published a later determination of e, obtained by following the same general plan as before but with certa.n improvements in technique, and gave the value e3.4 X 10-10.

Beautiful and ingenious as this determination of the charge on the individual corpuscle was, the method was open to certain criticisms, inasmuch as it involved certain assumptions which had not been shown to be valid, and which, in fact, were only approximately true. They were near enough to the truth for the method to yield a rough estimate of the value of e, but they were too imperfect to provide us with an accurate and dependable determination. It was not known, for example, that Stokes' formula for the rate of fall of spheres in a viscous fluid would apply with sufficient accuracy in the case of droplets of the exceedingly small size here under consideration. Nor was it known that every ion actually did surround itself by a liquid droplet, nor that there were no droplets containing more than one ion. Nor did the method make allowance for the effect of differences in the sizes of the droplets, nor for possible evaporation from their surfaces after they were formed. It is not possible, in the present place, to discuss these various points, but it must suffice to say that they have all received the most careful consideration in later researches, and Prof. R. A. Millikan, of the University of Chicago, has recently been able to publish a definitive and probably very accurate value of e, obtained by a method which apparently leaves little to be desired on the score of soundness or of experimental excellence. It does not detract in any way from the admiration that we must feel for Thomson's original work, to say that Millikan's research was still more ingenious and beautiful. He succeeded in trapping single corpuscles, and in measuring the value of the "electron" directly; and the account of his work that he gives in his book, "The Electron,' is extremely fascinating.

It

Millikan's fundamental idea was exceedingly simple, but in its practical application it called for an immense amount of ingenuity, experimental skill and patient labor. A tiny spherical droplet of oil was electrified and caused to take up a position, suspended in the air, between two horizontal metallic plates that could be electrified or grounded, at will. The drop was strongly illuminated from two opposite sides, and was observed by means of a telescope directed at right angles to the light-rays. appeared, in the field of the telescope, "like a bright star against a black background." The drop was first allowed to fall freely through a known distance (approximately equal to half a centimeter or one-fifth of an inch), the limits of which were marked by a pair of cross-hairs in the telescope. The time of fall through this distance, in one set of experiments, was about 13 seconds. Before the drop reached the lower metallic plate, both plates were electrified by connecting them to the terminals of a battery having a total electromotive force of from 5,000 to 10,000 volts, the charge of the lower plate having the same sign as the electrification on the oil drop. When the experiment was rightly conducted, the drop (already carrying an electric charge) would begin to rise, under the influence of the electric field to

The

which it was exposed, and the time required for it to make its upward journey from the lower cross-hair of the telescope to the upper one was noted. Before it reached the upper plate the electric field would be destroyed by grounding the metal plates. The drop would then fall again, and the time of its descent from the upper cross-hair to the lower one was once more observed, and so the experiment proceeded-keeping the droplet always in the air, and continually recording the times of its ascent and descent. (A single drop could thus be kept under constant observation for hours.) The size of the drop was determined from the measured time of its fall by means of a modified form of Stokes' formula for the descent of small spheres in viscous media — the original formula having been studied with great care (especially by Dr. H. D. Arnold) with reference to its accuracy in connection with droplets of the size used in these experiments. diameter of the droplet being known, its weight was readily ascertained, because the density of the oil of which it was composed was known. Then from a knowledge of the weight of the drop, and of the time of its downward passage under the influence of gravity and of its upward passage under the influence of the known electric field, it was easy to calculate the electric charge on the drop. An ingenious means was provided for changing the electrification of the drop at will, and in either direction, by ionizing the air between the plates by means of an X-ray discharge, and then throwing ions against the drop by electric repulsion. The original positive electrification of the drop was reduced every time a negative ion was taken in, and increased every time a positive ion was received. After a positive ion had been taken in, the upward journey would be performed more quickly than before, and the inclusion of a negative ion would cause a corresponding slowing of the upward motion. It was found to be quite possible to determine, from the circumstances of the motion, the number (as well as the sign) of the ions thus entering the drop; and by calculating the electric charges for all the different upward journeys that were observed, it became evident that these various charges either showed no change, or differed from one another either by a certain constant quantity, or by a low multiple of that quantity. It was even found that the original charge of the droplet was also an apparently exact multiple of this same quantity. The doctrine that electrification is a discontinuous process, and that it consists in adding to a body (or subtracting from it) a certain number of small-sized yet finite and equal charges, or "electrons," thereby received an exceedingly striking and definite confirmation; and the data available made it quite easy to calculate the magnitude of this elementary unit charge. After several years of study and observation, culminating in two years of work with a special apparatus constructed with exceeding care, the final conclusion was, that the charge on the electron is invariably e=4.774 X 10-10 absolute electrostatic units; and Millikan believes (apparently with good grounds) that the uncertainty in this result is not greater than the thousandth part of its own magnitude. (The

