# Popular Science Monthly/Volume 80/May 1912/New Proofs of the Kinetic Theory of Matter and the Atomic Theory of Electricity

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THE
POPULAR SCIENCE
MONTHLY
MAY, 1912
* NEW PROOFS OF THE KINETIC THEORY OF MATTER AND THE ATOMIC THEORY OF ELECTRICITY
By Professor ROBERT ANDREWS MILLIKAN, Ph.D., Sc.D.
UNIVERSITY OF CHICAGO
IT is my purpose herein to review the history of two of our most fundamental physical theories and to present some very simple and easily intelligible experiments which demonstrate the correctness of these theories, though they are by no means the only experiments which lead to the same goal.
If this statement seems too dogmatic and positive to be scientific let me say that I make it advisedly, for I wish vigorously to combat the point of view which I fear too many of those who are not engaged at first hand in scientific inquiry gain, both from the "revolutionary discoveries" which are continually being announced by the daily press, and also from the prominence which scientists themselves naturally give to the demolition of time-honored hypotheses in which they do not believe—the point of view that none of the theories of the scientists are after all any more than transient phenomena, that they are all just a part of the continual change and flux of things, that this generation discards wholesale all the hypotheses which were held adequate in the last and that the next generation will make equally short work of all the theories which hold sway to-day. In opposition to that point of view I wish to assert that there are some things, even in science, which we may safely say that we know, that there are some theories which we may be reasonably certain are going to endure—that in fact we may divide the theories of science into three categories, with broad and indefinite lines of division between them, it is true, but yet with real dividing areas, if not dividing lines.
In the first category may be placed the theories which we may say that we know are correct, using the word "know" not in the abstract ​philosophical sense, but in the common every-day intelligible sense. As an illustration of theories which are in this category we may take the germ theory of disease, meaning by that the theory that some diseases at least are due to definite micro-organisms which invade the system. In 1850, before Lister's and Pasteur's discoveries this was a pure hypothesis. To-day it is an hypothesis which has been definitely proved to be correct, and which henceforth we may indeed extend and modify but which we need never expect to see abandoned.
Again, the hypothesis that the earth is a round ball, rotating daily on its axis, and swinging annually around the sun was a few hundred years ago a mere assertion which almost nobody believed; to-day it is an established doctrine which we may count upon to endure, though of course the earth may not always 'keep on doing what it is doing to-day.
In the second category are a large group of theories which are probably correct, but which may at any time be proved to be false; while in the third category are theories which are very uncertain, some of them being little more than "pipe dreams," the best perhaps which we can do in the present state of our ignorance, but the ignorance upon which they are based is after all abysmal. The nebular hypothesis was a fine illustration of one of these dreams. It was not a part of our knowledge, because, as Kelvin so well says, there is no knowledge until we have been able to apply exact quantitative tests to our hypotheses. In other words, there is no science without exact measurement. There may be many good guesses without it, many plausible explanations, but no real knowledge. Such exact quantitative tests the nebular hypothesis has never been able to call to its support.
Now the progress of science consists simply in the slow but continuous sweep of these two broad lines of division in the direction of the last category, that is, it consists in nothing else save the continual transfer of theories from category 3 over to 2 and from 2 over into 1, and it is my purpose herein to trace the most fascinating history of the gradual transfer of two of these theories, from the outermost edge of 3 across the two boundaries over into 1, where they now rest so securely established that it is not too much to say that there is as much likelihood that man will some day cease to believe in the rotation of the earth as that the kinetic theory of matter and the atomic theory of electricity will ever cease to be the corner stones of all physical science.
But first, just a word about these revolutionary discoveries which are continually being announced. Nine tenths of them are just as revolutionary as was the discovery of the seven-year-old boy who came home from school one day altogether disgusted, saying that for a week his teacher had been telling him that 3 and 4 made seven, and he had just got it well learned when she told him that 5 and 2 make seven. So it is with our discoveries in science. We do indeed discover new relations, ​but for the most part the old ones remain. The atomic theory of matter, for example, was not even touched when radio-activity and the divisibility of the atom were brought to light, for nobody who had gone beyond the high school stage in science ever thought of asserting an indivisible atom, and that simply because we had 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 to the future, and the future proved itself abundantly able to take care of the trust.
Coming now to the first of our two theories, it is probably carrying coals to Newcastle to explain to an intelligent audience to-day what are the essential elements of the kinetic theory of matter, but I will at least carry enough of these coals to make a logical stepping-stone from the familiar to the unfamiliar.
The kinetic theory, then, when divorced from all non-essentials, is merely the assertion that everything in this world of ours is in a state of restless, ceaseless, seething motion, that all matter is composed of minute parts called molecules which are eternally pounding and jostling against one another. In gases these molecules are so far apart that the forces of attraction which exist between them are quite negligible and they dart hither and thither like gnats in a swarm, only with the stupendous speed of a mile a second (in the case of hydrogen) and richochette unceasingly against one another and the walls of the containing vessel, producing by this bombardment all the familiar phenomena of pneumatic tires and gaseous bodies generally. If you could magnify the air in an ordinary room just a thousand million times, that is, enough to make a good-sized marrowfat pea swell to the size of the earth, yore would see objects about as big as a football—we will not say of what shape, because we do not know anything about it, but they would probably be of the same shape in a given gas—and if the motions would stop long enough to enable us to get a snap shot of the whole situation, you would see on the average one of these objects in a cubical space ten feet on a side. Then if you let them go again you would see each of these footballs shoot on the average through thirty such imaginary cubical rooms before it hit another. This distance we call the mean free path of a gas molecule.
In the liquid state the molecules are packed closely together by cohesive forces, yet they continually wriggle and squirm over and around one another, so that if you will be content this time with a 10 million-fold magnification, the liquid would look very much like a mass of wriggling squirming maggots—not a pretty picture perhaps, but a fairly accurate one I think.
In solids the molecules are for the most part locked up tightly in crystalline forms so that their motions are reduced to mere trembling. ​unavailing protests against their hard imprisonment. If a biological analogy would make the picture more vivid you can imagine the cages of a menagerie arranged in squares or other regular figures, while the caged animals pace restlessly to and fro between their bars.
