It would not be in keeping with the method of modern science to make any dogmatic assertion as to the indivisibility of the electron. Such assertions used to be made in high-school classes with respect to the atoms of the elements, but the far-seeing among physicists, like Faraday, were always careful to disclaim any belief in the necessary ultimateness of the atoms of chemistry, and that simply because there existed until recently no basis for asserting anything about the insides of the atom. We knew that there was a smallest thing which took part in chemical reactions and we named that thing the atom, leaving its insides entirely to the future.

Precisely similarly the electron was defined as the smallest quantity of electricity which ever was found to appear in electrolysis, and nothing was then said or is now said about its necessary ultimateness. Our experiments have, however, now shown that this quantity is capable of isolation and exact measurement, and that all the kinds of charges which we have been able to investigate are exact multiples of it. Its value is .

I. A SECOND METHOD OF OBTAINING

I have presented one way of measuring this charge, but there is an indirect method of arriving at it which was worked out independently by Rutherford and Geiger[95] and Regener.[96] The unique feature in this method consists in actually counting the number of -particles shot off per second by a small speck of radium or polonium through a given solid angle and computing from this the number of these particles emitted per second by one gram of the radium or polonium. Regener made his determination by counting the scintillations produced on a diamond screen in the focal plane of his observing microscope. He then caught in a condenser all the -particles emitted per second by a known quantity of his polonium and determined the total quantity of electricity delivered to the condenser by them. This quantity of electricity divided by the number of particles emitted per second gave the charge on each particle. Because the -particles had been definitely proved to be helium atoms[97] and the value of found for them showed that if they were helium they ought to carry double the electronic charge, Regener divided his result by 2 and obtained He estimated his error at 3 per cent. Rutherford and Geiger made their count by letting the -particles from a speck of radium shoot into a chamber and produce therein sufficient ionization by collision to cause an electrometer needle to jump every time one of them entered. These authors measured the total charge as Regener did and, dividing by 2 the charge on each -particle, they obtained All determinations of from radioactive data involve one or the other of these two counts, namely, that of Rutherford and Geiger or that of Regener. Thus, Boltwood and Rutherford[98] measured the total weight of helium produced in a second by a known weight of radium. Dividing this by the number of -particles (helium atoms) obtained from Rutherford and Geiger’s count, they obtain the mass of one atom of helium from which the number in a given weight, or volume since the gas density is known, is at once obtained. They published for the number of molecules in a gas per cubic centimeter at 0°76 cm., , which corresponds to This last method, like that of the Brownian movements, is actually a determination of , rather than of , since is obtained from it only through the relation . Indeed, this is true of all methods of estimating , so far as I am aware, except the oil-drop method and the Rutherford-Geiger-Regener method, and of these two the latter represents the measurement of the mean charge on an immense number of -particles. Thus a person who wished to contend that the unit charge appearing in electrolysis is only a mean charge which may be made up of individual charges which vary widely among themselves, in much the same way in which the atomic weight assigned to neon has recently been shown to be a mean of the weights of at least two different elements inseparable chemically, could not be gainsaid, save on the basis of the evidence contained in the oil-drop experiments; for these constitute the only method which has been found of measuring directly the charge on each individual ion. It is of interest and significance for the present discussion, however, that the mean charge on an -particle has been directly measured and that it comes out, within the limits of error of the measurement, at exactly two electrons—as it should according to the evidence furnished by measurements on the -particles.

II. THE EVIDENCE FOR THE EXISTENCE OF A SUB-ELECTRON

Now, the foregoing contention has actually been made, and evidence has been presented which purports to show that electric charges exist which are much smaller than the electron. Since this raises what may properly be called the most fundamental question of modern physics, the evidence needs very careful consideration. This evidence can best be appreciated through a brief historical review of its origin.