corresponding value of the charge, in absolute electromagnetic units is e=1.592 X 10-2).

Millikan obtained his oil drop by perforating the upper of the two metallic plates by means of a minute pinhole, and then sending a fine spray of the oil into the space above the plate, by blowing a puff of air through an atomizer. In the course of time one of the droplets of the spray would fall through the pinhole into the region between the plates, and the experiment could be started. The friction to which the oil was subjected in the atomizer electrified the droplets of spray positively, and, as has been stated above, the charge communicated to the droplet in this way was always found to be an exact multiple of the value given above. This fact is highly interesting, because here we have, for the first time, direct evidence that an electric charge communicated to a body by friction consists in an excess or deficit of a definite, finite number of electrons. In one experiment, for example, the positive charge communicated to the droplet by the initial friction of the atomizer was found to correspond to a loss (or deficiency) of nine negative electrons.

Millikan varied his drop-experiments in many ways, using numerous substances (including mercury) for the drops, and experimenting with drops of widely different sizes, and with various gases between his electrified plates; and he concludes that "the apparent value of the electron is not in general a function of the gas in which the particle falls, of the materials used, or of the radius of the drop on which it is caught." In other words, he strikingly confirmed the theory that the negative corpuscle has an actual, physical existence, apart from the existence of the kinds of matter heretofore contemplated by the chemist.

The determination of the mass m of a free, slowly-moving negative corpuscle is an easy

X 10" grammes.

(It may be shown, from this, that it would require 1,845 slowly-moving negative corpuscles, to have a combined mass equal to the mass of one hydrogen atom.)

We do not yet know the shape of the negative corpuscle, nor do we positively know that the word "shape" has any definite meaning when applied to it. Larmor, for purposes of discussion, assumed the corpuscle to be a mathematical point endowed with a finite charge of electricity, which creates a certain type of strain in the surrounding ether; but the prevailing conception (in which Larmor would doubtless concur) is that the actual, physical corpuscle has some kind of spatial extension, though it may not have definite boundaries. Nicholson, in a paper read before the Physical Society of London in October 1917, suggested that the corpuscle is a region of strain in the ether, the strain being intense in the immediate

= 4

vicinity of a certain central point, and diminishing with extreme rapidity as we pass away from that point. According to this view the corpuscle would have no definite boundaries, and therefore (in a strict sense) no definite shape, though on account of the intense localization of the region in which the strain is really significant, we might treat the corpuscle for most purposes almost as though it were mathematical point. If we desired to assign a "radius" to such a corpuscle, we should have to define the radius arbitrarily, either as extending to a region where the strain is some definite fraction of the maximum central strain, or in some other way.

a

In the absence of data concerning the shape of the negative corpuscle, it is natural to try, first, the simplest assumption we can make with regard to it and to see how well this fits such facts as we have. The simplest shape, from a mathematical standpoint, is a sphere; and we find that the three best-known theories as to the shape of the negative corpuscle assume it to be spherical, at all events when it is at rest.

(1) Abraham considers the corpuscle to be rigid and spherical at all times, whether it is moving_rapidly or at rest.