Increase in temperature means in all cases increase in the kinetic energy of agitation of the molecules, whatever state they may be in, and one of the fundamental assumptions of the kinetic theory, and one which we can now definitely prove, at least for gases, is that at a given temperature the average kinetic energy of agitation of a molecule is a universal constant, independent of whether the molecule is little or big. If the exact meaning of this statement is not clear, then imagine a lot of molecules of different weights from the big mercury unit down to the little hydrogen unit, one two-hundredth as heavy, led out in succession to a punching bag or to the striking machine at a county fair, and asked to register their strengths. They would, by virtue of a single impact, drive the index to just the same height, the lubberly mercury molecule being able to hit no harder, despite his size, than the tiny hydrogen molecule. This means of course that the hydrogen molecule must have a much larger speed, in fact a speed fourteen times as great in order to make up for his small avoirdupois. Such in brief is the kinetic hypothesis.
This hypothesis has had a long and checkered career in the course of which it has met with nearly all the vicissitudes which can befall a physical theory. Put forth in its most fundamental aspects by Leuoippus and Democritus in the early dawn of Greek thought (about 440 B.C.) it was violently combated by the idealistic philosophers of the ancient world, especially by Plato and Aristotle, and remained altogether fruitless for two thousand years and more, in part, no doubt, because of the adverse influence of these great names. At the beginning of the modern awakening of the intellectual life it was resurrected by Descartes about 1630, and elaborated in considerable detail by Daniel Bernouilli in 1738. Nevertheless, up to the middle of the nineteenth century it remained to the world at large the rather fanciful and naive speculation of a mere handful of philosophers. And although it is significant that this handful contains the names of the most prominent and productive of the makers of modern physics—Newton, Boyle, Eumford. Joule, Clausius, Maxwell, Kelvin, Boltzmann—nothing is more surprising to the student brought up in the atmosphere of the scientific thought of the present than the fact that the relatively complex and intricate phenomena of light and electricity had been built together into fairly consistent and satisfactory theories long before the much simpler phenomena of heat and molecular physics had begun to be correctly understood.
The first tremendous success of the kinetic hypothesis came about ​the middle of the nineteenth century, when it gave birth to the principle of conservation of energy, a generalization which grew immediately and inevitably out of the mechanical theory of heat as it lay in the minds of Rumford, Joule and their co-workers. Between 1860 and 1890 the proofs of the kinetic hypothesis came in so rapidly through the brilliant work of such masters as Joule, Clausius, Maxwell, Kelvin and Boltzmann that the scientific world began to be convinced, and only here and there was found a man of standing among the scoffers. Then, about 1887, a reaction set in, and the school of energetics arose in Germany, which attempted to force the principle of conservation of energy to devour its own mother. The most spectacular of the onslaughts was made by Ostwald, who in 1895 wrote a widely circulated essay, entitled "The Demolition of Scientific Materialism," elsewhere printed under the title, "The Route of Modern Atomism." Led by such a bell-wether, the sheep began to jump back over the wall, and the results of that backward movement are still felt in the United States, particularly in high-school texts, despite the fact that to-day the opposition among scientific men to the kinetic hypothesis is absolutely gone, and even Ostwald has admitted his error. Indeed, so direct and so convincing is now the evidence that it is not too much to say that any one who wishes can now have immediate ocular demonstration of the perpetual dance of the molecules of matter.
But since we are here as much concerned with the atomic or granular theory of electricity as with the kinetic theory of matter, let us turn for a moment to consider the present status of our knowledge as to the nature of electricity. Unlike the kinetic theory of matter, the granular theory of electricity can, boast of no great antiquity. Indeed, in its present form it is but ten or fifteen years old, and in no form is it more than one or two hundred years old. For there are no electrical theories of any kind which go back of our own Benjamin Franklin. It is true that the Greeks discovered that rubbed amber had the power of attracting to itself light objects placed in its neighborhood, but this is all until A.D. 1600, when Queen Elizabeth's surgeon, Gilbert, found that a glass rod and some twenty other bodies, when rubbed with silk, acted like the rubbed amber of the Greeks, and he consequently decided to describe the phenomenon by saying that the glass rod had become electrified (amberized, electron being the Greek word for amber) or had acquired a charge of electricity. In 1733, Dufay, a French physicist, further found that sealing wax, when rubbed with cat's fur, was also electrified, but that it differed from the electrified glass rod, in that it strongly attracted any electrified body which was repelled by the glass, while it repelled any electrified body which was attracted by the glass. About 1847, Benjamin Franklin adopted the following purely arbitrary convention, and said. We will consider that there are ​two kinds of electrification, which we will distinguish by the terms positive and negative, and we will call any body positively electrified if it is repelled by a glass rod which has been rubbed with silk, and we will call any body negatively electrified if it is repelled by sealing wax which has been rubbed with cat's fur. These are to-day our definitions of positive and negative electrical charges. Notice that in setting them up we propose no theory whatever of electrification, but content ourselves simply with describing the phenomena. In the next place it was surmised by Franklin in 1750, and proved very accurately by Faraday in 1837, that when glass is positively electrified by rubbing it with silk, the silk itself takes up a negative charge of exactly the same amount as the positive charge received by the glass, and, in general, that positive and negative electrical charges always appear simultaneously and in exactly equal amounts. So far, still no theory! But in order to have a rational explanation of the phenomena so far considered, particularly this last one, Franklin now made the assumption that something which he chose to call the electrical fluid or "electrical fire" exists in normal amount as a constituent of all matter in the neutral, or unelectrified state, but that more than the normal amount in any body is manifested as a positive electrical charge, and less than the normal amount as a negative charge, Æpinus, an English admirer of Franklin's theory, pointed out that, in order to account for the repulsion of two negatively electrified bodies, it was necessary to assume that matter, when divorced from Franklin's electrical fluid, was self-repellent, i. e., that it possessed properties quite different from those which are found in ordinary unelectrified matter. In order to leave poor old matter, whose independent existence was thus threatened, endowed with its familiar old properties, other physicists of the day preferred to assume that matter in a neutral state shows no electrical properties because it contains as constituents equal amounts of two fluids which they called positive and negative electricity, respectively, and that a positively charged body is one in which there is more positive than negative, and vice versa. The two theories are not, at bottom, very different, since Franklin's modified one-fluid theory required that matter, when divorced entirely from the electrical fluid, have exactly the same properties which the two-fluid theory ascribed to negative electricity, barring only the property of fluidity; so that the most important distinction between the theories was that the two-fluid theory assumed the existence of three distinct entities, named positive electricity, negative electricity and matter, while the one-fluid theory reduced these three entities to two which Franklin called matter and electricity, but which might perhaps as well have been called positive electricity and negative electricity, unelectrified matter being reduced to a mere combination of these two. Whether the electrical fluid (or fluids) was supposed to ​be made up of particles, or to be indefinitely divisible, is not usually stated, though Franklin himself certainly believed in the existence of an electrical particle or atom, for he says: "The electrical matter consists of particles extremely subtle, since it can permeate common matter, even the densest, with such freedom and ease as not to receive any appreciable resistance." When Franklin wrote that, however, he could scarcely have dreamed that it would ever be possible to isolate and study by itself one of the ultimate particles of the electrical fluid. The atomic theory of electricity was to him a pure speculation.
