from the two points where the circuit is broken into the two plates of the condenser. (In other words, to produce a spark, a definite potential difference is re- quired, depending upon the distance ; and the differ- ence of potential of the two plates of the condenser does not rise sufficiently high to allow a spark to pass, provided the capacity is great; for Vl—V^ = ^> See page 652.) Thus, if the extra current on breaking the primary circuit is prevented, the change in the field through the " secondary " circuit B is very sudden, and the induced E. M. F. is intense. FKJ. 418 «. — Induction coll.., -,,., i\i>i < /•:/> CUBES* 743 When the current in the primary is sixain made, the change in the magnetic field is comparatively slow, and so the induced E. M. F. in the secondary is not great Self and Mutual Induction. — 1. Self-induction. If a cur- rent is Mowing in a circuit, it has a field of force of its own : if / is the current strength, the number of tubes of magnetic induction which thread this current is proportional to it and may he written LL where A is a constant for the given con- ductor and for a given medium surrounding it. L is called the "coefficient of self-induction" or the "inductance." It is evident that L -varies directly as /A, the permeability of the medium ; for the magnetic induction equals p times the mag- netic force, and the latter depends simply upon the current and the shape of the conducting circuit. (Thus the effect of introducing an iron rod into the circuit is explained. In the case of iron it must be remembered that /u, is not a constant, lor it depends upon the intensity of magnetization. So L is not a constant unless the medium is kept the same.) 1 Hither, L must increase as the area of
the circuit in- creases, because the circuit will include more tubes. In tin- case of a solenoid which has N turns per unit length, the magnetic force inside has been shown to be 4 irNi ; therefore, it I is the length of the solenoid, each tube of force passes through the current Nl times; and, it.1 is the area of the cross section of the solenoid, L = 4 7rjV-/M it' the medium is air, and equal> 4 Tr^N^lA in general. Therefore, if the em-rent is varied in any \\a\...;/. by alter- ing the K. M. V. of the cell, there will be an induced I-;. M. V. whose value equals the rate of cha ii-'..l A/: and the greater /. i, so moch the greater is the indaoed K..M.K. The induced quantity of « urrent equals the total change in the number of tubes of induction divided l>\ the resistance of the circuit. If the applied K. M. V. is 1 1 1 ; i 1. so as to tend to increase the current, and thu^ Increase the li«-M. l he induced '•nrr. -MI must he in the opposite direction ; and as a c<- 744 ELECTRODYNAMICS quence the current does not rise instantly to the value corre- sponding to the applied E. M. F. Similarly, if the applied K. M. F. is decreased, the induced current is in the direction of the original current ; and so this does not decrease instantly to its final steady value. These facts may be expressed in a formula by writing the induced E. M. K. =, where the minus sign means that if AJVis positive, the induced E. M. F. is negative, while if AiV is negative, it is positive. Particular cases of these changes are -when the circuit is suddenly broken and when it is suddenly made, e.g. by removing one of the electrodes from the cell and by then plunging it in. In the former case, the current does not instantly fall to zero ; there is the extra current, as shown by the spark, etc., as observed by Henry and Faraday. In the latter case, the current does not rise instantly to its fixed value. The time taken for
these changes evidently varies directly as L ; so that L measures what may be called the 44 inertia of the current." When the circuit is broken, the energy of the magnetic field is no longer maintained by the cell, and it returns into the conductor, continuing the current until all the energy is consumed in heating the conductor. Then the current ceases. Similarly, when the circuit is closed, part of the energy fur- nished by the cell is spent in producing the magnetic field, and only a portion of it is available for producing the cur- rent in the conductor. It is not until the magnetic field is established, then, that all the energy supplied by the cell goes into maintaining the current. As a consequence it takes time to produce a steady current. These intervals of time required for a current to come practically to rest when a circuit is broken, or to be produced, are, as a rule, extremely short, a few milliontlis of a second; but if the circuit has ti large value of L, e.g. if it is in the form of a D rr/;/;/-;.vrs 71-". solenoid inclosing a rod of iron, the time may be as great second. The energy of the current, i.e. of the magnetic field due to it, is thus in the surrounding medium. 2. Mutual induction. — If a circuit carrying a current is near another circuit also carrying a current, some of the tubes of force due to each current will pass through the other riivuit. Thus if the currents in the two circuits are tj and /2. the number of tubes due to the first current which pass through the circuit carrying the second one may be written Mfa. (It must be noted that if the second circuit has n turns, the tubes pass through its current n times.) Simi- larly, the number of tubes due to the second current that pass through the first may be written Mj,v It may be proved by the infinitesimal calculus that Afj = Mv and that this quantity is a constant for the two circuits, depending upon their shape, size, number of turns, and relative positions, and also upon the permeability of the surrounding medium ; it :lled the coefficient of "mutual induction," or the "mu- tual inductance." (The unit of induction is called the •• Henry." It is the induction which a coil has if it is of such a size and shape
and an exact calculation can be made of the effect of all the coils, not simply of those near the middle. If n^ is the total number of turns in the primary, and n2 that in the secondary, the coefficient of self-induction of the primary is proportional to nf ; and the coefficient of mutual induction of the two coils is proportional to n$iv So, if the current in the primary suddenly ceases, or if it is reversed in direction, the E. M. F. induced in the primary is proportional to nf, and that induced in the sec- ondary is proportional to n^ny As will be shown in a few pages, it is possible to construct a machine that produces an E. M. F. that is rapidly reversed in a continuous man- ner ; this is called an " alternating" E. M. F. A particular case is one that may be written E=El cos pt, where El is INDUCED CURRENTS 717 a constant. In tliis cast- tin- K. M. F. obeys a "sine cur rising t<. a inaxiniuni value Er <l< :;,1 then being- reversed to — -#r etc. It such ail K. M. F. is apj to tin- primary of a transformer, it will produce a similar induced. E. M. F. in the secondary, which may be written 't—N). The phenomena are all then periodic, with a period -TT/P, or a frequency p/Ztr. From what has been shown above E1: E^=n^: 91^1., = i^ : n.,. Thus, if /^ = 100 14, L\ — WQE2. Therefore bv means of a transformer an alter- nating current with a large E. M. F. may be made to produce another alternating current with a small I-".. M. F. This plan is used in lighting houses with lamps rendered incandescent by means of alternating currents; the street current has a large E. M. F., but by means of a transformer the cunvnt produced in the house lias a small E. M. F., which is not dangerous to life or property. iee the energy supplied by the primary current is pro- portional to E^ and that spent in maintaining the current in the secondary is proportional to E^iv it follows that, if

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