Theory of a Contractile ^Ether to Optical Problems. 533 



persion we adopt the view due originally to Sellmeier* and 

 developed lately by Sir W. Thomson in the Baltimore 

 lectures. According to this view it arises from the absorp- 

 tion of some of the light energy by the molecules of the 

 body, owing to the fact that the period of the light-waves 

 nearly synchronizes with that of the natural vibrations of the 

 molecules. The term in U in our equation becomes appreci- 

 able. Of course in this case we need another equation to 

 determine the motion of the matter molecules. The forces 

 retarding this matter motion will arise partly from the reaction 

 of the rether and partly from that of the matter itself. As to 

 the expression for the latter we do not know what it is, but 

 in order that the linear wave may be propagated it must de- 

 pend on U and its differential coefficients. Let us suppose, 

 taking the case of a plane wave travelling parallel to the axis of 

 3, that the force is represented, as is assumed by Helmholtz, by 



2TT 2^U 



- aU -?V 



If differential coefficients of U with respect to z do come in, 

 we can allow for them by supposing a 2 and y 2 to be complex- 

 operators. Such a supposition will alter the form of the 

 expression for p, 2 . 



Now let us consider the aether and matter in a certain 

 element of volume dv. Let p be the density of the aether, 

 and let us further suppose, for the present, that a portion only 

 of the matter molecules in the element are disturbed ; we shall 

 have to deal with the average displacements of these matter 

 molecules ; let them be U, Y, W, parallel to the axis ; and 

 let p^v denote the mass of matter within the element which 

 is set in motion. If the whole of the matter in the element 

 moves, p! will be the density of the matter ; in general we 

 may suppose it to be less than the matter density and to 

 depend on the number of matter molecules set in motion by 

 the light-waves. 



Hence the equations become, 



f ■ ■ (44) 



Thus putting p + p' = p. p x + p' = p 2y so that p is the effective 

 density of aether when loaded by the matter, p 2 the effective 

 density of matter when loaded by aether, we have : — 



* Sellmeier, Pogg. Ann. t. cxlv. pp. 309, -520; t. cxlvii. pp. 386, 525. 



Phil. Mag. S. 5. Vol. 26. No. 163. Dec. 1888. 2 