The first bit of experimental evidence which appeared in its favor came in 1833, when Faraday found that the passage of a given quantity of electricity through a solution containing a compound of hydrogen, for example, would always cause the appearance at the negative terminal of the same amount of hydrogen gas, irrespective of the kind of hydrogen compound which had been dissolved, and irrespective also of the strength of the solution; that, further the quantity of electricity required to cause the appearance of one gram of hydrogen, would always deposit from a solution containing silver exactly 107.1 grams of silver. This meant, since the weight of the silver atom is exactly 107.1 times the weight of the hydrogen atom, that the hydrogen atom and the silver atom are associated in the solution with exactly the same quantity of electricity. When it was further found in this way that all atoms which are univalent in chemistry, that is, which combine with one atom of hydrogen, carry precisely the same quantity of electricity, and all atoms which are bi-valent carry twice this amount, and, in general, that valency, in chemistry, is always exactly proportional to the quantity of electricity carried by the atom in question, it was obvious that the atomic theory of electricity had been given very strong support.
But striking and significant as were these discoveries, they did not serve to establish the atomic hypothesis. Indeed, the attention which Faraday himself directed to the rôle played by the medium which surrounded a body carrying a charge, or the wire through which a charge was passing (an electric current) led to a point of view which was distinctly antagonistic to the atomic concept of electricity. This point of view was emphasized very strongly by the followers of Maxwell, notably by Oliver Lodge, who through his book on "Modern Views of Electricity" influenced very largely the points of view adopted by the text-books of the last two decades of the nineteenth century. This view was that an electric charge is nothing more than a "state of strain in the ether," and an electric current, instead of representing the passage of anything definite along the wire, corresponded merely to a continuous "slip" or "breakdown of a strain" in the medium within the wire, whatever these terms may mean. Now there can be no doubt that ​when an electrical charge is placed upon a body, the medium about the body becomes the seat of new forces, and this may be described by saying that the medium about the body has been thrown into a state of strain. But it is one thing to say that the electrical charge on the body produces a state of strain in the surrounding medium, and quite another thing to say that the electrical charge is nothing but a state of strain in the surrounding medium, just as it is one thing to say that when a man stands on a bridge he produces a mechanical strain in the timbers of the bridge, and another thing to say that the man is nothing more than a mechanical strain in the bridge. The practical difference between the two points of view is that in the one case you look for other attributes of the man besides the ability to produce a strain in the bridge, and in the other case you do not look for other attributes. So the strain theory, although not irreconcilable with the atomic hypothesis, was actually antagonistic to it, because it led men to think of the strain as distributed continuously about the surface of the charged body, rather than as radiating from definite spots or centers peppered over the surface of the body. Between 1850 and 1900, then, the physicist was in the following anomalous and inconsistent position: When he was thinking of the passage of electricity through a solution, he pictured to himself definite specks or atoms of electricity as traveling through the solution, each atom of matter carrying an exact multiple of a definite elementary electrical atom; while, when he was thinking of the passage of a current through a metallic conductor, he gave up altogether the atomic hypothesis, and attempted to picture the phenomenon to himself as a continuous "slip" or "breakdown of a strain" in the material of the wire.
About 1900, however, a great stride forward was taken when the atomic hypothesis began to be applied to metallic conductors as well as to solutions, and electrical currents, even in wires, began to be looked upon as due to the transport through the wire of discrete units of electricity, now beginning to be called electrons, these units being either handed on from atom to atom or else being pushed along through the interstices between the atoms. This point of view, which was a return to Franklin's way of thinking, found its new justification in the fact that it was found possible in vacuum tubes of the X-ray type to obtain from all kinds of matter very minute electrically charged bodies of negative sign, which under all circumstances showed exactly the same behavior in electrical and magnetic fields and which had a mass which was computed to be but 1/1,760 the mass of the atom of hydrogen, the smallest known atom of matter. There was indeed no direct proof that the charges of these bodies were all the same, since no method had been found of examining them individually, nevertheless, it was pretty conclusively shown, as early as 1899, by Townsend of ​Oxford, that the mean value of the charge carried by these electrons was the same as the charge carried by the hydrogen atom in electrolysis; and about the same time Sir J. J. Thomson found a way of making a rough determination of the absolute value of this mean charge. This method was improved in 1902 by H. A. Wilson, now of McGill University, and actually formed the starting point some five years later of the work out of which grew, by a series of natural steps, the experiments which are herewith presented and which have made it possible to capture and make accurate measurements upon one single isolated
electron or any desired number of such electrons up to one hundred and fifty.
Imagine two circular plates M and N (Fig. 1) 22 centimeters (about 10 inches) in diameter and 16 millimeters (f inch) apart which can be electrically charged, one positively and the other negatively, by making them the terminals of a ten-thousand-volt storage battery B. Suppose also that with the aid of a switch S the plates can be instantly discharged when desired so as to possess no electrical properties at all. Now when the plates are suddenly charged the air between them is found to remain perfectly quiet and free from convection currents of any kind—a result which shows that practically all of the air molecules between the plates are electrically neutral. But if now a beam of ​X-Rays is allowed to play upon the air between these two plates, it is found that some of these neutral air molecules are split up by the X-rays into electrically charged parts, which fly instantly, one part to plate M and the other part to plate N. This shows conclusively that the ordinary neutral molecules of the air possess electrical constituents, that is, that they contain equal quantities of positive and negative electricity.
