in Singly and Doubly Refracting Media. 519 



A 2 [e(a 2 -6 2 )-^V 2 } 



= A /2 {[6 / (a 2 -6 2 )-/c / 1 \ 2 ]cos2A-6 / 2a6sm2A} ; I rjj£\ 

 A 2 e2ab = A! 2 {\_e\a 2 -b 2 ) - k\X 2 ^ sin 2 A + e 7 '2ah cos 2A} ; J 

 from which are developed 



A /2 cos 2 A __ [e(fl 2 -6 2 )-^ 2 ][6V-6 2 )-^X 2 ] + 4« 2 5W 

 A 2 " [Y(a 2 - b 2 ) - TjsFf + WWd* 



A 2 sin2A_ 2ab(e 1 K 1 — ef</ 1 )\ 2 



A 2 " " [e / (a 2 -6 2 )-/c / 1 X^] 2 + 4a^V 2 ' 



And if for abbreviation 



A!'! 6' 



be put and these values introduced into equation IV., we get, 

 as the law of the curve of dispersions, 





a*-& 2 -l = 2- 



2cZ5 = X 



(« 2 -Z, 2 -^W 

 me \ Lv 



\_ 2 

 L- 



uf 



(a'-tf-^j + ^b 2 ^ 



2abD 



L 2 



(,. 



& 2 -pY + 4cr'Z> 2 



(B) 



If only one complex zone is present, so that the summation- 

 symbol may be omitted, (a) and (b) can easily be developed 

 explicitly; and then, if we designate the now occurring limit- 

 values of the refracting force for an indefinitely oreat and an 

 indefinitely little wave-length as 



1 



nL — 1 = — 7- tor A. = :o , 



n~ — 1= — r for \ = 0, 



2 me 



D' 



-nl = V>, 



(Cl) 



and now write \ m = n^ L, we get :- 



2 *=^ \A-K i+D -S) 2 = \/^-^ + S) 



■(D) 