The first measurements on the mobilities in electric fields of swarms of charged particles of microscopically visible sizes were made by H. A. Wilson[99] in 1903, as detailed in chap. III. These measurements were repeated with modifications by other observers, including ourselves, during the years immediately following. De Broglie’s modification, published in 1908,[100] consisted in sucking the metallic clouds discovered by Hemsalech and De Watteville,[101] produced by sparks or arcs between metal electrodes, into the focal plane of an ultra-microscope and observing the motions of the individual particles in this cloud in a horizontal electrical field produced by applying a potential difference to two vertical parallel plates in front of the objective of his microscope. In this paper De Broglie first commented upon the fact that some of these particles were charged positively, some negatively, and some not at all, and upon the further fact that holding radium near the chamber caused changes in the charges of the particles. He promised quantitative measurements of the charges themselves. One year later he fulfilled the promise,[102] and at practically the same time Dr. Ehrenhaft[103] published similar measurements made with precisely the arrangement described by De Broglie a year before. Both men, as Dr. Ehrenhaft clearly pointed out,[104] while observing individual particles, obtained only a mean charge, since the different measurements entering into the evaluation of were made on different particles. So far as concerns , these measurements, as everyone agrees, were essentially cloud measurements like Wilson’s.

In the spring and summer of 1909 I isolated individual water droplets and determined the charges carried by each one,[105] and in April, 1910, I read before the American Physical Society the full report on the oil-drop work in which the multiple relations between charges were established, Stokes’s Law corrected, and accurately determined.[106] In the following month (May, 1910) Dr. Ehrenhaft,[107] having seen that a vertical condenser arrangement made possible, as shown theoretically and experimentally in the 1909 papers mentioned above, the independent determination of the charge on each individual particle, read the first paper in which he had used this arrangement in place of the De Broglie arrangement which he had used theretofore. He reported results identical in all essential particulars with those which I had published on water drops the year before, save that where I obtained consistent and simple multiple relations between charges carried by different particles he found no such consistency in these relations. The absolute values of these charges obtained on the assumption of Stokes’s Law fluctuated about values considerably lower than . Instead, however, of throwing the burden upon Stokes’s Law or upon wrong assumptions as to the density of his particles, he remarked in a footnote that Cunningham’s theoretical correction to Stokes’s Law,[108] which he (Ehrenhaft) had just seen, would make his values come still lower, and hence that no failure of Stokes’s Law could be responsible for his low values. He considered his results therefore as opposed to the atomic theory of electricity altogether, and in any case as proving the existence of charges much smaller than that of the electron.[109]

The apparent contradiction between these results and mine was explained when Mr. Fletcher and myself showed[110] experimentally that Brownian movements produced just such apparent fluctuations as Ehrenhaft observed when the is computed, as had been done in his work, from one single observation of a speed under gravity and a corresponding one in an electric field. We further showed that the fact that his values fluctuated about too low an average value meant simply that his particles of gold, silver, and mercury were less dense because of surface impurities, oxides or the like, than he had assumed. The correctness of this explanation would be well-nigh demonstrated if the values of computed by equations (28) or (29) in chap. VII from a large number of observations on Brownian movements always came out as in electrolysis, for in these equations no assumption has to be made as to the density of the particles. As a matter of fact, all of the nine particles studied by us and computed by Mr. Fletcher[111] showed the correct value of , while only six of them as computed by me fell on, or close to, the line which pictures the law of fall of an oil drop through air (Fig. 5, p. 106). This last fact was not published in 1911 because it took me until 1913 to determine with sufficient certainty a second approximation to the complete law of fall of a droplet through air; in other words, to extend curves of the sort given in Fig. 5 to as large values of as correspond to particles small enough to show large Brownian movements. As soon as I had done this I computed all the nine drops which gave correct values of and found that two of them fell way below the line, one more fell somewhat below, while one fell considerably above it. This meant obviously that these four particles were not spheres of oil alone, two of them falling much too slowly to be so constituted and one considerably too rapidly. There was nothing at all surprising about this result, since I had explained fully in my first paper on oil drops[112] that until I had taken great precaution to obtain dust-free air “the values of came out differently, even for drops showing the same velocity under gravity.” In the Brownian-movement work no such precautions to obtain dust-free air had been taken because we wished to test the general validity of equations (28) and (29). That we actually used in this test two particles which had a mean density very much smaller than that of oil and one which was considerably too heavy, was fortunate since it indicated that our result was indeed independent of the material used.

