11 



(aj, = to X 



1 



7i{i—fiy 



n ^1 \-(p log' 



l/l+rp + l/(l + P)fp 





7^ 



1+^ |/r/) 



l/l-F 



T' 



(13) 



As ^0^ 



l/l4-<p4- 1/(1 +F)y 



l/l-F 



'P 



^/^ 



+ ^> 



+ K 1+rp ( /(1+F)r/) 



I /(l+^^)r/> 

 k i+y 



,,,!+i^^./,,|±i;^^.V.^ + |()' + etc., 

 l/l-F</) 1— A;|/(p 



(aj, will evidently at hu/h temperature {(f near 0) approach to 



1 



(aj, = coX 



7/(1— n') _ 

 i. e. with P r=: 7i' : (1— 7l') to 



n K 1 +f/) A,' <p 



1+<P 



1 r n 



(a,), = ioX -7^ ^ -. 



n (1 — n ) |_l — n 



</> 



or 



(a,), = «, X 



X 





<r 



(13a) 



n(l— w'') 1+w 



when r/) is sirnplj' written for (f-. V^l -\- (p. Tliis becomes therefore 

 properly =0 for T=cc. Then the limits of the original integral 

 (/J,, viz. /; and 1, are equal, viz. =. 1, which causes the limits ot 

 the angle of incidence to lie between (0°) and 0° (see also the 

 end of § XVII). 



For low temperatures {cp near cp^ = 1 : k"^) we shall have : 



(aj, = to X 



1 



v{l—n') 



log' 



log' 



because then n^l-{-(fi is = 1, and 1^(1 +^')(^ = 1^1 +y) = 1 : 7Z. 



/I 2\ 1 2 



And as log { \ = log j- log — , we may tinally write with 



1 

 omission of log''— in comparison with the infinitely large terms: 



2 



1 1 



(a,), == to X --7, r X log— X log 



\/l-P 



{<P = ^,=.\:k^) . (13^) 



<P 