Fig. 2. A, arc light for illuminating droplet. H, chronograph for measuring speeds of droplet. R, lens for making the beam from the arc parallel or slightly convergent. I, shutter for intercepting altogether the light from the arc save when a reading of a transit of an "oil star" over a cross-hair was to be taken. This was used to insure entire stagnancy of the air between the plates M and N (Fig. 1). E, high potential static voltmeter from measuring PD produced by B. P, mercury pressure gauge or manometer for measuring the pressure of the air within C. C, airtight brass chamber containing the plates M and N of Fig. 1. W, pressure pump for forcing a puff of air through the atomizer inside of C and above the plates M and N. The same pump is also used for exhausting the cylinder C. T, telescope for observing illuminated droplet. S, switch for throwing on or off the electric field between the plates. B, ten-thousand-volt storage battery. T, spot of light produced by the beam after passing through the two windows of the chamber C. Q, opening in lead box through which X-ray beam emerges on its way to chamber C, where it ionizes the gas between plates M and N of Fig. 1. X, X-ray bulb. O, cylindrical glass trough 80 cm. long filled with water for absorbing the heat rays from the arc.
Both ultra-violet light and the rays from radium possess, like the X-rays, the power of thus ionizing a gas, and even when no external ionizing agent whatever is at hand, it is found that out of the 27 billion billion molecules which are present in each cubic centimeter of ordinary air, from two tO twenty split up per second into ions. As will presently be shown, this process of ionization consists in the detaching from a neutral molecule of an exceedingly minute fraction of its ​constituent negative electricity—an electron—so that the residue of the molecule is probably just like the neutral molecules of the surrounding gas, save that it now carries a free or unbalanced positive charge corresponding to the negative charge of the electron which it has lost. The escaped electron probably soon attaches itself to a neutral molecule, so that shortly after the decomposition of a molecule, the gas is in the same condition as it was before the decomposition, save that two of its previously neutral molecules are now electrically charged, one positively and the other negatively. Whether this molecular decomposition which goes on continually in ordinary air is due to rays from traces of radio-active substances, which are present at all times in the air, or whether it is due to an occasional spontaneous explosion of a molecule, we can not as yet be absolutely certain, though the evidence is at present strongly in favor of the former hypothesis. But, however they may be formed, there can be no doubt of the presence of these ions in the atmosphere at all times, to the extent of from 1 to 15 per cubic millimeter, nor can there be any doubt that it is these atmospheric ions which are responsible for all the manifestations of atmospheric electricity which have been the object of man's awe and worship throughout all ages.
Now the problem which was set for this investigation was to catch individual ones of these atmospheric ions and to find what sort of charges they possess. A detective which could be set on the trail of a thing so small had evidently to be a distinctly undersized member of the force. It was in fact an oil-drop so minute as to be little more than visible through the most powerful microscope. In these experiments, however, no such high-power microscope was needed, for in a sufficiently powerful beam of light the oil droplet could be made to appear as a bright dot even to the naked eye in spite of its minuteness. The method of setting it at work was this. A spray of oil was blown from an ordinary commercial atomizer A into a dust-free chamber C, and one or more of the oil droplets was allowed to fall through a pin hole at p into the space between M and N. As it floated there, slowly falling under gravity, it was illuminated by a powerful beam from an arc light, which passed through diametrically opposite windows in the encircling ebonite strip c. It was viewed through a third window placed on the emergent side of the beam about fifteen degrees from its direction. A glance at the accompanying photograph, which shows a modification of the device, used for work at low pressures (see below), will make clear the arrangement of the different parts of the apparatus in the experiment now under consideration. The appearance of this drop of oil in the observer's short focus telescope through which it was viewed was that of a brilliant star on a black background. ​Before this star reached the lower plate the electrical field was thrown on and it straightway began to rise again toward the plate M. This was because in the atomizing process the droplet in general received a frictional charge; for, as is well known, strong frictional processes always produce electrification. If this charge was of the wrong sign to cause the drop to rise, rather than descend, when the 10,000-volt battery was thrown on, the signs of the charges on M and N were reversed. When the drop had been pulled up close to M the plates were discharged and the drop allowed to fall under gravity again until it was close to N. In this way, by alternately throwing on and off the electrical field, the oil drop detective was kept pacing its beat up and down between the plates in the hope that it would catch and hold some unwary ion which came within its reach. The first time the experiment was tried an ion was caught within a few minutes and the fact of the capture had been signalled to the observer by the change in the speed with which the drop moved up when the electrical field was on; for since the ion carried an electrical charge, its advent upon the drop changed the charge on the latter and therefore changed the speed with which it was pulled up toward M. If the sign of M was positive, then the drop itself, in order to be pulled up by the field, must have had a negative charge and in that case the capture of a positive ion reduced this negative charge and therefore reduced the speed in the field, while the capture of a negative ion increased the negative charge and hence increased the speed in the field. From the sign, then, and the magnitude of this change in speed, taken in connection with the constant speed under gravity, the sign and the exact value of the charge carried by the captured ion could be easily determined.
A drop would often be kept traveling back and forth in the manner described for four or five hours at a time, in the course of which it would change its charge twenty or thirty times because of the capture of ions and the value of each of these different charges would be computed. The beauty and precision of the measurements and the certainty with which the atomic theory of electricity follows from the results obtained can best be appreciated by inserting in full the record of an experiment made upon a particular drop. The column headed G gives the successive times which the droplet required to fall between two fixed cross-hairs in the observing telescope whose distance apart corresponded in this case to an actual distance of fall of.5222 centimeter. It will be seen that these numbers are all the same within the limits of error of a stop watch measurement. The column marked F gives the successive times which the droplet required to rise under the influence of the electrical field produced by applying in this case 5,051 volts of potential difference to the plates M and N. It will be seen that after the second trip up, the time changed from 12.4 to 21.8, indicating, since in ​this case the drop was positive, that a negative ion had been caught from the air. The next time recorded under F, namely, 34.8, indicates that another negative ion has been caught. The next time, 84.5, indicates the capture of still another negative ion. This charge was held for two trips, when the speed changed back again to 34.6, showing that a positive ion had now been caught which carried precisely the same charge as the negative ion which before caused the inverse change in time, i. e., that from 34.8 to 84.5.
