144 



as a new variable and put 



(21) 



1 ( / 3 Nc e' 



üiy = i + -\Xr- -AP-^Q)^ ■ ■ ■ ■ (22) 



IV In muii' 



where 



n 



-fi 



and 



+ 00 



Q = k f e- f ('"+■')' dw. 



— 00 



We observe that these fornudae determine the indices of refraction 

 and of absorption for light whose frequency is given by (19). 



^ 8. We may now avail ourselves of the circumstance that, 

 according to (20), (21) and the inequality (18), which we suppose 

 to hold for I/, 



/'■'7«1 (23) 



In the first place we luid by a simple transformation 



r' w 







showing that i^=0 for r = — oc, 1^ = and i- 1= + oc, that the 

 sign of P is always opposite to that of r, and that P{ — r) = — P(+v)- 

 We have therefore only to consider positive values of r. For tiiese 

 the absolute value of F lies beneath 



ƒ? = 1^ je-ï'^C"'-')- — e-<)\"'+-'y\ dw , 







or 



GO 



J «' 







Developing 



in a series according to the ascending powers of 2q''Yio and inte- 

 grating each term separately we find 



