PROFESSOR KELLAND ON THE THEORY OF WAVES. 123 



or S^(l- W 3 )-n 2 (S n -Dy-S^D nW? = w 2 a 2 D^ 



__ nq /|-4rc 2 ( a 2 -l)(l-2rc 2 ) + rcVl 



D n -2(X-2w 2 ) V I 4(l-2ny J 



Again, .by the same two equations, 



s _ 



D m = a . 



. 

 ~ 



D,, 



[77s Pn 9 1 ~ s + aD 



* in 



_, S n D n y 1 ;T~ " ) 



JL ~r j 



4 W 



= 1 fLz!s^a 2 D 2 ) 



. .SJJnS-l 2 J 



4n 



1/1 9 "49 \ 



/I w 4 _ . 1 n' VT\\ 

 <= O~T; ( D^ + 4 a 2 D,,J 



1+-^ 

 4 ' 



D,,= 3*J_ (18) 



v 



From the same analysis we obtain 



i - 5 

 1 W J 



(19) 



The equations (17), (18), and (19), give the limits to the value of n, 



