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atoms are themselves intrinsic mobile configurations of stress or motion, or both together, in the ultimate medium.
[It is not without interest to consider how far the conception mentioned above of an isotropic solid medium of very small density, with very massive minute nodules imbedded in it but exerting no direct forcives on each other, will carry us in forming a representation of optical phenomena. The theory is of the Young-Sellmeier type, because each nodule has one or more free periods conditioned by its form and by the surrounding elasticity.
On eliminating (1, 1, 1) from the equations expressed above, we obtain the vibrational equations of the æther, supposed thus loaded. Its elastic properties are found to be conserved intact, but the effective density as regards vibra
tions of period 7 is increased by ap/(a-4p). When the (a–
coefficient a is of aeolotropic type, by reason either of the form or the distribution of the nodules, we have effectively an isotropically elastic medium with aeolotropic inertia ; this leads to Fresnel's wave-surface, provided the elasticity is labile in Lord Kelvin's sense. The theory also leads to a formula for ordinary dispersion, of the usually admitted type (Ketteler's) for isotropic media; but, on the other hand, it is in default by assigning a dispersional origin to double refraction. If we wish to include the minute effect known as the dispersion of the optic axes in crystals, it will be necessary to assume for the elastic stress between æther and matter a somewhat more general form, involving (after von Helmholtz) absolute as well as relative displacement, but always of course remaining linear.
The assumption of elasticity of labile type also allows an escape from the usual difficulties of a solid æther in the matter of reflexion. In that problem the elasticity would naturally be taken continuous across the interface, the volume occupied by the molecules being on this hypothesis extremely small compared with that occupied by the æther.
We may further amend the theory by getting rid of the difficulties associated with lability, at the same time avoiding the difficulty as to how a body can move through a perfect solid medium, if we take the æther to be a rotationally elastic fluid, and retain the material load as before.
But an essential and fundamental difficulty will still remain. It is the extremely small volume-density of the energy involved in radiation which permits a very small inertia, and consequently a small elasticity, to be assigned to the æther, and so prevents it from acting as an appreciable drag or exerting an
appreciable force on finite bodies moving through it. But these very properties would incapacitate it for acquiring the very large volume-densities of energy that would have to be associated with it in order to explain electrodynamic phe
Any representation which would make the æther consist of molecules of ordinary matter is open to the objection that the thermal kinetic energy of gases and other material systems must then, in accordance with Maxwell's law of distribution of energy, largely reside in it. But, on the other hand, if we hold to the view of matter which was first rendered precise by Lord Kelvin's theory of vortex atoms, namely, that the æther is the single existing medium and that atoms of matter are intrinsic singularities of motion or strain which belong to it, then there is no inducement to assume for the æther a molecular structure at all, or to make its inertia anything comparable with the inertia of the atoms on whose play the thermal energy of the movements of the matter consists. On such a theory the inertia, and the resulting kinetic energy, of the matter may be hard to explain, but it is certainly something different from the inertia of the underlying medium in which the atom is merely a form of strain or motion. On such a theory refraction, and also double refraction, will be caused by the atmosphere of intrinsic strain which represents the electric charge on the atom; and only dispersion will be assigned to the influence of sympathetic vibrations in the atoms or molecules, thus doing away with any difficulty of the kind mentioned above.
In the theory of gases the ordinary kinetic energy of the molecules represents sensible heat, and as such may be derived for example from the dissipation by friction or otherwise of the mechanical energy of ordinary masses: it is of the nature of kinetic energy of the masses of the atoms. But the store of energy which keeps up radiation is of electromotive kind, is concerned with displacing electricity, not with moving matter except indirectly; at least no consistent scheme has yet been forthcoming which includes both. It is quite conceivable that the disturbances which occur in the ordinary encounters of molecules are of far too gentle a character to excite the very powerful elasticity which on a certain form of the electric theory binds together the continuous medium taking part in optical propagation, any more than a system of solid balls rushing about in an enclosure bounded by a heavy continuous rigid solid can excite sensibly the elastic qualities of that body. The opinion has been widely supported, both on theoretical and experimental grounds, that a
gas will not emit its definite radiations however high the temperature to which it is raised, unless there is chemical decomposition of the molecules going on. If that be so, the æther does not act as an equalizer of the kinetic energy between the different modes of vibration of the molecules, and the ordinary theory of gases need make no reference to the æther.
