where 



The expression /? has a maximum for x = 0.83. 

 Tliis greatest value is 1.92, so that in ail cases 



|i'|<],92. 

 The integral Q can be evaluated by remarking that the fraction 



is a maximum for iv = and becomes very much smaller 



than this maximum when the absolute value of lo exceeds a certain 

 limit tv,, which is a moderate multiple of X-. The interval ( — ?fi, +;f\) 

 therefore contributes by far the greater part to the value of Q. Now, 

 in this interval, as is sliown by the inequality (23), the function 



e~iK"'+-')* 



differs very little from the \alue 



e-v"-'", 

 corresponding to to =^ 0. We may therefore write 



^ , /* diu 



J w^ + P 



It is remarkable that l\ and thei-efore the coefficient </ ha\e dis- 

 appeared from the result. 



We see by these considerations that P is snuxller tlian the highest 

 value of Q. Thus, if even for that highest value of Q the factor 

 of / in (22) is small compared with unity, this will also be true of 



1~ Nee- 



'V\ 



«1/ . ^; 



2 V 2jt m u 91^' 

 we may then deduce from (22) 



1 I y's' Nee' 



Combining this with (4), we find, first the value of the real index 

 of refraction, which we shall not now consider, and secondly that 

 of the index of absorption Ji, viz. (if in (4) loo we replace n by ??„) 



h=: - \/ - JT é!-9'»', 



4 K 2 m ui\ 

 or 



/<=/.„r^^"' (2^) 