It is worthy of remark that in general, even with oil drops, almost all of those behaving abnormally fall too slowly, that is, they fall below the line of Fig. 5 and only rarely does one fall above it. This is because the dust particles which one is likely to observe, that is, those which remain long in suspension in the air, are either in general lighter than oil or else expose more surface and hence act as though they were lighter. When one works with particles made of dense metals this behavior will be still more marked, since all surface impurities of whatever sort will diminish the density. The possibility, however, of freeing oil-drop experiments from all such sources of error is shown by the fact that although during the year 1915-16 I studied altogether as many as three hundred drops, there was not one which did not fall within less than 1 per cent of the line of Fig. 5. It will be shown, too, in this chapter, that in spite of the failure of the Vienna experimenters, it is possible under suitable conditions to obtain mercury drops which behave, even as to law of fall, in practically all cases with perfect consistency and normality.

When E. Weiss in Prag and K. Przibram in the Vienna laboratory itself, as explained in chap. VII, had found that for all the substances which they worked with, including silver particles like those used by Ehrenhaft, gave about the right value of , although yielding much too low values of when the latter was computed from the law of fall of silver particles, the scientific world practically universally accepted our explanation of Ehrenhaft’s results and ceased to concern itself with the idea of a sub-electron.[113]

In 1914 and 1915, however, Professor Ehrenhaft[114] and two of his pupils, F. Zerner[115] and D. Konstantinowsky,[116] published new evidence for the existence of such a sub-electron and the first of these authors has kept up some discussion of the matter up to the present. These experimenters make three contentions. The first is essentially that they have now determined for their particles by equation (29); and although in many instances it comes out as in electrolysis, in some instances it comes out from 20 per cent to 50 per cent too low, while in a few cases it is as low as one-fourth or one-fifth of the electrolytic value. Their procedure is in general to publish, not the value of , but, instead, the value of obtained from by inserting Perrin’s value of () in (29) and then solving for . This is their method of determining “from the Brownian movements.”

Their second contention is the same as that originally advanced, namely, that, in some instances, when is determined with the aid of Stokes’s Law of fall (equation 12, p. 91), even when Cunningham’s correction or my own (equation 15, p. 101) is employed, the result comes out very much lower than . Their third claim is that the value of , determined as just explained from the Brownian movements, is in general higher than the value computed from the law of fall, and that the departures become greater and greater the smaller the particle. These observers conclude therefore that we oil-drop observers failed to detect sub-electrons because our droplets were too big to be able to reveal their existence. The minuter particles which they study, however, seem to them to bring these sub-electrons to light. In other words, they think the value of the smallest charge which can be caught from the air actually is a function of the radius of the drop on which it is caught, being smaller for small drops than for large ones.

Ehrenhaft and Zerner even analyze our report on oil droplets and find that these also show in certain instances indications of sub-electrons, for they yield in these observers’ hands too low values of , whether computed from the Brownian movements or from the law of fall. When the computations are made in the latter way is found, according to them, to decrease with decreasing radius, as is the case in their experiments on particles of mercury and gold.

III. CAUSES OF THE DISCREPANCIES

Now, the single low value of which these authors find in the oil-drop work is obtained by computing from some twenty-five observations on the times of fall, and an equal number on the times of rise, of a particle which, before we had made any computations at all, we reported upon[117] for the sake of showing that the Brownian movements would produce just such fluctuations as Ehrenhaft had observed when the conditions were those under which he worked. When I compute by equation (29), using merely the twenty-five times of fall, I find the value of comes out 26 per cent low, just as Zerner finds it to do. If, however, I omit the first reading it comes out but 11 per cent low. In other words, the omission of one single reading changes the result by 15 per cent. Furthermore, Fletcher[118] has shown that these same data, though treated entirely legitimately, but with a slightly different grouping than that used by Zerner, can be made to yield exactly the right value of . This brings out clearly the futility of attempting to test a statistical theorem by so few observations as twenty-five, which is nevertheless more than Ehrenhaft usually uses on his drops. Furthermore, I shall presently show that unless one observes under carefully chosen conditions, his own errors of observation and the slow evaporation of the drop tend to make obtained from equation (29) come out too low, and these errors may easily be enough to vitiate the result entirely. There is, then, not the slightest indication in any work which we have thus jar done on oil drops that comes out too small.

