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the atom, I used Maxwell's relation K1 = N12, where N1 is the refractive index of the stuff of the atom. For ten metallic ions, namely those of the Li family, those of the Be family from Mg to Ba, and for Zn, and for the six negative fatty acid radicals from formic to caproic, the equation (16) was found to be verified in a broad way. But in the case of the halogens from F to I the relation seemed to break down completely, as also in the case of the ions H and OH. By means of further data I have found that Cd ranges itself with the metals mentioned, while Ag and Pb rank as further exceptions. In the case of the halogens it was suggested that, as their atoms are heptad as well as monad, we must imagine each halogen to have associated with it four negative electrons and three positive ones. Three of the negative electrons unite with the positive ones when the halogen atom acts as a monad, and so form inside the halogen atom three electric doublets. With a notation which I have proposed this idea would be expressed by writing the following as the formula for the Clion: CI(()3. In this way we can briefly record the fact that Cl is a monad with heptad capabilities. Now, if the three electric doublets inside the halogen ion produce an abnormal effect on the propagation of light through the halogen ion, we shall not be justified in using Maxwell's relation for finding the dielectric capacity from the refractive index. Just as water and a number of similar substances have two limiting dielectric capacities, namely 80 and 2 in the case of water, with every intermediate value for electric alternations of suitable frequency, so it seems to me that the halogen atoms have a dielectric capacity K, which is different from N1" for the conditions under which their ionic velocities are measured. Accordingly I propose to use equation (16) for finding the dielectric capacities of the halogen atoms and of atoms in general. By means of the data given on page 175 of the paper mentioned and the assumption that K,=N,2 on the average for the regular ions, the equation becomes one for K1 in the following form:

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where B is the volume of a gramme-atom of the ion.

(17)

The following table contains the values of the ionic velocities given by Kohlrausch except for Cd and Pb, the values of B taken from "Further Studies on Molecular Force" (Phil. Mag. [5] xxxix.), and also the values of K, calculated by (17), using for v the value 1 for the monad atoms and 2

for the dyads. In the last row of the table are given the

values of 10K,B/v, to be discussed immediately.

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In the case of the halogens it is interesting to compare the values of the dielectric capacity thus derived with the values of N12, thus

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A study of those values shows that in the halogen atoms K1, instead of being equal to N,2, varies inversely as N12.

Returning to the main table, we find that K,B/v is constant without a single marked exception, although the halogens have just been shown to be so exceptional in regard to Maxwell's law. We have therefore this result, that the dielectric capacity of an atom is directly proportional to the valency and inversely proportional to the square root of the volume of the atom. It is interesting to find that valency, which Faraday proved to be of fundamental importance in his electrolytic law, is of similar importance in connexion with dielectric capacity, that predominating electric property of matter which Faraday discovered. As to the physical signification of our law for K,, it seems that it may be sought by the following short train of speculation. I have shown that cohesion can be traced to the mutual attractions of the electric doublets in molecules acting like minute magnets. Thus cohesion is an electrical phenomenon. By following out a similar train of reasoning it can be shown that rigidity in solids is a mechanical result of the electric doublets in the molecules. At absolute zero the rigidity is equal to the electric energy of these doublets per unit volume. But to express this electric energy we must regard it as proportional

to the square of an electric quantity associated with the molecule. Thus rigidity is proportional to the square of an electric quantity. Now our law for the dielectric capacity of an atom means that the square of K1/v for an atom when multiplied by the volume of the atom is the same for all. It seems, then, as though a certain stock of electric energy associated with the electrons in an atom were the same for all atoms. The law for K1, then, seems to be of a similar nature to that of Dulong and Petit and of the fundamental law of molecular physics which makes the kinetic energy of translation of all molecules at a given temperature the same.

But to return from speculation to the immediate bearings of the formula K,B/v=constant; we find that in (16) it makes the ionic velocity of an atom directly proportional to the sixth root of the volume of the atom-that is to say, to the square root of its radius. This brings out neatly the old paradox about ionic velocities. Hitherto it has been assumed that the ionic velocities have all been measured with the same driving force for all ions. The result that a large ion like that of K travels faster than a small one like that of Li under the same driving force in a resisting medium is, indeed, puzzling until, in taking account of the dielectric capacity of the atom, we see that the driving forces assumed equal are in reality not so at all.

Melbourne, December 1903.

L. The Crémieu-Pender Discovery.

By WILLIAM SUTHERLAND *.

