Photographic Action of Stationary Light-Waves. 101 



be a considerable fraction of its diameter ; and this is suf- 

 ficiently secured by the large value of e above that which is 

 required to keep down the density of the aether, combined with 

 the great relative density of the atom. It would thus seem to 

 be possible to account for sufficiently large differential trac- 

 tions between the component atoms of a molecule, especially 

 if some of them lie well under the lee of others, to produce 

 brisk internal vibration. 



In this way we could imagine the construction of a sort of 

 model illustrative of an elastic solid theory of refraction, 

 including selective absorption and other such phenomena, in 

 the form in which it is presented by von Helmholtz and 

 others. In the simpler case, in which the atoms are not 

 grouped into systems capable of synchronous free internal 

 vibrations, let (J, 77, f) denote the mean displacement of the 

 free aether, and (f 1? %, f x ) that of the atoms. Then the 

 equations of vibration assume the forms 



P J(E, v, ?)= C V 2 (|, v, D-(j£> J. Qp+^-^vx-v, ?!-?), 



d 2 



-, . T / /CfE drj d{\ -ill p 



in which p = c ( T~ + ~r + ;jz ) 5 anc * ^ ne phenomena 01 crys_ 



talline media could be included by assuming a vector-coefficient 

 instead of the scalar a. 



The conclusion, then, is that in this limited range an elastic- 

 solid, theory of a very rare aether is not so much at fault as 

 would at first sight appear. 



A theory based, on difference of rigidity without difference 

 of inertia, after MacCulhigh's manner, would have to be 

 realized by ascribing to the atom an atmosphere of, intrinsic 

 aethereal strain, instead of endowing it with great inertia ; 

 and this could only be possible in a rotational aether, and 

 would in fact form a mechanical representation of the electric 

 theory. As such it must be expected to give an account of 



* There are introduced by von Helmholtz (Wiss. Abh. ii. p. 216) in 

 addition, a forcive proportional to the absolute displacement of the atom, 

 and a irictional one proportional to its absolute velocity. The former is 

 derived from the idea that the heavy central masses of the atoms are 

 unmoved by the aether, and only outlying satellites are affected by its 

 motion. On our present view this restriction might be dispensed with, 

 except in so far as it renders possible an illustrative theory of absorption 

 of an analytically simple character. The consequences of the above equa- 

 tions are set out by various writers, e. g. Carvallo (Comptes Rendus, cxii. 

 p. 522). 