Next consider the apparent variation in when it is computed from the law of fall. Zerner computes from my law of fall in the case of the nine drops published by Fletcher, in which came out as in electrolysis, and finds that one of them yields , one , one , one , while the other five yield about the right value, namely, . In other words (as stated on p. 165 above), five of these drops fall exactly on my curve (Fig. 5), one falls somewhat above it, one somewhat below, while two are entirely off and very much too low. These two, therefore, I concluded were not oil at all, but dust particles. Since Zerner computes the radius from the rate of fall, these two dust particles which fall much too slowly, and therefore yield too low values of , must, of course, yield correspondingly low values of . Since they are found to do so, Zerner concludes that our oil drops, as well as Ehrenhaft’s mercury particles, yield decreasing values of with decreasing radius. His own tabulation does not show this. It merely shows three erratic values of , two of which are very low and one rather high. But a glance at all the other data which I have published on oil drops shows the complete falsity of this position,[119] for these data show that after I had eliminated dust all of my particles yielded exactly the same value of “” whatever their size[120]. The only possible interpretation then which could be put on these two particles which yielded correct values of , but too slow rates of fall, was that which I put upon them, namely, that they were not spheres of oil.

As to the Vienna data on mercury and gold, Dr. Ehrenhaft publishes, all told, data on just sixteen particles and takes for his Brownian-movement calculations on the average fifteen times of fall and fifteen of rise on each, the smallest number being 6 and the largest 27. He then computes his statistical average from observations of this sort. Next he assumes Perrin’s value of , namely, , which corresponds to , and obtains instead by the Brownian-movement method, i.e., the method, the following values of , the exponential term being omitted for the sake of brevity: 1.43, 2.13, 1.38, 3.04, 3.5, 6.92, 4.42, 3.28, .84. Barring the first three and the last of these, the mean value of is just about what it should be, namely, 4.22 instead of 4.1. Further, the first three particles are the heaviest ones, the first one falling between his cross-hairs in 3.6 seconds, and its fluctuations in time of fall are from 3.2 to 3.85 seconds, that is, three-tenths of a second on either side of the mean value. Now, these fluctuations are only slightly greater than those which the average observer will make in timing the passage of a uniformly moving body across equally spaced cross-hairs. This means that in these observations two nearly equally potent causes were operating to produce fluctuations. The observed ’s were, of course, then, larger than those due to Brownian movements alone, and might easily, with but a few observations, be two or three times as large. Since appears in the denominator of equation (29), it will be seen at once that because of the observer’s timing errors a series of observed ’s will always tend to be larger than the due to Brownian movements alone, and hence that the Brownian-movement method always tends to yield too low a value of , and accordingly too low a value of . It is only when the observer’s mean error is wholly negligible in comparison with the Brownian-movement fluctuations that this method will not yield too low a value of . The overlooking of this fact is, in my judgment, one of the causes of the low values of recorded by Dr. Ehrenhaft.