If I have understood aright, a similar view has been expressed as at any rate a possible explanation of the difficulty as to the application of Maxwell's distribution theorem in the theory of gases, by Prof. Boltzmann himself. The law of distribution of energy is perhaps unassailable for the case of molecules like small spheres, with three degrees of freedom, all translational. By including the rotational modes of freedom, which may be none at all for a monad gas, only two for a diad, and three for other types, and these possibly not complete, a sufficient number of freedoms is obtained to cover the known range of values of the ratio of the specific heats. The introduction of any vibrational types would make too many; so on this ground also it is not likely that such types can enter into those among which the thermal energy is divided. December 4.]
VI. The Role of Atomic Heat in the Periodic Series of the Elements. By C. T. BLANSHARD, M.A.*
Y a study of the latest, or most accurate data of atomic
arrive at definite relationships between them, which I will endeavour to set forth. In Grundzüge der theoretischen Chemie, Leipzig, 1893, p. 106, Lothar Meyer says:-"The periods of fusibility do not coincide with those of other physical characters, are also less regular than these, but are in close relationship to the atomic volume." With regard to Dulong and Petit's law, W. Ostwald says (Outlines of General Chemistry,' English translation, p. 177):—“ We can only note empirically that the law holds good for substances with atomic weights higher than thirty."
A survey of the accompanying curve of atomic heats, made to correspond with Lothar Meyer's curve of atomic volumes, will, notwithstanding several blanks and several doubtful values, demonstrate the two following laws of atomic heat:
1. The atomic heat decreases in any series from the monad to the tetrad element, and then increases till a maximum is reached with the heptad element.
* Communicated by the Author.
Curve of Atomic Heat.
The ordinates are the atomic heats. The abscissæ give the elements in the order of their atomic weights.
2. The variation is greatest with elements of low atomic weights, becoming less and less as the atomic weight increases. I hope in the next place to show in a tabular form that the melting-points of the elements are intimately connected with their atomic heats, and that four general laws govern this connexion. Were sufficient data to hand with regard to latent heat of fusion &c., there is no doubt that many similar relationships would be established. There is evidently plenty of work before physical chemists in this direction. In the arrangement of the groups of elements I follow a plan used by Lothar Meyer, of using Roman numerals combined with lettering. Thus the Li group is I., the Cu is I.a.; Group II. is Ca &c. ; II. a Be &c.; II. Fe, Ru, Os. In placing the iron elements here, and not in a separate group, I am following W. Preyer, Das genetische System der chemischen Elemente, Berlin, 1893. The groups are entirely arranged by their atomic heats, but will be found to be practically identical with Lothar Meyer's classification. The melting-points taken are the most correct up to date, from (1) the late T. Carnelley's Physico-Chemical Constants, 1887; (2) H. Landolt and R. Börnstein, Phys.Chemische Tabellen, Berlin, 1894; (3) The Chemical Society's Journal. Several determinations are very rough, others are altogether wanting. The specific heats, which are much more complete, are from the last two sources and Watts' Dictionary of Chemistry.' They are all taken at as near as possible the constant t°, 15°. The atomic weights are from Landolt and Börnstein and the Chemical Society's Journal. From these and the specific heats I have calculated the atomic heats with much greater accuracy than has hitherto been thought necessary. Blanks denote that no reliable data are to hand. A query denotes that the observation has been made, but not accurately.
*Bunsen's value for Ca seems too high; the atomic heat of this element will probably prove to be less than that of K.