386 Dr. Oliver Lodge on Opacity. 



The equation for the second case, that of predominant con- 

 ductivity, is 



da? " <r dt> U 



F being practically any vector representing the amplitude of 

 the disturbance ; for since we need not trouble ourselves with 

 geometrical considerations such as the oblique incidence of 

 waves on a boundary &c, we are at liberty to write the y 

 merely as d/dx, taking the beam parallel and the incidence 

 normal. 



No examples are given by Maxwell of the solution of this 

 equation, because it is obviously analogous to the ordinary 

 heat diffusion fully treated by Fourier. 



Suffice it for us to say that, taking F at the origin as 

 represented by a simple harmonic disturbance Y =e ipt . the 

 solution of equation (1) 



f? = ^?F (!') 



dx 2 a 



is F = F e~^ = 0-Q*+fc«, 



where Q = ^/(M) = ^/&. (1 + i , ; 



wherefore 



F = r(^)Sos(^-(^J,), ... (2) 



an equation which exhibits no true elastic wave propa- 

 gation at a definite velocity, but a trailing and distorted 

 progress, with every harmonic constituent going at a diffe- 

 rent pace, and dying out at a different rate ; in other words, 

 the diffusion so well known in the case of the variable stage of 

 heat-conduction through a slab. 



In such conduction the gain of heat by any element whose 

 heat capacity is cpdx is proportional to the difference of the 

 temperature gradient at its fore and aft surfaces, so that 



, dB , _ dO 

 r dt dx 



or, what is the same thing, 



(Pd^cpdd 

 da? Tdt> 



the same as the equation (1) above ; wherefore the constant 

 cp/k, the reciprocal of the thermometric conductivity, takes the 



