CHAPTER IXTHE STRUCTURE OF THE ATOM
We have shown in the preceding chapters how within the last two decades there has been discovered beneath the nineteenth-century world of molecules and atoms a wholly new world of electrons, the very existence of which was undreamed of twenty years ago. We have seen that these electrons, since they can be detached by X-rays from all kinds of neutral atoms, must be constituents of all atoms. Whether or not they are the sole constituents we have thus far made no attempt to determine. We have concerned ourselves with studying the properties of these electrons themselves and have found that they are of two kinds, negative and positive, which are, however, exactly alike in strength of charge but wholly different in inertia or mass, the negative being commonly associated with a mass which is but ¹⁄₁₈₄₅ of that of the lightest known atom, that of hydrogen, while the positive appears never to be associated with a mass smaller than that of the hydrogen atom. We have found how to isolate and measure accurately the electronic charge and have found that this was the key which unlocked the door to many another otherwise inaccessible physical magnitude. It is the purpose of this chapter to consider certain other fields of exact knowledge which have been opened up through the measurement of the electron, and in particular to discuss what the physicist, as he has peered with his newly discovered agencies, X-rays, radioactivity, ultra-violet light,etc., into the insides of atoms, has been able to discover regarding the numbers and sizes and relative positions and motions of these electronic constituents, and to show how far he has gone in answering the question as to whether the electrons are the sole building-stones of the atoms.
1. THE SIZES OF ATOMS
One of the results of the measurement of the electronic charge was to make it possible to find the quantity which is called the diameter of an atom with a definiteness and precision theretofore altogether unattained.
It was shown inchap. Vthat the determination ofgave us at once a knowledge of the exact number of molecules in a cubic centimeter of a gas. Before this was known we had fairly satisfactory information as to the relative diameters of different molecules, for we have known for a hundred years that different gases when at the same temperature and pressure possess the same number of molecules per cubic centimeter (Avogadro’s rule). From this it is at once evident that, as the molecules of gases eternally dart hither and thither and ricochet against one another and the walls of the containing vessel, the average distance through which one of them will go between collisions with its neighbors will depend upon how big it is. The larger the diameter the less will be the mean distance between collisions—a quantity which is technically called “the mean free path.” Indeed, it is not difficult to see that in different gases the mean free pathis an inverse measure of the molecular cross-section. The exact relation is easily deduced (seeAppendix E). It isin whichis the molecular diameter andis the number of molecules per cubic centimeter of the gas. Now, we have long had methods of measuring,for it is upon this that the coefficient of viscosity of the gas largely depends. When, therefore, we have measured the viscosities of different gases we can compute the corresponding’s, and then from equation (31) the relative diameters,sinceis the same for all gases at the same temperature and pressure. But the absolute value ofcan be found only after the absolute value ofis known. If we insert in equation (31) the value offound fromby the method presented inchap. V, it is found that the average diameter of the atom of the monatomic gas helium is,that of the diatomic hydrogen molecule is a trifle more, while the diameters of the molecules of the diatomic gases, oxygen and nitrogen, are 50 per cent larger.[135]This would make the diameter of a single atom of hydrogen a trifle smaller, and that of a single atom of oxygen or nitrogen a trifle larger than that of helium. By the average molecular diameter we mean the average distance to which the centers of two molecules approach one another in such impacts as are continually occurring in connection with the motions of thermal agitation of gas molecules—this and nothing more.
As will presently appear, the reason that two molecules thus rebound from one another when in their motion of thermal agitation their centers of gravity approach to a distance of aboutis presumably that the atom is a system with negative electrons in its outer regions. When these negative electrons in two different systems which are coming into collisionapproach to about this distance, the repulsions between these similarly charged bodies begin to be felt, although at a distance the atoms are forceless. With decreasing distance this repulsion increases very rapidly until it becomes so great as to overcome the inertias of the systems and drive them asunder.
II. THE RADIUS OF THE ELECTRON FROM THE ELECTROMAGNETIC THEORY OF THE ORIGIN OF MASS
The first estimates of the volume occupied by a single one of the electronic constituents of an atom were obtained from the electromagnetic theory of the origin of mass, and were therefore to a pretty large degree speculative, but since these estimates are strikingly in accord with results which follow from direct experiments and are independent of any theory, and since, further, they are of extraordinary philosophic as well as historic interest, they will briefly be presented here.
