144 Mr. W. Sutherland on Molecular Refraction. 



Lorenz assumes that throughout a heterogeneous non- 

 absorbing medium composed of aether and molecules (the 

 sether being quite uniform in properties), the differential 

 equation for the vibratory disturbance of an element during 

 the propagation of a wave of light may be written 



^^ = ,.^im^ ^"^ = -^17^^ and v^? = -2 ■ 



0) 



^ dt^' ^ ' ~ 0)2 dt""' ^ •* ~ 0)2 dt^ 



where o) is a function of x,y,z, the coordinates of the position 

 of the element when undisturbed ; o) for a homogeneous 

 medium is the constant velocity of light in it. Considering 

 only plane waves, he assumes that a solution of the above 

 equations exists in the form 



I = (^0 + 02)cos [kt — Ix —my— nz — d), 



with similar expressions for t] and ^ -, where ^oj Vq) ?oj ^j ^) *^^ 

 n, d are all constants, but ^gj ^2) ?2 are periodic functions of x, 

 Vi z', ^0, rjQ, ^0 being so chosen that the mean values of fgj Vi^ 

 ^2 throughout a finite volume are zero. Thus f^, tjq, ^q ^''s the 

 components of a certain constant mean amplitude. Now, 

 although a variable amplitude is thus provided for as the dis- 

 turbance passes from sether into matter, we see that the con- 

 dition that k, I, m, n, and d are constant commits us to the 

 assumption of an invariable ivave-length. 



Apart from all mathematical symbols, we may state Lorenz^s 

 fundamental assumption thus, that in a medium composed of 

 aether and molecules light may be considered as propagated 

 with a certain mean velocity, but with a periodically varying 

 amplitude of vibration. Now there can be no question as to 

 the fact that a wave of light does pass through such a discon- 

 tinuous mixed medium with a certain mean wave-length and 

 a corresponding mean velocity, no matter how different the 

 actual wave-lengths in pure a3ther and in pure matter may be; 

 but a serious mathematical difficulty arises when, in deducing 

 an integral relation from the original differential equation, 

 Lorenz assumes this mean wave-length to hold through the 

 substance of a single molecule, throughout which he performs 

 certain integrations involving wave-length, while for all we 

 know the wave-length in matter may be milhons of times 

 smaller than in aether. It appears to me that if there is to be 

 integration over a single molecule and its " domain " of aether, 

 then we must employ a solution of the differential equation 

 which provides not only for variable amplitude, but also for 

 variable wave-length, as we pass from sether into matter. 

 The logical consequence of Lorenz's assumption of a mean 

 wave-length is that, like Cauchy, he must replace the mixed 