(2) Lorentz considers it to be spherical when at rest, but assumes that when it moves it becomes transformed into an ellipsoid of revolution with its equatorial radius unchanged, but with its polar radius (which is parallel to the direction of the motion) shortened to r V1-x2 where r is the original radius and x is the ratio that the speed of the corpuscle bears to the speed of light.

(3) Bucherer and Langevin also consider the corpuscle to be spherical when at rest and assume that when it is in motion it takes the form of an ellipsoid of revolution with its polar radius shortened and directed parallel to the motion; but they assume that the polar radius becomes (1-x) and that the equatorial radii are increased in consequence of the motion, so that each becomes equal to r(1 — x2)—3, where and have the same significance as before. (It is to be observed that these relations of Bucherer and Langevin leave the volume of the corpuscle unchanged, whatever the speed may be).

Each of these conceptions has something in its favor, and each has something against it, but they should all be regarded merely as convenient mathematical fictions for the presentfictions that are worth considering because they may serve to suggest further researches when their consequences are investigated. The experiments of Kaufmann (to which reference will presently be made) appear to be incompatible with Lorentz's conception of the corpuscle, while the theory of relativity suggests that those of Abraham and of Bucherer and Langevin are untenable.

The general theory of electricity, as applied to static charges moving rapidly through space, brings us face to face with an exceedingly interesting topic in connection with the negative corpuscle, namely, that its apparent mass is doubtless in some measure of electrical origin, and that it is quite within the bounds of possibility that it is wholly electrical. Sir J. J. Thomson pointed out, as long ago as 1881, that a moving body (for example, a sphere) pos

sesses a somewhat greater apparent inertia, or mass, when it is electrically charged than it does when it is not charged. (Recent Researches in Electricity and Magnetism,' p. 21.) This is due to the fact that the charged body has Faraday "tubes of force" radiating from it, and these tubes are supposed to carry a certain amount of ether along with them and to encounter a sort of hydrodynamic resistance from the surrounding ether. This resistance is not analogous to friction, however. It does not necessarily entail any dissipation of energy, but has the general effect (when considered mathematically) of increasing the apparent mass of the charged body. Thomson showed, for example, that a sphere having a radius of r centimeters, and bearing an electric charge of e absolute electromagnetic units, has an apparent mass

equal to (m+grammes, if it is station

ary or moving with a speed that is small in comparison with the speed of light; m being its mass, in grammes, when the electric charge is absent.

When a charged sphere is caused to move with greater and greater speed, the Faraday tubes of force shift their positions in relation to it, and Heaviside showed (in 1889) that as the speed increases, each tube, whatever its original direction, will be displaced more and more toward a plane passing through the centre of the sphere perpendicularly to the line of motion. In other words, if we call the diameter that coincides with the direction of motion of the sphere its "polar axis," the tubes of force that radiate from the sphere will crowd closer and closer toward the equatorial plane, the faster the sphere moves. Moreover, the shifting of each tube (according to Heaviside's analysis) will take place in such a way that the original distance of every point in the tube from the equatorial plane will be reduced by the motion in the proportion of √ √22 to V, where is the speed of the sphere, and Vis the speed of light. (It is to be observed, in particular, that the tubes approach the equatorial plane in the same way, whether they lie in front of it or behind it, as the sphere moves through space).

Now the effect of the ether upon a Faraday tube is very different when the tube is moving endwise than when the tube is moving sidewise (or perpendicularly to its own length); and in consequence of this fact, the part of the apparent mass that is due to the electrification increases when the speed of the sphere becomes great enough for the equatorial crowding of the tubes of force to become significant. It is not possible to deal with this phase of the subject more than superficially in the present article, but it should be specially noted that mathematical analysis has shown (1) that owing to the existence of the Faraday tubes of force that stretch out into the ether from an electrified

body, that body, whether its charge be positive or negative and whether it be stationary or in motion, has an apparent mass greater than the mass it has when the charge is absent; (2) that owing to the crowding of the Faraday tubes toward the equatorial region when the speed of the body increases, the apparent mass of the body increases as the speed increases; (3) that at any ordinary speed this increase in apparent

mass is insignificant and does not have to be reckoned with; but (4) that it becomes significant as soon as the body attains a speed equal to a few tenths of the speed of light, and (5) the apparent mass increases with extreme rapidity as the speed approaches closely to the speed of light, and (6) it would become infinite if that speed were fully attained.