| | G. | F. |
| | 13.6 | 12.5 |
| | 13.8 | 12.4 |
| | 13.4 | 21.8 |
| | 13.4 | 34.8 |
| | 13.6 | 84.5 |
| | 13.6 | 85.5 |
| | 13.7 | 34.6 |
| | 13.5 | 34.8 |
| | 13.5 | 16.0 |
| | 13.8 | 34.8 |
| | 13.7 | 34.6 |
| | 13.8 | 21.9 |
| | 13.6 | |
| | 13.5 | |
| | 13.4 | |
| | 13.8 | |
| | 33.4 | |
| Mean | 13.595 |
Now all of the successive values of the charge carried by the drop throughout the experiment can be easily computed from the constant speed under gravity and the successive values of the speed in the electric field. To find the absolute values of these charges it is indeed necessary to know the weight of the drop, and the determination of this weight may involve an error of a fraction of a per cent, at most, but since this weight remains constant throughout the experiment the relative values of the successive charges can be found with absolute certainty and with great precision without any knowledge of this weight. They are in fact simply proportional to the successive values assumed by the sum of the two speeds, viz., that under gravity and that in the field. ​Similarly the charge carried by any captured ion is proportional to the change produced in this sum by the capture. Now the change in this sum produced by the capture of the ion which caused the time in column F to change from 34.8 to 84.5 was, as any one who wishes can verify, .00891 cm. per sec. and the successive values of this sum arranged in order of magnitude were .04456, .05347, .06232, .07106, .08038. If now electricity is atomic in structure all the different charges appearing in this experiment, those on the ions and those on the drop, should be exact multiples of the elementary unit of charge, which means that all of the numbers above given should be exact multiples of something. Dividing the above five numbers by 5, 6, 7, 8 and 9, respectively, gives .008912, .008911, .008903, .008883 and 008931, which are all seen to be within one fifth of one per cent, of the value of the change in the sum of speeds produced by the capture of the ion which caused the numbers in the column F to change from 34.8 to 84.5. Hence the charge carried by this ion was itself the elementary unit out of which all of the other charges which appeared in the experiment were built up. The results on another drop which was observed through a much longer time, namely, about four and a half hours, are given in the following table:
| n | 4.197 $\times$ n | Observed Charge | n | 4.197 $\times$ n | Observed Charge |
| 1 | 4.917 | —— | 10 | 49.17 | 49.41 |
| 2 | 9.834 | —— | 11 | 54.09 | 53.91 |
| 3 | 14.75 | —— | 12 | 59.00 | 59.12 |
| 4 | 19.66 | 19.66 | 13 | 63.92 | 63.68 |
| 5 | 24.59 | 24.60 | 14 | 68.84 | 68.65 |
| 6 | 29.50 | 29.62 | 15 | 73.75 | —— |
| 7 | 34.42 | 34.47 | 16 | 78.67 | 78.34 |
| 8 | 39.34 | 39.38 | 17 | 83.59 | 83.22 |
| 9 | 44.25 | 44.42 | 18 | 88.51 | —— |
In this table 4.917 is merely a number obtained, precisely as above, from computing the change in the "sum of speeds" produced by the capture of a particular ion, while the column headed "observed charge" gives the successive values of the sum of speeds. It will be seen that during the experiment this drop carried all possible multiples of the elementary charge between 4 and 18, save only 15. No more exact or more consistent multiple relationship is found in the data which chemists have amassed on the combining powers of the elements, and on which the atomic theory of matter rests, than is found in the above numbers.
Nearly a thousand different drops have been examined in the manner indicated, some of them being of oil, a non-conductor, some of glycerine, a semi-conductor, some of mercury, a good conductor, and some of other substances, and in every case, without a single exception, the initial charge placed upon the drop by the frictional process, and all of the dozen or more charges which have resulted from the capture by the drop of a larger or smaller number of ions, have been found to be exact ​multiples of the smallest charge caught from the air. Some of these drops have started with no charge at all, and one, two, three, four, five and six elementary charges or electrons have been picked up. Others have started with seven or eight units, others with twenty, others with fifty, others with a hundred, others with a hundred and fifty elementary units and have picked up in each case half a dozen elementary charges on either side of the starting point, so that in all oil drops containing every possible number of electrons between one and 150 have been observed and the number of electrons which each drop carried has been accurately counted. It is not found possible to count with certainty the number of electrons in a charge containing more than 200 of them, for the simple reason that the method of measurement used fails to detect the difference between 200 and 201. But it is quite inconceivable that large charges such as are dealt with in the commercial applications of electricity can be built Tip in an essentially different way from that in which the small charges whose electrons we are able to count are found to be. Furthermore, since it has been definitely proved that an electrical current is nothing but the motion of an electrical charge over or through a conductor, it is evident that the experiments under consideration furnish not only the most direct and convincing of evidence that all electrical charges are built up out of these very units or electrons which we have been dealing with as individuals in these experiments, but that all electrical currents consist merely in the transport of these electrons through the conducting bodies.
The next important question which the above method of experimenting seemed calculated to throw additional light upon is, "What does the ionization of a gas molecule consist in?" Since it is now practically certain that a molecule of air, that is a molecule of nitrogen or oxygen, contains at least a hundred electrons, and possibly very many more, the act of ionization might consist in the knocking out from a single one of these molecules of a large number of electrons, or it might consist in the complete shattering of an atom by some sort of explosive process; or, on the other hand, it might consist merely in the detaching of a single electron from a neutral molecule, thus leaving the molecule essentially the same sort of thing that it was before the ionization took place, save that it has acquired an amount of electricity of the opposite sign equal to that of the charge detached. Some little light can be thrown on this question by studying the observations already presented. In these observations, however, all the changes of charge took place when the drop was falling under gravity, that is, when the electrical field was off, and this for the reason that the chance which a drop has of capturing an ion when the field is off is enormously greater than its chance of catching one when the field is on, since, in the latter case, the electrically charged fragments of an atom, formed by the ionization of a ​neutral molecule, are thrown instantly to the plates M and N, their speeds in the field here used being something like five or ten thousand centimeters per second; but, when the field is off, these ions remain in the air between the plates, and, sooner or later, as their number increases, one or more of them comes into contact with a drop and sticks to it. If we look now at the changes which occurred in the experiment recorded, we see that the first change in the time in the field, namely, that from 12.45 to 21.85, represented the advent upon the drop of 2 unit charges, since the 16-second time which is found later in the table was skipped in this catch. All the other changes in the table, save one, namely, that from 34.8 to 16.0, represented the advent of single charges, and this one represents again the advent of a double charge since the 21.9 second speed was here skipped. This indicates that there are probably no ions which have a very large number of units of excess of one kind of electricity upon them, but it gives us no information as to whether the act of ionization consists in the detachment of only one elementary electrical charge from a neutral molecule, or of two or three; for, so long as the changes are occurring when the field is off, it is impossible to distinguish between the capture of a single ion carrying two or three units of charge, and the successive capture of two or three ions each carrying the unit charge.
