or

2 2

for a factor the square of the harmonic function m sin (at +c), m2 m2 cos 2(at+c). The pressure on the atom is consequently partly such as a current corresponding to the indication of the first term would produce, and partly such vibratory motion as would be due to the pressure indicated by the second term. The former gives rise to motion of translation of the atom, and to acceleration of such motion. The acceleration may either be from or towards the source of the vibrations, according to the relation between the magnitude of the atom, and the breadth and intensity of the waves. The waves which emanate from individual atoms by reason of reaction from their surfaces, are all of such small magnitude that they act in the directions from the centres of the atoms on all surrounding atoms. This force is atomic repulsion. The composite waves resulting from the coexistence of those emanating from a vast number of atoms constituting a molecule may be supposed of such magnitude and breadth as to be capable of producing acceleration of exterior atoms in the direction towards the centre of the molecule. This is molecular attraction. The equilibration of the two kinds of forces maintains the aggregation of atoms which constitutes visible and tangible bodies. The arguments on which these statements are based are given in the article in the Philosophical Magazine for September 1872, already cited, and in a "Supplementary Discussion of the Hydrodynamical Theory of Attractive and Repulsive Forces," contained in the Number for September 1876. The statements are introduced here for the purpose of making intelligible the following General Theorems, to which the investigations referred to conduct :

I. Assuming that the repulsive and attractive forces of nature are all resultants of modes of pressure of the æther, the actions of such forces on atoms are in every instance attributable to æthereal currents, whether the atoms be immediately acted upon by steady motions of the æther or by æthereal vibrations.

II. In any instance in which a gradation of atomic density exists in the interior of any body, in so far as this condition is persistent, molecular attraction in the direction from rarer to denser parts must be counteracted by atomic repulsion in the contrary direction; and according to theorem I. these actions are accompanied by æthereal currents.

In the case in which an atom in the interior of a homogeneous body is kept at rest by atomic repulsion and molecular attraction, the resultant of each kind of force is zero, and there is consequently no direct evidence of the action or existence of æthereal currents. But if the atom be near the superficies

of the body, in order that it may be in equilibrium there must be (as Poisson first indicated) a diminution of density through a small superficial stratum in the direction towards the surface. Within this stratum the resultant atomic repulsion from within to without is controlled by molecular attraction from without to within. The latter force is due to æthereal currents extending beyond the boundary of the substance, being, in fact, the force which gives rise to the phenomena of capillary attraction.

But when the state of the atoms in the superficial stratum is violently disturbed, as by friction, the positions of equilibrium of all the atoms, both superficial and interior, are in some degree changed; and in order that they may take new positions of equilibrium it is necessary that there should be a gradation of atomic density, and that the resultant atomic repulsion on any atom in the direction of decreasing density should be counteracted by the resultant molecular attraction on the same in the contrary direction. According to the particular constitution of the substance, the new state of equilibrium of the atoms is more or less persistent, and the substance is more or less electric. Now, by the above-stated general theorems, such actions, whether repulsive or attractive, are accompanied by æthereal currents which in their aggregate extend beyond the boundaries of the substance (much further than those above mentioned to which capillary attraction was attributed), and operate, in fact, in producing the mutual attractions or repulsions which are observed to take place between electrified bodies. These views are treated of in detail in The Principles of Physics,' pp. 505–555, and in the Philosophical Magazine for October 1860. I have referred to them here for the purpose of stating that the Theoretical Explanation of the action of the Radiometer which I have given in the Numbers of the Philosophical Magazine for May and November 1876, rests on the same principles-with, however, the difference that the disturbance of the superficial stratum, instead of being produced by friction, is considered to be due to the difference of action of light, or radiant heat, on the blackened and bright surfaces of the vanes. It is proved that, under these circumstances, æthereal currents are generated, the action of which on the component atoms of the vanes is such as to produce rotation in the direction in which the vanes of a freely suspended radiometer are observed to move. For these reasons I regard the motion of the radiometer as due to a force which is of the same kind as that which is induced in a body electrified by friction.

6

The explanation of the action of the Otheoscope is a simple corollary from the above theory of the action of the radiometer.

It is evident that, under the conditions of "otheoscope, No. 1," described in p. 177 of No. 180 of the 'Proceedings of the Royal Society,' the action of the light of a candle on the fixed plate blacked on one side is just the same as that on a vane, blacked on one side, of the revolving radiometer; but as motion of the plate is prevented, there is a reflux of the æthereal current-the effect of which, judging theoretically, I should expect to be like that of wind emanating from the black surface, and (in accordance with Mr. Crookes's description) "blowing away whatever easily movable body happens to be in front of it, irrespective of colour, shape, or material," causing thus the rotation of the contiguous four-armed fly. In this respect the action resembles that of a body electrified by friction on small particles of any kind in its neighbourhood, which, in fact, under particular circumstances has been named electric wind.

Experiment has shown that a radiometer will rotate under the influence of light when both sides of each vane are equally bright, if only the vane be cup-shaped-that is, convex on one side and concave on the other. This is a most remarkable fact, and may be regarded as an experimentum crucis, by which the truth of any proposed theory of the rotation of the radiometer may be tested. As far as I am aware, no other attempt has been made to account for this fact than that which I have produced in the Number of the Philosophical Magazine for April 1877, supplemented by some remarks in a letter addressed to the Editors in the Number for May 1877. The explanations there offered depend on the same principles of the hydrodynamical theory of physical force as those applied in the explanations of the motions of the radiometer and the otheoscope, with the addition of considerations respecting the variation of effect of the incident light at different points of the surface of the radiometer as depending on the convexity or concavity. The theoretical result is, that the radiometer rotates as if pushed on the convex side, which agrees with expe

riment.