Since Rowland proved that an electrically charged body in motion is an electrical current the magnitude of which is proportional to the speed of motion of the charge, and since an electric current, by virtue of the property called its self-induction, opposes any attempt to increase or diminish its magnitude, it is clear that an electrical charge, as such, possesses the property of inertia. But inertia is the only invariable property of matter. It is the quantitative measure of matter, and matter quantitatively considered is calledmass. It is clear, then, theoretically, that an electrically charged pith ball must possess more mass than the same pith ball when uncharged. But when we compute how much the mass of a pith ball is increasedby any charge which we can actually get it to hold, we find that the increase is so extraordinarily minute as to be hopelessly beyond the possibility of experimental detection. However, the method of making this computation, which was first pointed out by Sir J. J. Thomson in 1881,[136]is of unquestioned validity, so that we may feel quite sure of the correctness of the result. Further, when we combine the discovery that an electric charge possesses the distinguishing property of matter, namely, inertia, with the discovery that all electric charges are built up out of electrical specks all alike in charge, we have made it entirely legitimate to consider an electric current asthe passage of a definite, material, granular substance along the conductor. In other words, the two entities, electricity and matter, which the nineteenth century tried to keep distinct, begin to look like different aspects of one and the same thing.
But, though we have thus justified the statement that electricity is material, have we any evidence as yet that all matter is electrical—that is, that all inertia is of the same origin as that of an electrical charge? The answer is that we haveevidence, but as yet noproof. The theory that this is the case is still a speculation, but one which rests upon certain very significant facts. These facts are as follows:
If a pith ball is spherical and of radius,then the massdue to a chargespread uniformly over its surface is given, as is shown inAppendix D) by,The point of especial interest in this result is that the mass is inversely proportional to the radius, so that the smaller the sphere upon which we can condense a given chargethe larger the mass of that charge. If, then, we had any means of measuring the minute increase in mass of a pith ball when we charge it electrically with a known quantity of electricity,we could compute from equation (32) the size of this pith ball, even if we could not see it or measure it in any other way. This is much the sort of a position in which we find ourselves with respect to the negative electron. We can measure its mass, and it is found to be accurately ¹⁄₁₈₄₅ of that of the hydrogen atom. We have measured accurately its charge and hence can compute the radiusofthe equivalent sphere, that is, the sphere over whichwould have to be uniformly distributed to have the observed mass, provided we assume that the observed mass of the electron is all due to its charge.
The justification for such an assumption is of two kinds. First, since we have found that electrons are constituents of all atoms and that mass is a property of an electrical charge, it is of course in the interests of simplicity to assume that all the mass of an atom is due to its contained electrical charges, rather than that there are two wholly different kinds of mass, one of electrical origin and the other of some other sort of an origin. Secondly, if the mass of a negative electron is all of electrical origin, then we can show from electromagnetic theory that this mass ought to be independent of the speed with which the electron may chance to be moving unless that speed approaches close to the speed of light. But from one-tenth the speed of light up to that speed the mass ought to vary with speed in adefinitely predictable way.
Now, it is a piece of rare good fortune for the testing of this theory that radium actually does eject negative electrons with speeds which can be accurately measured and which do vary from three-tenths up to ninety-eight hundredths of that of light.It is further one of the capital discoveries of the twentieth century[137]that within these limits the observed rate of variation of the mass of the negative electron with speed agrees accurately with the rate of variation computed on the assumption that this mass is all of electrical origin. Such is the experimental argument for the electrical origin of mass.[138]
Solving then equation (32) for,we find that the radius of the sphere over which the chargeof the negative electron would have to be distributed to have the observed mass is but,or but one fifty-thousandth of the radius of the atom (). From this point of view, then, the negative electron represents a charge of electricity which is condensed into an exceedingly minute volume. In fact, its radius cannot be larger in comparison with the radius of the atom than is the radius of the earth in comparison with the radius of her orbit about the sun.
In the case of the positive electron there is no direct experimental justification for the assumption that the mass is also wholly of electrical origin, for we cannot impart to the positive electrons speeds which approach the speed of light, nor have we as yet found in nature any of them which are endowed with speeds greater than aboutone-tenth that of light. But in view of the experimental results obtained with the negative electron, the carrying over of the same assumption to the positive electron is at least natural. Further, if this step be taken, it is clear from equation (32), sincefor the positive is nearly two thousand times larger thanfor the negative, thatfor the positive can be only ¹⁄₂₀₀₀ of what it is for the negative. In other words, the size of the positive electron would be to the size of the negative as a sphere having a two-mile radius would be to the size of the earth. From the standpoint, then, of the electromagnetic theory of the origin of mass, the dimensions of the negative and positive constituents of atoms in comparison with the dimensions of the atoms themselves are like the dimensions of the planets and asteroids in comparison with the size of the solar system. All of these computations, whatever their value, are rendered possible by the fact thatis now known.