Now until the last few years this rather striking conclusion was of academic interest only and it had no practical bearing because we could not produce any such prodigious speeds, in electrified bodies, as were necessary in order to give rise to any sensible increase in their apparent mass. When, however, it was discovered that the negative corpuscles in high vacuum tubes are moving with speeds comparable with (though always materially less than) the speed of light, the conclusions summarized above began to have an important practical bearing and physicists asked themselves whether any increase in the apparent mass of these corpuscles could be detected, that could be assigned to the causes indicated- that is, whether any experimental evidence could be adduced, to show that the apparent mass of a swiftly-moving electrified particle increases with the speed with which the particle is traveling. The question became far more interesting and important when it was shown that the so-called "beta rays" emitted by radium are identical with the negatively electrified corpuscles observed in vacuum tubes, because the speed of these beta particles has been found to be as high as from 95 to 97 per cent. of that of light in some cases, and hence they should show a marked increase of apparent mass, if the previous theoretical conclusions about the effect of speed upon mass were sound.

Partly with the object of testing this point, and partly with the broader idea of gaining a general insight into the nature of mass and inertia and into the constitution of the negative corpuscle, W. Kaufmann, of Göttingen, undertook to determine the ratio of charge to mass for these rapidly-moving particles, at various speeds. An interesting semi-popular account of his best-known experiments will be found in Sir Oliver Lodge's 'Electrons.' (For the original papers, see Comptes rendus, 13 Oct. 1902; Physikalische Zeitschrift, 4, 1902-03, p. 55; Annalen der Physik, Vol. XIX, 1906). The method employed by Kaufmann was a modification of the one outlined above for determining the speed of cathode-ray corpuscles by subjecting the particles simultaneously to magnetic and electrostatic fields of force, except that Kaufmann made use of a stream of beta particles, emitted by radium, and arranged his apparatus so that the magnetic field tended to deflect each corpuscle toward (say) the north, while the electric field, instead of being disposed so as to neutralize this effect, was arranged so that it tended to deflect the corpuscle (say) toward the east. The stream of beta particles impinged against a photographic plate in such a way that a small, round, single spot was registered upon it when neither field was active. When the magnetic field alone was excited, the spot would have been merely displaced toward the north if the beta particles all had the same speed; but inasmuch as they had a great variety of speeds, it was drawn out into a straight line, extending in a north-and

ame particles. If it is assumed (in accordance with all the other evidence that we have) that è remains invariable, the data thus obtained show the relation between the mass, m, of a negative particle and the speed, u, with which the particle is moving.

The relation between speed and mass, as revealed by these experiments, was very marked. For example, at the highest speed observed (which was about 97 per cent, of that of light) the apparent mass of a corpuscle was found to be about three times as great as the mass of the same corpuscle when at rest.

Kaufmann's experiments provide us with means of testing, to a certain extent, theories of the constitution of the negative corpuscle, inasmuch as for every theory concerning the general nature of the corpuscle there will be a corresponding law of variation of mass with speed. This was recognized immediately, and was, in fact, largely what led to the making of the experiments to which we have just referred. A curious fact that has to be reckoned with, in applying tests of this kind to the observational data, is, that every negative-corpuscle theory yet proposed indicates that the mass of a body moving at high speed is a vector quantity — that is, that the mass of the body, as measured in the direction of the motion (i.e., the so-called longitudinal mass) is different from the mass of the same body as measured at right angles to the direction of the motion (i.e., different from the so-called transversal mass). It is the transversal mass, as Abraham pointed out in 1902, with which we have to deal in discussing experiments such as Kaufmann's.