It was necessary, therefore, to catch the ions at the very instant of their formation, or better, to catch a molecule in the very act of splitting up into ions. Accordingly, the experiment was modified as follows. By suitably adjusting the PD between the plates M and N, it was found possible to hold a minute positively charged drop suspended, like Mohammed's coffin, as long as desired between heaven and earth, that is, in this case between M and N, the downward pull of gravity being exactly neutralized
by the upward pull of the field. Having obtained a drop in this position, there was produced beneath it a sheet of X-ray ionization in the manner shown in Fig. 3, so that when the X-ray bulb was excited, the drop was in a veritable shower of the charged positive residues of the molecules broken up by the X-rays. Now, if two or more electrons were ​knocked out of a molecule at once, the residue of the molecule would possess a corresponding number of unit charges, and if this residue were caught by the oil drop, the latter should be seen to jump forward at the instant of capture because of the destruction of the equilibrium between gravity and the electric field; and, furthermore, from the speed which it assumed, as measured by the time which it took to move over a given number of the divisions in the scale of the eye-piece of the observing telescope, the size of the charge of the captured ions could be determined. The experiment was found to be as interesting and as exciting as trout fishing. The star under observation would often stand perfectly still for five, ten, fifteen or even sixty seconds and then suddenly start forward with a speed which was big or little according to the size of the catch and the size of the drop. When we were using large drops, it was found that two or three adjacent molecules were in occasional instances ionized at once, and therefore two or three separate ions were thrown simultaneously upon the drop, but when the drops were very small, we observed in the course of three months about 500 different catches without finding a single one which corresponded with certainty to the advent of an ion carrying more than one elementary electrical charge, and not more than three or four out of the five hundred which were in any way uncertain. This seems to prove conclusively that the act of ionization by all the types of X-rays and gamma and beta rays of radium which we have been able to try consists in the detachment from a neutral molecule of one single electron.
So far we have considered merely the proof afforded by the present experiments of the atomic theory of electricity. I have not attempted to tell "what electricity is," but have been content with demonstrating, that whatever it is it always appears as an exact multiple of a definite electrical unit. If you ask me to tell you what it is, I should answer by asking you first to tell me what matter is, and if you responded that matter is that out of which this world and the planets and the stars of this universe are made; that it is something which exists in the form of about 100 different units, or atoms, of relative weights between 1 and 240, which atoms unite together in different ways to form molecules; that the average diameter of one of these atoms is two hundred-millionths of a centimeter, then I should answer. Very well, if you are content with that sort of a definition of matter, I will define electricity for you in a similar way and say that electricity is something which is still more fundamental than your atoms of matter since it is a constituent of every one of these hundred different types of atoms which you have been describing. It is something too, which like matter is built up out of definite units, but it is unlike matter, in that all of these units are exactly alike so far as we are able to determine, save, however, that a marked difference is found between the positive and negative units. For ​while the two possess the same charge, the inertia or mass which, so far as we know, is inseparably associated with a positive unit is that of a hydrogen atom, while that inseparably associated with the negative unit is 1/1.760th as much. The negative units, furthermore, or electrons, are so small in volume and are separated from one another within the atom by so large spaces, that one of them can shoot through hundreds and thousands of atoms without hitting anything or doing anything whatever to these atoms. Its diameter is about one one-hundred-thousandth of that of the atom. It is the smallest thing we know anything about so far—probably the smallest thing in existence. Such an enumeration of properties is as near to a definition of electricity as we can come now or are ever likely to be able to come. For, since electricity is the most fundamental thing thus far known to us, it is obviously incapable of definition in terms of anything more fundamental. Its elementary unit, according to the best determination which we have yet been able to make, is 4.80 times 10$^{-10}$ so called electrostatic units, a quantity so small that the electrical charge produced by a single stroke of a cat's back contains billions of them, while the number which courses each second through the filament of a common 16 candle power incandescent lamp is about a billion billion. The electron is thought by many reputable scientists of the present day to be the primordial thing out of which all matter is built up, so that from this point of view the different atoms of ordinary matter are merely different groupings of these fundamental electrical units.
Turning next to the kinetic theory of matter, what have the present experiments to do with it? There are three different ways in which they bring to it powerful support. When these experiments were begun it was anticipated that positively charged ions would be caught by negatively charged oil drops and negatively charged ions by positively charged oil drops, but it had not been predicted that positively charged drops would catch positive ions and negatively charged drops negative ions; for since electrical charges of like sign always repel each other, it might be thought that positive drops would push away positive ions and negative drops negative ions. As a matter of fact, however, positive ions were found to be caught by positive drops about as readily as the negative ions and vice versa. The above table shows several catches of this kind. Whence, then, do positive ions obtain the energy which enables them to push themselves up to the surface of a positive drop against the electrical repulsion existing between the two? This energy could not have been obtained from the field, since the capture of the ions occurred when the field was not on. It could not have been obtained from any explosive process which frees the electron from the molecule at the instant of ionization, since in this case, too, ions would have been caught as well, or nearly as well, when the field was on as when ​it was off. Here, then, is an absolutely direct proof that the ion must he endowed with a kinetic energy of agitation which is sufficient to push it up to the surface of the drop against the electrostatic repulsion of the charge already existing on the drop, and when we remember that an ion is nothing but a molecule containing an unneutralized electrical charge, it will be clear that we have here direct proof that the molecules of the gas are endowed with motion.
Furthermore, it is easy to obtain the energy of this motion, for, if we load up the drop with more and more positive charges, the push which it will exert on positive ions within the gas must become greater and greater, and hence the frequency with which positive ions will be captured from the gas should become less and less. Now this is exactly what was observed to be the case, and, indeed, in one instance, a relatively heavily charged drop was watched for four hours, during which time it succeeded in picking up but one single ion of its own sign while the field was off, although it was continually picking up ions of the opposite sign. Its charge was during all this time maintained at about the same value by forcing ions of its own kind upon it when the field was on. We had then here a charged drop which exerted just enough repulsion upon the positive ions of the gas to overcome their kinetic energy of agitation when they shot toward it. By knowing the size of the drop and the charge which it carried, it was easy to compute from these two quantities just what this kinetic energy of agitation had to be in this case. It came out within a few per cent, of the value of the kinetic energy of agitation of the molecules as given by the kinetic theory.