Now we know from methods which have nothing to do with the electromagnetic theory of the origin of mass, that the excessive minuteness predicted by that theory for both the positive and the negative constituents of atoms is in fact correct, though we have no evidence as to whether the foregoing ratio is right.
III. DIRECT EXPERIMENTAL PROOF OF THE EXCESSIVE MINUTENESS OF THE ELECTRONIC CONSTITUENTS OF ATOMS
For at least twenty years we have had direct experimental proof[139]that the fastest of the-particles, or helium atoms,which are ejected by radium, shoot in practically straight lines through as much as 7 cm. of air at atmospheric pressure before being brought to rest. This distance is then called the “range” of these-rays. Figs.14and15show actual photographs of the tracks of such particles. We know too, for the reasons given onp. 139, that these-particles do not penetrate the air after the manner of a bullet, namely, by pushing the molecules of air aside, but rather that they actually shoot through all the molecules of air which they encounter. The number of such passages through molecules which an-particle would have to make in traversing seven centimeters of air would be about a hundred and thirty thousand.
Further, the very rapid-particles, or negative electrons, which are shot out by radium have been known for a still longer time to shoot in straight lines through much greater distances in air than 7 cm., and even to pass practically undeflected through appreciable thicknesses of glass or metal.
We saw inchap. VIthat the tracks of both the- and the-particles through air could be photographed because they ionize some of the molecules through which they pass. These ions then have the property of condensing water vapor about themselves, so that water droplets are formed which can be photographed by virtue of the light which they reflect.Fig. 17shows the track of a very high-speed-ray. A little to the right of the middle of the photograph a straight line can be drawn from bottom to top which will pass through a dozen or so of pairs of specks. These specks are the water droplets formed about the ions which were produced at these points.
i014Fig. 14—Photographs of the Tracks of-Particles Shooting through Air
Fig. 14—Photographs of the Tracks of-Particles Shooting through Air
Fig. 14—Photographs of the Tracks of-Particles Shooting through Air
i015Fig. 15—Photographs of the Tracks of-Particles Shooting through Air
Fig. 15—Photographs of the Tracks of-Particles Shooting through Air
Fig. 15—Photographs of the Tracks of-Particles Shooting through Air
i016Fig. 16—Photographs of the Tracks of-Particles Shooting through Air
Fig. 16—Photographs of the Tracks of-Particles Shooting through Air
Fig. 16—Photographs of the Tracks of-Particles Shooting through Air
i017Fig. 17—Photographs of the Tracks of-Particles Shooting through Air
Fig. 17—Photographs of the Tracks of-Particles Shooting through Air
Fig. 17—Photographs of the Tracks of-Particles Shooting through Air
Since we know the size of a molecule and the number of molecules per cubic centimeter, we can compute, as in the case of the-particle, the number of molecules through which a-particle must pass in going a given distance. The extraordinary situation revealed by this photograph is that this particular particle shot through on an average as many as 10,000 atoms before it came near enough to an electronic constituent of any one of these atoms to detach it from its system and form an ion.This shows conclusively that the electronic or other constituents of atoms can occupy but an exceedingly small fraction of the space inclosed within the atomic system. Practically the whole of this space must be empty to an electron going with this speed.
The left panel in the lower half of the plate (Fig. 16) shows the track of a negative electron of much slower speed, and it will be seen, first, that it ionizes much more frequently, and, secondly, that instead of continuing in a straight line it is deflected at certain points from its original direction. The reason for both of these facts can readily be seen from the considerations onp. 139, which it may be worth while to extend to the case in hand as follows.
If a new planet or other relatively small body were to shoot with stupendous speed through our solar system, the tune which it spent within our system might be so small that the force between it and the earth or any other member of the solar system would not have time either to deflect the stranger from its path or to pull the earth out of its orbit. If the speed of the strange body were smaller, however,the effect would be more disastrous both to the constituents of our solar system and to the path of the strange body, for the latter would then have a much better chance of pulling one of the planets out of our solar system and also a much better chance of being deflected from a straight path itself. The slower a negative electron moves, then, the more is it liable to deflection and the more frequently does it ionize the molecules through which it passes.
