1885.] equations of vibrations of ether in a light wave. 291 



If we take into account the expressions we have found (12) 

 and (13) for the parts of the stresses depending on a> 2> we may 

 put d%/dx = xjra . d%/dt, etc., and n = a 2 , thence we get 



P = 



XX 



_/^|V p _d% dv p_^|^ 



~{dt) ' xy dt' df xy df df 



_fdv\ 2 p _dv dX p _(dX\ 2 

 r ™ " \dt) ' yz df dt' ss ~ \dt) ' 



It will be noticed that P xy = P yx , etc., only when the terms of 

 order \/r are neglected, so that in the neighbourhood of the source 

 the stresses are not of this particular nature, and some natural 

 phenomena (possibly magnetization) may be expected to shew 

 itself as an accompaniment. 



5. To compare this with Maxwell's Electro-magnetic Theory of 

 Light, let us suppose 



df drj d"C, 



v ir a - "dt =l3 - "rt = ^ (19) > 



. d% dH dO .... 



therefore ^_ BB ___ (20), 



etc. 



In the first part of this paper I shewed that F, 0, H can be 

 found from linear equations. Knowing this we may find them 

 more simply thus, 



d_(^X__^n\ = _ 2 F _ 1 d*F 

 ^ dt \dy dz) V a 2 df ' 



therefore ^=_^g_g 



4-7T 



= j- f (by Maxwell's theory); 



also kfid?=l, 



therefore 27rf= v ( -^ — -^ J and 2iru = v ( -^- — -p J , 



etc., etc. 



On this theory then the magnetic force is proportional to the 

 time variation of the actual displacement, and the electric dis- 

 placement to the molecular rotations, and these two vectors have 

 been shewn to be always at right angles. In an ordinary light 

 wave the actual disturbance would be coincident neither with the 

 magnetic force nor the electric displacement, but in a plane 



