202 Prof. Challis on the Hydrodynamical Theory of 



existence of SDiall vibrations. In the course of the reasoning it 

 is shovrn (p. 202) that; corresponding to motion along a recti- 

 linear axis^ the function /(/> has a maximum value^ which is con- 

 firmatory of the antecedent argument in art. 25. As the inves- 

 tigation conducts to motions of a definite kind prior to any sup- 

 position as to the mode of disturbing the fluids these motions 

 may be called sjjoataneous, to distinguish them from those that 

 result from arbitrary disturbances. The chief characteristic of 

 these spontaneous motions is that they are vibratory, and that 

 the directions of the vibrations are partly parallel and partly 

 transverse to the axes of motion. Moreover the investigation 

 shows^ to -whatever order of terms it be carried, that the vibra- 

 tory motion, whether direct or transverse, is such that the move- 

 ment of a particle in any direction is just equal to its movement 

 in the opposite direction, so that there is no permanent motion 

 of translation. This agrees with the principle stated in art. 10 

 of the Hydrodynamical Theoiy of Magnetism, according to 

 which there can on the whole be no transfer of fiuid across an 

 unlimited plane having any position in a mass of fiuid of unli- 

 mited extent. As in steady motions this necessary condition is 

 satisfied by movements in complete circuits (see art. 10 above 

 cited), so in unsteady motions it is satisfied by vibrations such 

 as those above described ; and hence it seems possible to per- 

 ceive an a priori reason for the spontaneity of these vibrations. 



28. In my researches on the Undulatory Theory of Light, I 

 have shown that those phenomena which depend only on properties 

 of the medium in which the light is generated, as especially the 

 characteristics of a polarized ray, are readily explaiued by the 

 laws of the spontaneous vibrations. Also by the coexistence and 

 combination of such vibrations we may account for a beam of 

 light of very small transverse section being transmitted to an 

 unlimited distance without undergoing lateral dispersion, and 

 for the limited lateral divergence of rays in phenomena of diffrac- 

 tion. But the phenomena which depend besides on the consti- 

 tution of visible and tangible substances are referred by the 

 theory to mutual action between the vibrations of the fether and 

 the atoms of the substance. In this respect light is to be ranked 

 with the physical forces^ and its dynamical action is equally to 

 be ascribed to pressure of the tether. In treating mathemati- 

 cally of this action, I have supposed the ?etherial waves to be 

 composite in such manner that the transverse \'ibrations are 

 neutralized. This supposition requires that d^, the exponent of 

 the elastic force of the medium, should be changed into another 

 constant a^^, as is done, for a different reason, in the usual mode 

 of treating hydrodynamical questions. Excepting what relates 

 to this difference, the reasoning I employ in the dynamics of the 