If R is the ratio that the speed of a given negative corpuscle bears to the speed of light when the electrical part of the transversal mass of the corpuscle is m, and if mo is the electrical part of the mass of this same corpuscle when it is at rest, then for mmo we have the following values for the respective theories of negative-corpuscle structure mentioned above: 3 1 1 + R2

log (1) -1 for the Abraham

(1 — R2)11⁄2

1-R

for the Lorentz theory; and

for the Bucherer-Langevin theory.

When the several hypotheses as to the constitution of the negative corpuscle are judged by comparing these formulas with Kaufmann's experimental data, it appears (1) that the Lorentz corpuscle, which is the only one of the three that conforms with the theory of relativity, does not fit the data at all well; and (2) that the experimental evidence agrees quite well with either the Abraham or the BuchererLangevin corpuscle.

From experiments of this nature we may

VOL. 10-14

obtain a certain amount of information with regard to the proportion of "electrical mass" to "real mass" in a corpuscle; for the experimental data reveal the law in accordance with which the total mass varies with speed, while the theory of the nature and constitution of the corpuscle yields a formula showing merely how the electrical part of the mass varies. If there is a "real mass" to the corpuscle, we may therefore reasonably hope, by comparing experiment with good theory, definitely to solve this question of the quantitative relation between the two kinds of mass. Kaufmann, soon after his original experiments were made, believed that they indicated that only a fraction of the total mass is electric; .but he had not then taken account of the difference (noted above) between longitudinal and transversal mass. Later, when due allowance was made for this difference, he came to the conclusion that most and perhaps al of the mass is electric; and there is a growing tendency among physicists not only to accept this view with regard to negative corpuscles, but also to generalize it broadly, and to assume (at least tentatively) that mass, wherever it is found, is exclusively electrical in nature, and due to the motion, within the atoms of bodies, of electrified corpuscles moving with great speeds. This conception is as fascinating as it is revolutionary. Many of its advocates, however, overlook the fact that even if this should prove to be the case, we have "explained mass only by shifting it to the ether, which, at the same time, we should apparently have to conceive as a medium far denser than anything we know of, in the visible and tangible world of direct experience.

Before attempting to estimate the size of a negative corpuscle, it is necessary clearly to understand that we have no way, as yet, to determine the dimensions of corpuscles, if we assume that the mass that they possess is only partially electrical and that the rest of it is mass in the usual or non-electrical sense. If, however, we assume that the mass is wholly of electrical origin, we can casily obtain an estimate of the size of the corpuscle. The value that we obtain will depend in some measure upon the views that we hold with regard to the shape of the corpuscle; but if, for present purposes, we consider it to be spherical, the estimate of size obtained will probably be of the right general order of magnitude, even if the spherical shape ultimately proves to be untenable, so far as concerns the relation of the negative corpuscle to phenomena in general.

To obtain the desired estimate of size (in conformity with the assumptions here outlined) we may make use of the expression given by J. J. Thomson, and already quoted above, for the electrical mass of a slowly-moving electrified sphere. Thus if m is the mass of the (stationary or slowly-moving) corpuscle in grammes, its radius in centimeters and e its charge in absolute electromagnetic units, we have 2 e2 3

m=

2 e2 3 r

orr

m

corpuscles were placed in a line and just touching one another, they would make a row about an inch and a half long. (An equal number of oranges, each three inches in diameter and placed in a row in like manner, would reach from the sun to the orbit of Jupiter). Atoms differ in size, but in a rough and general way it may be said that it would require something like 100,000 negative corpuscles, placed in a straight line and in contact with one another, to reach across the diameter of an atom.

