240 MR. J. C. MAXWELL GAENETT 



situated at any point, is independent of the position of that point; thus f w/i^S^r*' 

 depends only on r : and similarly for C. 



Suppose that when electromagnetic waves traverse this medium, the moments of" 

 the average molecule of A and C in the vicinity of the point (x, y, z) are 



f A (*) = (/* A, A) and f c (t) = (f Cl ,f c ,fc). 



Then f A and f c are both proportional to E', the electric force exciting the average 



molecule* ; thus 



f* = 0,vE', f c = #cE'. 



The polarisation f ' (t) of the compound medium is given by 



Writing now E for E in the general equation t 



E' = E +tnf', 



we obtain 



E' = 

 so that 



ft ( f \ _ 



' 

 But MAXWELL'S equations for the composite medium are 



. df'ft) clE , cZH , ,, 



4?r ji-i + r = c curl H, - = c curl E, 

 dt dt dt 



where c is the velocity of light in racuo. These may be written 



N' 2 j- = c curl H, ^-=- = c curl E, 

 dt dt 



when we put 



If now we write 



N 7 = 'fl iu-'\ (9\ 



r\ /t \ L iK ) \^j- 



then n' and /c' are the refractive index and absorption coefficient of the composite 

 medium. 



But the same analysis will show that if N A = n A (l IK A ) and N c = n c (l-iK c ) ; , 

 where W A> K A and n c , K C are the optical constants of A and of C, then 



h and 



* Of. 'Phil. Trans.,' A, vol. 203, pp. 392, 393. 

 t Loe. cit., equation (9), p. 393. 