But even this evidence is not sufficiently direct to convince a skeptic untrained to follow the computation, simple though it be. Hence a proof was sought which involved no knowledge whatever of either mathematical or physical theory. Fortunately the trail had already been blazed and nothing had to be done but to clear out some of the remaining underbrush which obscured it. It had been discovered as early as 1827 by an English botanist, Brown, that microscopic particles in a liquid keep up incessantly a very minute trembling motion and this phenomenon remained altogether unexplained for more than half a century. At last in 1888 it was suggested by Gouy in France that this trembling motion was probably due to the fact that when a particle is sufficiently small the molecular bombardment which it receives from the molecules surrounding it is not at a given instant exactly the same on opposite sides, and in consequence the particle is pushed first in one direction and then in another by these unbalanced molecular forces. In 1908, Perrin, in Paris, with the aid of a formula deduced by Einstein of Bern, had brought forward quite convincing evidence that this explanation was correct, but Perrin's observations had all been made upon ​minute particles suspended in liquids, and liquids are very much less suited to any convincing and accurate test of the kinetic hypothesis than are gases. Apparently the very great advantages of observing minute suspended particles in a gas at very low pressures, where the motions ought to be enormously increased, had not been appreciated, or, at least, had not been utilized, perhaps because the means had not before been at hand for keeping such particles in suspension. Accordingly, the plates M and N, shown in Fig. 1, with the atomizer attached, were placed inside a large brass cylinder, which could be sealed air tight and exhausted if desired. This apparatus is shown in the photograph on p. 426. When the air was at atmospheric pressure, the smallest particles produced by the aspirator showed clearly the incessant wiggling motions which are called, after their discoverer in liquids, the "Brownian movements." But, when the pressure was reduced to seven or eight millimeters of mercury (about 1/100 of an atmosphere), these motions had increased so enormously in violence that it was difficult to follow the smallest particles as they dashed hither and thither like wrigglers in a water barrel. The reason that reducing the pressure brings out the motion so much more clearly is obviously this; When the oil drop is surrounded by a dense swarm of bombarding molecules, it is like a football in a melee of densely packed players who are kicking it on all sides at once, but are unable to send it any appreciable distances. But when it gets out into the open, where the players are scarce, it begins its spectacular flights. Precisely so with the oil drops, and no football game was ever more spectacular or more fascinating than the behavior of one of these oil drops at low pressures. The fact that the motions increase in violence the rarer the gas becomes and the smaller the particles are taken (size being indicated by the speed with which a given particle settles under gravity) is obviously just what ought to happen. There can not then be the slightest doubt that what these oil drops are doing, namely, dancing about violently in all sorts of directions, is precisely what the molecules themselves are doing in a much more excited way for it would be absurd to suppose that the increased speed and the increased distance of the motions as size and mass diminish do not go on after the particles cease to be visible and shrink to molecular dimensions. From the standpoint of a molecule which is darting hither and thither with the speed of a rifle bullet, our dancing oil drops must look like snails crawling about with languorous slowness. But to us they have served their purpose, for they have enabled our minds to see the invisible molecular world doing in a large way just exactly what the oil drops are doing in their small way. They have proved the kinetic theory of matter even to the man on the streets.
But in order literally to pile Ossa upon Pelion in support of this hypothesis, let us next turn to a rigorously quantitative demonstration, ​for, while seeing the oil drops dance may satisfy the average man, it will not satisfy the scientist, for he is never content until he has two parallel columns headed, respectively, "calculated" and "observed" values. How shall we set about obtaining such parallel columns? The way was blazed by Einstein in 1905. He showed that if a body like one of our minute oil drops is dancing about in a resisting medium subjected to no forces but those arising from its own energy of agitation, that is, from the bombardment of the surrounding molecules, the mean distance which it will drift in a given time, say ten seconds, from its position at the beginning of this time, can be computed in terms of three factors: (1) its energy of agitation, (3) a resistance factor of the medium, and (3) the length of the time interval through which the drift is observed. But this same quantity can also be easily and directly observed in our experiment by simply balancing the force of gravity upon the drop by the force of an electrical field in the manner already described, and then noting over how large a distance on the average it wiggles in a given time by virtue of its energy of agitation. In the actual experiments we took, in the case of each drop, the mean of several hundred observations on the distance moved in ten seconds in a vertical direction over a set of horizontal scale divisions placed in the eye-piece of the observing telescope; for Einstein's theory was developed in such a way that the movements to right and left did not need to be considered. The computed and the observed values of this average displacement were in every case in so perfect agreement as to satisfy the most skeptical of scientists that the kinetic theory can successfully meet a rigorous and exacting kind of quantitative test.
But in order to show how free from uncertainties of any sort are the results of this comparison it will be necessary to say just a word more about the theory, for the question is at once raised "how, in computing the theoretical value of the average displacement of the drop, do you obtain the first two of the factors in terms of which this displacement is given, namely, the kinetic energy of agitation of the drop and the resistance factor of the medium?" We obtain a partial answer to this question when we remember that one of the fundamental assumptions of the kinetic theory is that the energy of agitation of a molecule is determined by temperature alone, and is independent of ​whether the molecule is large or small. Hence, the energy of agitation of our oil drop ought to be exactly the same as that of one of the molecules of the gas which surrounds it. But this is the quantity which we have just determined experimentally, and which, furthermore, can be computed with great precision from the kinetic theory.
Hence, we may consider that this quantity is known. The second factor, however, is not known with certainty, except under conditions which may or may not be fulfilled in any experimental work, and herein lies the uncertainty in all preceding attempts like those of Perrin to subject the kinetic theory of Brownian movements to any rigorous experimental test. Fortunately for the present work, however, this factor does not need to be known at all. For obviously the resistance which the medium offers to the motion at a given speed of this particular drop though it must be the same whether it is an electrical force, a gravitational force, or a force arising from molecular bombardments which is causing the motion. Consequently all that was necessary for us to do in order to eliminate this resistance factor entirely was first to observe the successive displacements of the balanced drop as indicated above and then to destroy the balance and measure how fast the drop moved on the average, both under gravity and under an electrical field of known strength, in precisely the way we had done when we were determining the successive values of the charge carried by the oil drops. From the results of the two experiments we could then eliminate the resistance factor and obtain the average displacement in terms of quantities every one of which was measurable with the greatest precision. Indeed the experimental error in measuring the ​average displacement was far 'greater than the uncertainty in any of the factors in terms of which this displacement was computed. Nevertheless, the final result obtained from the average of 1,735 displacement observations on nine different drops was within less than one fourth of one per cent, of the computed value, and the probable error in this result was but six tenths of one per cent.