This conclusion finds beautiful experimental confirmation in the three panels of the plate opposite this page, for the speed with which X-rays hurl out negative electrons from atoms has long been known to be much less than the speed of-rays from radium, and the zigzag tracks in these photographs are the paths of these corpuscles. It will be seen that they bend much more often and ionize much more frequently than do the rays shown in Figs.16and17.
But the study of the tracks of the-particles (Figs.14and15, oppositep. 190) is even more illuminating as to the structure of the atom. For the-particle, being an atom of helium eight thousand times more massive than a negative electron, could no more be deflected by one of the latter in an atom through which it passes than a cannon ball could be deflected by a pea. Yet Figs.14and15show that toward the end of its path the-particle does in general suffer several sudden deflections. Such deflections could be produced only by a very powerful center of force within the atom whose mass is at least comparable with the mass of the helium atom.
i018Fig. 18—Photographs of the tracks of-particles ejected by x-rays from molecules of air
Fig. 18—Photographs of the tracks of-particles ejected by x-rays from molecules of air
Fig. 18—Photographs of the tracks of-particles ejected by x-rays from molecules of air
i019Fig. 19—Photographs of the tracks of-particles ejected by x-rays from molecules of air
Fig. 19—Photographs of the tracks of-particles ejected by x-rays from molecules of air
Fig. 19—Photographs of the tracks of-particles ejected by x-rays from molecules of air
i020Fig. 20—Photographs of the tracks of-particles ejected by x-rays from molecules of air
Fig. 20—Photographs of the tracks of-particles ejected by x-rays from molecules of air
Fig. 20—Photographs of the tracks of-particles ejected by x-rays from molecules of air
These sharp deflections, which occasionally amount to as much as 150° to 180°, lend the strongest of support to the view that the atom consists of a heavy positively charged nucleus about which are grouped enough electrons to render the whole atom neutral. But the fact that in these experiments the-particle goes through 130,000 atoms without approaching near enough to this central nucleus to suffer appreciable deflection more than two or three times constitutes the most convincing evidence that this central nucleus which holds the negative electrons within the atomic system occupies an excessively minute volume, just as we computed from the electromagnetic theory of the origin of mass that the positive electron ought to do. Indeed, knowing as he did by direct measurement the speed of the-particle, Rutherford, who is largely responsible for the nucleus-atom theory, first computed,[140]with the aid of the inverse square law, which we know to hold between charged bodies of dimensions which are small compared with their distances apart, how close the-particle would approach to the nucleus of a given atom like that of gold before it would be turned back upon its course (seeAppendix F). The result was in the case of gold, one of the heaviest atoms, about,and in the case of hydrogen, the lightest atom, about.These are merely upper limits for the dimensions of the nuclei.
However uncertain, then, we may feel about the sizes of positive and negative electrons computed from the electromagnetic theory of the origin of the mass, we may regard it as fairly well established by such direct experiments as these that the electronic constituents ofatoms are as small, in comparison with the dimensions of the atomic systems, as are the sun and planets in comparison with the dimensions of the solar system. Indeed, when we reflect that we can shoot helium atoms by the billion through a thin-walled highly evacuated glass tube without leaving any holes behind, i.e., without impairing in the slightest degree the vacuum or perceptibly weakening the glass, we see from this alone that the atom itself must consist mostly of “hole”; in other words, that an atom, like a solar system, must be an exceedingly loose structure whose impenetrable portions must be extraordinarily minute in comparison with the penetrable portions. The notion that an atom can appropriate to itself all the space within its boundaries to the exclusion of all others is then altogether exploded by these experiments. A particular atom can certainly occupy the same space at the same time as any other atom if it is only endowed with sufficient kinetic energy. Such energies as correspond to the motions of thermal agitation of molecules are not, however, sufficient to enable one atom to penetrate the boundaries of another, hence the seeming impenetrability of atoms in ordinary experiments in mechanics. That there is, however, a portion of the atom which is wholly impenetrable to the alpha particles is definitely proved by experiments of the sort we have been considering; for it occasionally happens that an alpha particle hits this nucleus “head on,” and, when it does so, it is turned straight back upon its course. As indicated above, the size of this impenetrable portion, which may be defined as the size of the nucleus, is in no case larger than ¹⁄₁₀₀₀₀ the diameter of the atom,and yet there may be contained within it, as will presently beshown, several hundred positive and negative electrons, so that the excessive minuteness of these bodies is established, altogether without reference to any theory as to what they are.