The corpuscular theory has developed marvelously in the last 15 years, and it has been applied, in one form or another, to the explanation of the mechanism of many phenomena, such as radiation, X-rays, radioactivity, and electrical and thermal conduction. It has also been pressed into service to explain chemical affinity and valency and to elucidate the structure of atoms and molecules. It has proved to be a fruitful conception, and some modification of it will no doubt remain with us, as a permanent addition to our physical theories. It should be recognized, however, that when, in discussing particles so exceedingly small, we apply the general physical and mechanical laws and principles that we have deduced from observation in our grosser world of experience, we are very likely committing a serious error-an error which, though it will no doubt be corrected in the course of time, may be blinding us, meanwhile, to some very large facts. Many of the "laws" that apply to larger masses of matter are probably statistical laws, due to the averaging of many millions of separate events that do not individually follow these laws. That the properties of the negative corpuscle are far different from those that we have heretofore assigned to "gross" matter is already sufficiently shown by what we have learned about the mass of such corpuscles. In a general way, however, it may be said that we have made progress enough in the study of the negative corpuscle to have it become a real thing to us—or at least a symbol of a real thing; and J. J. Thomson has well said that although the negative corpuscle is a recent discovery, we already know more about it than we do about the atom. See also ELECTRICITY; MOLECULAR THEORY; RADIATION; RADIOACTIVITY.

Bibliography.-A creditable and interesting popular account of the negative_corpuscle and its various relations is given in E. E. Fournier d'Albe's 'Electron Theory, though the numerical data therein given have now been largely superseded by better values, as indicated in the present article. A more recent and more authoritative review of the relation of the corpuscular theory to physical phenomena in general is given by J. P. Minton in a series of papers printed in The General Electric Review for 1915 (Vol. 18.) Consult also Thomson, J. J., 'The Corpuscular Theory of Matter, The Conduction of Electricity through Gases' and 'Electricity and Matter'; Campbell, Modern Electrical Theory); Lodge, 'Electrons'; Larmor, 'Aether and Matter'; Millikan, The Electron; Comstock and Troland, (The Nature of Matter and Electricity'; Bucherer, 'Mathematische Einführung in die Elektronentheorie'; Abraham, Theorie der Elektrizität' (Vol. II).

ALLAN D. RISTEEN, Ph.D.

ELECTROPLATING, the art of plating or covering solid objects with a coating of metal by electro-deposition. This is the most common method of applying silver or gold plate for ornament, or copper or nickel plate, as for rendering an article more durable. Given a solution of the salts of a metal, say, for instance, sulphate of copper (the constituents of which are sulphuric acid and copper oxide), in which are immersed a copper plate connected with the positive pole of a source of electromotive force and a metal plate connected with the negative pole; when an electric current is passed through the solution an action takes place which may be described as follows: First, the salt is decomposed into sulphuric acid and oxide of copper. At the same time a portion of the water of the solution is also decomposed. setting free hydrogen and oxygen. The oxygen of the oxide of copper is drawn to the negative pole, where it unites with a portion of the hydrogen just freed, forming water, and the metallic copper thus set free is deposited uniformly on the negative metal plate. Simultaneously with this action sulphuric acid and oxygen arrive at the positive plate, where the oxygen unites with a particle of the copper plate, forming oxide of copper, with which the sulphuric combines, forming sulphate of copper; which process is continued as long as there is any metal left in the positive plate. For each atom of copper thus dissolved at the positive plate another is set free at the negative plate. Actions analogous to these underlie all electroplating and electrotyping operations. If it is desired to deposit nickel, silver, gold or other metal on the object, salts of those metals instead of copper will be used in the solution or bath, as it is termed.

Silver is the easiest metal to use in plating, one ampere of current depositing 4.02 grams of metal per hour; with the same current copper deposits 1.17 and nickel 1.09 grams per hour. If 10 baths are worked in series of eight hours a day, depositing each 10 pounds of copper, they will require 4,830 amperes of current all the time; and with copper anodes the pressure will be about 16 volts for the 10 baths.

The art of electroplating is extensively practised. The current for the decomposition of the electrolyte, in solution, is usually supplied by continuous-current dynamo machines which are specially designed to give large currents at low electromotive force, rarely exceeding three to five volts. Sufficient electromotive force must be provided to decompose the solution, but the amount of chemical decomposition depends altogether on, and is proportional to, the rate or amperage of the current. If too high electromotive force is employed the plating is uneven and granular. Storage or primary batteries may also be used for this purpose,