As respects the Telephone, an essential part of the explanation of its action is furnished by the general Theorems before enunciated. In the ordinary use of this instrument the voice of the speaker, by setting an iron plate in vibration, is supposed to generate electric or galvanic currents, which being intensified as to their efficiency, and conducted, by known experimental methods, are made to act on another plate at a distant position, causing it to vibrate in such manner as to produce by agitating the contiguous air, sounds that correspond with more or less exactness to the pronounced words of the

speaker. These facts have received experimental explanations on the hypothesis of the generation of electric currents; but how or why the means employed should produce such currents has not been accounted for. For the following reasons I consider that the hydrodynamical theory of physical force furnishes the required explanation. The component atoms of the plate which the speaker's voice puts in vibration, move to and fro by forces which result from the simultaneous action of atomic repulsion and molecular attraction, varying in direction according as the one or the other is in excess. Hence, as these forces are due to harmonic vibrations of the æther, according to the general Theorem I. æthereal currents are continually being generated, and coexist with the vibrations of the plate. In order that cognizable effects of these currents may be produced, it is necessary to provide means of circulation by conducting wires, or by earth-connexion, inasmuch as all æthereal currents, as already intimated, must satisfy this condition. The usual arrangements in the application of the Telephone do, in fact, fulfil this requirement. This theory of the action of the telephone is especially confirmatory of the electrical character of the æthereal streams to which in the previous explanation of the action of the radiometer the rotation has been ascribed.

An article "On certain movements of the Radiometer," dated November 1, 1877, is contained in No. 184 of the Proceedings of the Royal Society, p. 546. The author, Professor Stokes, has said nothing about" theoretical explanations" of the phenomena in the sense in which I use these terms in the title to the present communication; but by "coordinating the experiments he has arrived at conclusions of essential importance as regards the part which the theorist has to perform. He concludes that we must recognize, as distinct conditions under which motion may be obtained in a radiometer, (1) difference of temperature of the two faces, (2) curved form of the disk, (3) roughness of surface on one face; but he does not decide whether condition (3) is different from (2). From a theoretical point of view, I should say that it is only required to take account of the effect of difference of temperature when there is no curvature, or the faces are plane, and to take ac count of the effect of curvature of the faces when there is no

difference of temperature. The theories I have proposed

account for the movements of the radiometer under the two conditions considered separately; and hence, on the allowabl supposition that these conditions operating conjointly produc independent effects, it may be said that all phenomena of th radiometer are thus accounted for on the principles of th general hydrodynamical theory of physical force.

In order to indicate the extent of the applicability of Theorems I. and II., I take occasion to add that whereas in the phenomena of frictional electricity the condition of gradation of atomic density is produced by disturbance of the superficial atoms of the electrified body, in the case of the phenomena of galvanic force the same condition is a necessary accompaniment of the chemical action going on in the battery; and in the case of the magnet a gradation of interior atomic density is maintained by the mutual counteraction of atomic repulsion and molecular attraction, and with more or less persistence according to the quality of the magnet and the degree of magnetization. In all three classes of phenomena æthereal currents are produced by reason of the gradation of atomic density, and as these currents are subject to the condition of circulating, it follows, as a consequence of such motion, that polarity is recognizable in electric, galvanic, and magnetic phenomena. This theoretical inference is confirmed by experiment.

1.

Cambridge, May 16, 1878.

LXII. On some remarkable Instances of Crookes's Layers, or Compressed Strata of Polarized Gas, at ordinary Atmospheric Tensions. By GEORGE JOHNSTONE STONEY, M.A., F.R.S.*

IN

Na recent communication I gave some instances † of Crookes's layers at ordinary atmospheric tensions, and among them described one which accounts for the great

* Communicated by the Author, having been read before the Royal Dublin Society, November 19, 1877.

† Viz. those which support light powders in heated capsules, or liquids in the "spheroidal" state, including the case of drops upon the surface of a liquid (see Phil. Mag. for last December, p. 441 et seq.). The theory of unequal stresses in polarized gas has thus fulfilled an anticipation which Mr. Crookes entertained so long ago as 1873, that whatever theory would account for the motion of radiometers would probably also explain the spheroidal state of liquids, and the mobility of finely divided precipitates in heated capsules; for he enumerates these among phenomena probably due, at least in part, to the same repulsive action of radiation manifested in radiometers. (See Philosophical Transactions, vol. clxiv. p. 526.) I was not aware of this passage when writing the paper on Penetration above quoted; otherwise I should have there referred to it.

66

as is

The heat which diffuses across a layer of gas passes under what are called "the laws of conduction" if the number of gaseous molecules present is sufficiently large. If fewer molecules are present, the heat passes under other laws, which may be distinguished from the laws of conduction by calling them the laws of penetration. In writing the paper on Penetration, I was under the misapprehension that the flow of heat by penetration between a heater and cooler of which the temperatures and