All of these computations relating to the Brownian movements were carried out most skilfully by Dr. Harvey Fletcher. It should be added, too, that in only a portion of the experiments was the observed value of the displacement obtained in precisely the manner indicated above, for it was found that greater accuracy could be obtained in the measurement of this displacement by a slight modification of the method. To make this modification applicable, however, a considerable amount of new and important theoretical work had to be done. This work was most ably and successfully carried out by Dr. Fletcher, and can be found in the August number of the Physical Review.
It would seem as though the evidence for the kinetic theory were so overwhelming as to convince every type of skeptic except the one whose mental attitude is that of the farmer who had never seen any save farm-yard animals until he went one day to the circus and stood for some moments looking in amazement at the dromedary; then turning away, he exclaimed, "By gosh, there ain't no such animal." That type of disbeliever I am at a loss to know how to convert.
In conclusion it may be pointed out that not only has it now become possible to prove the correctness of the kinetic theory of matter and the granular theory of electricity, but that, through the results of experiments like the above on the elementary electrical charge, we are now able to determine the exact weight of every atom and every molecule of every known kind of matter, the exact number of molecules in any weight of any substance, the exact value of the kinetic energy of agitation of a molecule, the mean diameter of any kind of molecule, and quite a series of other important physical magnitudes. The first three of these quantities can be found with precisely the degree of accuracy attained in the measurement of the elementary electrical charge, and this is an accuracy of about one part in a thousand. Not that I am ready to assert that the value which has been given above possesses that degree of certainty; but rather that we now have a method which is capable of yielding such precision, and the rest is merely a matter of
​time and of careful work. We are at present engaged not only in checking this value under new sets of conditions, but in redetermining all of the quantities which enter into it. Assuming it as the basis of our computation there are in a cubic centimeter of gas under normal conditions $2.70\times 10^{19}$ molecules and the weight of a hydrogen atom is $1.735\times 10^{-24}-grams$. These numbers can be made more significant to the ordinary reader with the aid of an illustration. If a million men were to be set counting as fast as they could count, say at the rate of 200 a minute, they could count out the number of molecules in a cubic centimeter in just 252 thousand years if none of them ever stopped to eat, sleep, or die.
"But," says some one, "What of it any way? Does the triumph or defeat of the kinetic theory of matter or the atomic theory of electricity have anything to do with the practical problems of the modern world? Is anybody going to be better fed or better clothed because of it?" the answer is, "Within the past seventy-five years—the merest drop in the bucket of recorded time—the conditions of human life on this earth have been completely revolutionized, and that solely because, for the first time in history, man has become interested in considerable numbers, rather than, as heretofore in isolated instances, in patiently and persistently seeking merely to uncover nature's 'useless' secrets, and then, when the inner workings have been laid bare, has in many cases seen a way to put his brain inside the machine and drive it where he would. Every increase then in man's knowledge of the way in which nature works must in the long run increase by just so much man's ability to control nature and to turn her hidden forces to his own account."
* ↑ For in the case of bodies moving slowly and uniformly through a resisting medium any two forces produce velocities which are proportional to the forces. The downward force due to gravity is here mg and the upward force due to the field is Fe, in which F denotes the strength of the field and e the charge on the drop. Hence, if v$_1$ is the downward velocity due to gravity and v$_2$ the upward velocity due to the excess of the upward pull of the field over the downward pull of gravity, we have $\scriptstyle {\frac {v_{2}}{r_{1}}}={\frac {mg}{Fe-mg}}\ or\ e={\frac {mg}{Fv_{1}}}\ (v_{1}+v_{2})$
* ↑ Einstein's actual equation is $\scriptstyle D^{2}=4/3\ .\ E/K\ .\ t$, in which $D^{2}$ is a quantity obtained by squaring each individual displacement and then taking the mean of these squares, E is the mean kinetic energy of agitation of the drop, K is a resistance factor depending upon both the medium and the drop, and t is the length of the time interval used. If the average displacement D is used instead of the average square of the displacements $D^{2}$ the correct form of the equation is $\scriptstyle D={\sqrt {\frac {8}{3\pi }}}{\frac {E}{K}}t$.
* ↑ The kinetic theory equation is $\scriptstyle E=3/2.RT/N$ in which E is the mean energy of molecular agitation, R an accurately known gas constant, T the absolute temperature, and N the number of molecules in 2 grams of hydrogen. Although N is not accurately known save through experiments of this sort, it fortunately does not need to be known, as will be shown in the next footnote, for the quantitative test here sought. When the above value of E is substituted in the equation of the last footnote it becomes $\scriptstyle D={\sqrt {\frac {4}{\pi }}}{\frac {RT}{NK}}t$.
* ↑ When the drop is moving down through the medium under the force of gravity, mg, alone, its average velocity v is given by $\scriptstyle mg=Kv_{1}$. The substitution of this value of $\scriptstyle mg/v_{1}$ in the equation of the footnote on page —— gives $\scriptstyle e=K/F.(v_{1}+v_{2})$ and the elimination of K between this equation and that given in the preceding footnote gives $\scriptstyle D={\sqrt {\frac {4}{\pi }}}{\frac {RT(r_{1}+v_{2})t}{FE(Ne)}}$. Since D was of course different for different drops instead of making the comparison between the observed and calculated values of D it was thought preferable to make the comparison in every case between the value of Ne obtained from this equation and these experiments and the value of Ne obtained from experiments on electrolysis; for Ne is merely the amount of electricity required to separate by electrolysis one gram-equivalent of any substance from a solution. The value of $\scriptstyle {\sqrt {N}}e$ obtained from the most accurate experiments on the electrolysis of silver is $\scriptstyle 1.702\times 10^{7}$ electrostatic units. The mean value of $\scriptstyle {\sqrt {N}}e$ obtained from 1,735 displacement measurements upon nine different drops was $\scriptstyle 1,698\times 10^{7}$ electrostatic units.