Again, in the original work on mercury droplets which I produced both by atomizing liquid mercury and by condensing the vapor from boiling mercury,[121] I noticed that such droplets evaporated for a time even more rapidly than oil, and other observers who have since worked with mercury have reported the same behavior.[122] The amount of this effect may be judged from the fact that one particular droplet of mercury recently under observation in this laboratory had at first a speed of 1 cm. in 20 seconds, which changed in half an hour to 1 cm. in 56 seconds. The slow cessation, however, of this evaporation indicates that the drop slowly becomes coated with some sort of protecting film. Now, if any evaporation whatever is going on while successive times of fall are being observed—and as a matter of fact changes due to evaporation or condensation are always taking place to some extent—the apparent will be larger than that due to Brownian movements, even though these movements are large enough to prevent the observer from noticing, in taking twenty or thirty readings, that the drop is continually changing. These changes combined with the fluctuations in due to the observer’s error are sufficient, I think, to explain all of the low values of e obtained by Dr. Ehrenhaft by the Brownian-movement method. Indeed, I have myself repeatedly found coming out less than half of its proper value until I corrected for the evaporation of the drop, and this was true when the evaporation was so slow that its rate of fall changed but 1 or 2 per cent in a half-hour. But it is not merely evaporation which introduces an error of this sort. The running down of the batteries, the drifting of the drop out of focus, or anything which causes changes in the times of passage across the equally spaced cross-hairs tends to decrease the apparent value of . There is, then, so far as I can see, no evidence at all in any of the data published to date that the Brownian-movement method actually does yield too low a value of “”, and very much positive evidence that it does not was given in the preceding chapter.

Indeed, the same type of Brownian-movement work which Fletcher and I did upon oil-drops ten years ago (see preceding chapter) has recently been done in Vienna with the use of particles of selenium, and with results which are in complete harmony with our own. The observer, E. Schmid,[123] takes as many as 1,500 “times of fall” upon a given particle, the radius of which is in one case as low as —quite as minute as any used by Dr. Ehrenhaft—and obtains in all cases values of by “the Brownian-movement method” which are in as good agreement with our own as could be expected in view of the necessary observational error. This complete check of our work in Vienna itself should close the argument so far as the Brownian movements are concerned.

That and computed from the law of fall become farther and farther removed from the values of and computed from the Brownian movements, the smaller these particles appear to be, is just what would be expected if the particles under consideration have surface impurities or non-spherical shapes or else are not mercury at all.[124] If, further, exact multiple relations hold for them, as at least a dozen of us, including Dr. Ehrenhaft himself, now find that they invariably do, there is scarcely any other interpretation possible except that of incorrect assumptions as to density.[see footnote 124] Again, the fact that these data are all taken when the observers are working with the exceedingly dense substances, mercury and gold, volatilized in an electric arc, and when, therefore, anything not mercury or gold, but assumed to be, would yield very low values of and , is in itself a very significant circumstance. The further fact that Dr. Ehrenhaft implies that normal values of e very frequently appear in his work,[125] while these low erratic drops represent only a part of the data taken, is suggestive. When one considers, too, that in place of the beautiful consistency and duplicability shown in the oil-drop work, Dr. Ehrenhaft and his pupils never publish data on any two particles which yield the same value of , but instead find only irregularities and erratic behavior,[126] just as they would expect to do with non-uniform particles, or with particles having dust specks attached to them, one wonders why any explanation other than the foreign-material one, which explains all the difficulties, has ever been thought of. As a matter of fact, in our work with mercury droplets, we have found that the initial rapid evaporation gradually ceases, just as though the droplets had become coated with some foreign film which prevents further loss. Dr. Ehrenhaft himself, in speaking of the Brownian movements of his metal particles, comments on the fact that they seem at first to show large movements which grow smaller with time.[127] This is just what would happen if the radius were increased by the growth of a foreign film.

Now what does Dr. Ehrenhaft say to these very obvious suggestions as to the cause of his troubles? Merely that he has avoided all oxygen, and hence that an oxide film is impossible. Yet he makes his metal particle by striking an electric arc between metal electrodes. This, as everyone knows, brings out all sorts of occluded gases. Besides, chemical activity in the electric arc is tremendously intense, so that there is opportunity for the formation of all sorts of higher nitrides, the existence of which in the gases coming from electric arcs has many times actually been proved. Dr. Ehrenhaft says further that he photographs big mercury droplets and finds them spherical and free from oxides. But the fact that some drops are pure mercury is no reason for assuming that all of them are, and it is only the data on those which are not which he publishes. Further, because big drops which he can see and measure are of mercury is no justification at all for assuming that sub-microscopic particles are necessarily also spheres of pure mercury. In a word, Dr. Ehrenhaft’s tests as to sphericity and purity are all absolutely worthless as applied to the particles in question, which according to him have radii of the order .—a figure a hundred times below the limit of sharp resolution.