IV. THE NUMBER OF ELECTRONS IN AN ATOM
If it be considered as fairly conclusively established by the experiments just described that an atom consists of a heavy but very minute positively charged nucleus which holds light negative electrons in some sort of a configuration about it, then the number of negative electrons outside the nucleus must be such as to have a total charge equal to the free positive charge of the nucleus, since otherwise the atom could not be neutral.
But the positive charge on the nucleus has been approximately determined as follows: With the aid of the knowledge, already obtained through the determination of,of the exact number of atoms in a given weight of a given substance, Sir Ernest Rutherford[141]first computed the chance that a single helium atom in being shot with a known speed through a sheet of gold foil containing a known number of atoms per unit of area of the sheet would suffer a deflection through a given angle. This computation can easily be made in terms of the known kinetic energy and charge of the-particle, the known number of atoms in the gold foil, and the unknown charge on the nucleus of the gold atom (seeAppendix F). Geiger and Marsden[142]then actually counted in Rutherford’s laboratory, by means of the scintillations produced on a zinc-sulphide screen, what fraction of, say, a thousand-particles, which were shot normally into the gold foil, were deflected through a given angle, and from this observed number and Rutherford’s theory they obtained the number of free positive charges on the nucleus of the gold atom.
Repeating the experiment and the computations with foils made from a considerable number of other metals, they found that in every casethe number of free positive charges on the atoms of different substances was approximately equal to half its atomic weight. This means that the aluminum atom, for example, has a nucleus containing about thirteen free positive charges and that the nucleus of the atom of gold contains in the neighborhood of a hundred. This result was in excellent agreement with the conclusion reached independently by Barkla[143]from experiments of a wholly different kind, namely, experiments on the scattering of X-rays. These indicated that the number of scattering centers in an atom—that is, its number of free negative electrons—was equal to about half the atomic weight. But this number must, of course, equal the number of free positive electrons in the nucleus.
V. MOSELEY’S REMARKABLE DISCOVERY
The foregoing result was only approximate. Indeed, there was internal evidence in Geiger and Marsden’s work itself that a half was somewhat too high. The answer was made very definite and very precise in 1913 through the extraordinary work of a brilliant young Englishman, Moseley, who, at the age of twenty-seven, had accomplished as notable a piece of research in physics as has appeared during the last fiftyyears. Such a mind was one of the early victims of the world-war. He was shot and killed instantly in the trenches in Gallipoli in the summer of 1915.
Laue in Munich had suggested in 1912 the use of the regular spacing of the molecules of a crystal for the analysis, according to the principle of the grating, of ether waves of very short wave-length, such as X-rays were supposed to be, and the Braggs[144]had not only perfected an X-ray spectrometer which utilized this principle, but had determined accurately the wave-lengths of the X-rays which are characteristic of certain metals. The accuracy with which this can be done is limited simply by the accuracy in the determination of,so that the whole new field of exact X-ray spectrometry is made available through our exact knowledge of.Moseley’s discovery,[145]made as a result of an elaborate and difficult study of the wave-lengths of the characteristic X-rays which were excited when cathode rays were made to impinge in succession upon anticathodes embracing most of the known elements, was that these characteristic wave-lengths of the different elements, or, better, their characteristic frequencies, are related in a very simple but a very significant way.These frequencies were found to constitute the same sort of an arithmetical progression as do the charges which we found to exist on our oil drops. It was the square root of the frequencies rather than the frequencies themselves which showed this beautifully simple relationship, but this is an unimportant detail. The significant fact is that,arranged in the order of increasing frequency of their characteristic X-rayspectra, all the known elements which have been examined constitute a simple arithmetical series each member of which is obtained from its predecessor by adding always the same quantity.
The plate opposite this page shows photographs of the X-ray spectra of a number of elements whose atomic numbers—that is, the numbers assigned them in Moseley’s arrangement of the elements on the basis of increasing X-ray frequency—are given on the left. These photographs were taken by Siegbahn.[146]The distance from the “central image”—in this case the black line on the left—to a given line of the line spectrum on the right is approximately proportional to the wave-length of the rays producing this line. The photographs show beautifully, first, how the atoms of all the elements produce spectra of just the same type, and, secondly, how the wave-lengths of corresponding lines decrease, or the frequencies increase, with increasing atomic number. The photograph on the left shows this progression for the highest frequency rays which the atoms produce, the so-calledseries, while the one on the right shows the same sort of a progression for the rays of next lower frequency, namely, those of the so-calledseries, which have uniformly from seven to eight times the wave-length of theseries. The plate oppositep. 200shows some very beautiful photographs taken by De Broglie in Paris[147]in October, 1916.
