250 Dr. J. W. Nicholson on the Number of 



because proportional to e 2 . Of these magnitudes C appears 

 in the absorption due to such vibration, neglected in Schuster's 

 investigation after the manner of Sellmeier, and, in fact, in 

 accordance with custom. But Dp may be important, and if 

 this occurs, a consideration of i 2 and i z shows that it would 

 manifest itself as a change in K, so that K is replaced by 

 K— 4z7rc 2 D. Thus K would, appear to be decreased, and if 

 small, might become a negative quantity. We shall return 

 to this question later, in a comparison with Drude's theory. 



If the positive electricity were actually free its effect could 

 be neglected on account of its value of e/m. Neglecting all 

 effects of this kind, as will be possible usually, we may 

 take as the total current i x = i 1 -±i 2 . This is usually done in 

 the electron theory without question. Thus 



^=(A + ?>B-KyV^7rC 2 )a^-^. . . . (15) 



If R and L are the equivalent resistance and self-induction 

 of a unit element of the metallic medium, we may also write 



(R—Jjip)i x =ae- i P\ (16) 



and therefore 



(R-Lip)- l = A + ip-B-i P KI±7rC 2 , . . (17) 



from which R and L may be determined. These results are 

 of interest in other connexions, and are simple, with the 

 Values of A and B given later. It is to be noticed that the 

 only ions we have considered are negative electrons, and 

 positive atoms which have lost them. 



Derivation of Optical Constants. 



Let us consider the propagation of a plane wave in a 

 medium, along a direction z, the current being along x. The 

 current u and electric force X are related by 



Ldu/dt + R>u = X. 



Moreover, ; 



4™= -30/3*, £=-3X/3*. 

 Thus 



3 2 X/3 z 2 = 4tt "dufdt = - 4tti>X/(R - Lip), 



or 



B 2 P/d; 2 + 6> 2 P = 0, (18) 



provided that 



2 = ±7Tip(R + Lip)/B. 2 + L 2 p 2 = 47r 2 {vi-U)l\ 2 , . (19) 



where v and k are certain optical constants, X being the 