N the experiments carried out by the happy collaboration

practically the whole of the difficulty in reconciling the apparently contradictory results obtained by Rowland and his pupils and Röntgen, Himstedt, and others on the one hand, and by Crémieu on the other, concerning the magnetic effects of electric convection was traced to the one fact that Crémieu covered his metallic electrified surfaces with solid dielectric. The solid dielectric rotating with the revolving charged metallic disk reduces the magnetic effect considerably, so as in some experiments to make it appear to vanish. The combined experiments have brought into prominence a fundamental property of dielectrics. Now exactly the same property made itself apparent in my theoretical

*Communicated by the Author.

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investigation on "Ionization, Ionic Velocities, and Atomic Sizes (Phil. Mag. Feb. 1902). It was there shown that if a, and a, are the radii, and K, and K, the dielectric capacities of the two atoms of a binary electrolyte forming a very dilute solution in water (m gramme-equivalents per litre) of viscosity and dielectric capacity K, the current per em. in the solution due to a rate of fall of potential dE/dx is for ionization i

η

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This expression is derived on the usual supposition that in electrolytic conduction the atom of an ion simply carries its electron from one electrode to the other. But the same reasoning if not supplemented by a further principle would make the work done in carrying an electron e in an atom of dielectric capacity K down a step of potential E1-E to be Kop(E1-E2)/K, whereas it is in reality e(E1-E). It was therefore pointed out that the electrolytic current cannot consist solely of the waftage of electrons by atoms. The further principle necessary to make equation (9) consistent with the conservation of energy can be ascertained by considering the following very simple case. A unit charge of electricity is placed inside a very thin slab of dielectric capacity K between two plates at potentials E1 and E2 at distance D apart in vacuum and parallel to them. The force acting on the charge is (E1-E)/DK according to usual electrostatic principles, and the work done in moving the charge inclosed by dielectric of capacity K from the one plate to the other is (E1-E)/K. But, on the contrary, we know that this work must be E-E2. Evidently, then, (E,E)/K is not a full determination of the work involved. It gives the work due to a certain displacement of the unit charge relative to the matter of the two plates. But there has been also a displacement of the æther relative to the two plates. If the displacement of the æther is written down as D(1-1/K), and the force producing this is taken to be (E-E)/D, the force anywhere between the two plates except in the dielectric slab, then the work due to æther displacement is (E1-E2) (1-1/K), which when added to the work for displacement relative to matter gives the whole work E1-E2.

Now the expression D(1-1/K) for the displacement of the æther is just what is required by Fresnel's theory that the velocity of the æther in a moving transparent body is

1-1/2 of that of the body, whose index of refraction is μ. By Maxwell's law K, and so Fresnel's law makes the velocity of the æther 1-1/K of that of the transparent dielectric. This formula of Fresnel's is the one verified by Fizeau's experiment with running water, repeated by Michelson and Morley. Thus, then, the phenomenon which presented itself in "Ionization &c." and has just been discussed in a simpler form, turns out to be an electrical case of Fresnel's law. The Crémieu-Pender effect is another case. Consider the rotating charged disk in their experiments. The electricity at any point of the disk takes the velocity of the disk at that point. The solid dielectric attached to the disk imparts to its æther at that point the velocity (1-1/K). Thus the velocity of the electricity on the disk relative to the æther in the rotating disk is r/K. If, then, this slip v/K of the electricity past the adjacent æther is the cause of the magnetic effect of electric convection, we see why Crémieu's use of solid dielectrics reduced the magnitude of the effects he was investigating. One gathers by implication that Crémieu and Pender are investigating the effect of the dielectric quantitatively. In one quantitative result given (loc. cit. p. 460) a magnetic effect measured by 140 when air was the dielectric was reduced to 15 when mica was attached to the metallic surfaces; these are in the ratio of 1: 9, while the corresponding ratio of /K with the same in both cases is the ratio of the dielectric capacity of air to that of mica or 1: 66. As further experimental results are to be expected soon, it will be better to await their appearance before proceeding with the theory that the magnetic effect of electric convection is due to the slip between electricity and æther, and not to the relative motion of electricity and remote æther. Crémieu and Pender have secured evidence of a phenomenon noticed by Himstedt, that beyond a certain density of charge the magnetic effect ceases to be proportional to the density of the moving charge. This will doubtless receive the experimental attention it merits Meanwhile it may be pointed out that the results calculated from many of the recent experiments on ionic velocities in gases will need to be revised in order to take account of the dielectric capacity of the stuff of the atom, as I have attempted to do in the case of ions moving through

water.

Melbourne, January 1904.

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