The upper one is the X-ray emission spectrum of tungsten. It consists of general radiations, corresponding to white light, scattered throughout the whole length of the spectrum as a background and superposed upon these two groups of lines.
i021aFig. 21a—PHOTOGRAPHS OF THE SPECTRA OF THE CHARACTERISTIC X-RAYS FROM CERTAIN SUBSTANCES
Fig. 21a—PHOTOGRAPHS OF THE SPECTRA OF THE CHARACTERISTIC X-RAYS FROM CERTAIN SUBSTANCES
Fig. 21a—PHOTOGRAPHS OF THE SPECTRA OF THE CHARACTERISTIC X-RAYS FROM CERTAIN SUBSTANCES
The remarkable element in these photographs is the exact similarity of the spectra produced by the different elements and the step-by-step shortening of the wave-length (which is proportional to the distance from the line on the left to the spectral lines) as the atomic numberincreases. This is shown both in theseries, which is produced by stimulating the inmost pair of electrons in each atom, and theseries, which is produced by stimulating the group of eight electrons in the second ring or shell from the center.
i021bFig. 21b—PHOTOGRAPHS OF THE SPECTRA OF THE CHARACTERISTIC X-RAYS FROM CERTAIN SUBSTANCES
Fig. 21b—PHOTOGRAPHS OF THE SPECTRA OF THE CHARACTERISTIC X-RAYS FROM CERTAIN SUBSTANCES
Fig. 21b—PHOTOGRAPHS OF THE SPECTRA OF THE CHARACTERISTIC X-RAYS FROM CERTAIN SUBSTANCES
The twolines are here close to the central image, for thewave-lengths are here very short, since tungsten has a high atomic number (74). Farther to the right is theseries of tungsten lines which will be recognized because of its similarity to theseries in the plate oppositep. 198. Between theand thelines are two absorption edges markedand.The former represents the frequency above which the silver absorbs all the general radiation of tungsten but below which it lets it all through. The latter is the corresponding line for bromine. In a print from a photograph absorption in the plate itself obviously appears as a darkening, transmission as a lightening. Just below is the spectrum obtained by inserting a sheet of molybdenum in the path of the beam, i.e., before the slit of the spectrometer. Absorption in the molybdenum will obviously appear as a lightening, transmission as a darkening. It will be seen that the molybdenum absorbs all the frequencies in the X-ray emission of tungsten higher than a particular frequency and lets through all frequencies lower than this value. This remarkable characteristic of the absorption of X-rays was discovered by Barkla in 1909.[148]The absorption edge at which, with increasing frequency, absorption suddenly begins is very sharply marked.
This edge coincides with the highest emission frequency of which molybdenum is theoretically capable, and is a trifle higher than the highest observed emission frequency. De Broglie has measured accurately these critical absorption frequencies for all the heavy elements up tothorium, thus extending theseries from atomic numberwhere he found it, to,a notable advance. The two absorption edges characteristic of the silver and the bromine in the photographic plate appear in the same place on all the photographs in which they could appear. The other absorption edges vary from element to element and are characteristic each of its particular element. The way in which this critical absorption edge moves toward the central image as the atomic number increases in the steps Br 35, Mo 42, Ag 47, Cd 48, Sb 51, Ba 56, W 74, Hg 80, is very beautifully shown in De Broglie’s photographs all the way up to mercury, where the absorption edge is somewhat inside the shortest of the characteristicradiations of tungsten. There must be twelve more of these edges between mercury (N = 80) and uranium ()and De Broglie has measured them up to thorium (). They become, however, very difficult to locate in thisregion of frequencies on account of their extreme closeness to the central image. But theradiations, which are of seven times longer wave-length, may then be used, andFig. 23of the plate opposite this page shows the-ray absorption edges, of which there are three, as obtained by De Broglie in both uranium and thorium, so that the position in the Moseley table of each element all the way to the heaviest one, uranium, is fixed in this way by direct experiment.Fig. 25shows the progression of square-root frequencies as it appears from measurements made on the successive absorption edges of De Broglie’s photographs and on a particular one of Siegbahn’s emission lines. It will be noticed that, in going from bromine (35) to uranium (92), the length of the step does change by a few per cent. The probable cause of this will be considered later.