IV. THE BEARING OF THE VIENNA WORK ON THE QUESTION OF THE EXISTENCE OF A SUB-ELECTRON

But let us suppose that these observers do actually work with particles of pure mercury and gold, as they think they do, and that the observational and evaporational errors do not account for the low values of . Then what conclusion could legitimately be drawn from their data? Merely this and nothing more, that (1) Einstein’s Brownian-movement equation is not universally applicable, and (2) that the law of motion of their very minute charged particles through air is not yet fully known.[128] So long as they find exact multiple relationships, as Dr. Ehrenhaft now does, between the charges carried by a given particle when its charge is changed by the capture of ions or the direct loss of electrons, the charges on these ions must be the same as the ionic charges which I have accurately and consistently measured and found equal to ; for they, in their experiments, capture exactly the same sort of ions, produced in exactly the same way as those which I captured and measured in my experiments. That these same ions have one sort of a charge when captured by a big drop and another sort when captured by a little drop is obviously absurd. If they are not the same ions which are caught, then in order to reconcile the results with the existence of the exact multiple relationship found by Dr. Ehrenhaft as well as ourselves, it would be necessary to assume that there exist in the air an infinite number of different kinds of ionic charges corresponding to the infinite number of possible radii of drops, and that when a powerful electric field drives all of these ions toward a given drop this drop selects in each instance just the charge which corresponds to its particular radius. Such an assumption is not only too grotesque for serious consideration, but it is directly contradicted by my experiments, for I have repeatedly pointed out that with a given value of I obtain exactly the same value of , whether I work with big drops or with little ones.

V. NEW PROOF OF THE CONSTANCY OF

For the sake of subjecting the constancy of to the most searching test, I have made new measurements of the same kind as those heretofore reported, but using now a range of sizes which overlaps that in which Dr. Ehrenhaft works. I have also varied through wide limits the nature and density of both the gas and the drops. Fig. 13 (I) contains new oil-drop data taken in air; Fig. 13 (II) similar data taken in hydrogen. The radii of these drops, computed by the very exact method given in the Physical Review[129] vary tenfold, namely, from .000025 cm. to .00023 cm. Dr. Ehrenhaft’s range is from .000008 cm. to .000025 cm. It will be seen that these drops fall in every instance on the lines of Fig. 13, I and II, and hence that they all yield exactly the same value of , namely, . The details of the measurements, which are just like those previously given, will be entirely omitted. There is here not a trace of an indication that the value of “” becomes smaller as “” decreases. The points on these two curves represent consecutive series of observations, not a single drop being omitted in the case of either the air or the hydrogen. This shows the complete uniformity and consistency which we have succeeded in obtaining in the work with oil drops.

That mercury drops show a similar behavior was somewhat imperfectly shown in the original observations which I published on mercury.[130] I have since fully confirmed the conclusions there reached. That mercury drops can with suitable precautions be made to behave practically as consistently as oil is shown in Fig. 13 (III), which represents data obtained by blowing into the observing chamber above the pinhole in the upper plate a cloud of mercury droplets formed by the condensation of the vapor arising from boiling mercury. These results have been obtained in the Ryerson Laboratory with my apparatus by Mr. John B. Derieux. Since the pressure was here always atmospheric, the drops progress in the order of size from left to right, the largest having a diameter about three times that of the smallest, the radius of which is .00003244 cm. The original data may be found in the Physical Review, December, 1916. In Fig. 13 (IV) is found precisely similar data taken with my apparatus by Dr. J. Y. Lee on solid spheres of shellac falling in air.[131] Further, very beautiful work, of this same sort, also done with my apparatus, has recently been published by Dr. Yoshio Ishida (Phys. Rev., May, 1923), who, using many different gases, obtains a group of lines like those shown in Fig. 13, all of which though of different slopes, converge upon one and the same value of “”, namely, .