140 PROFESSOR KELLAND ON THE THEORY OF WAVES. 



p 2 <p s ,p2 



/co g" /-=> -%- +, n 1> V 1 g " * ^~ * 



cos ne d<p = I (e + e ) d ' (/> 



Jo 



<p 2 



r e -2 a ? 

 Let A =y d(f>. 



dA r -? 



dt 'Jo e 



< 



/ ~ 

 c 



e + a A + const. 



= 1 + aA 



~~ 2" /* 



/. by integration A . e = I da 

 Let A n be the value of A when 0=0. 



e 2 +C. 



A a =r dae 2 + C = f dl>e~ b ' 

 J Jo 



a' 



and Ae 2 A = 



a * Co- 



~2~ ~2~ / j ~ 2 



A ;= A,, e + e J dae 

 By putting V-l and w\/Hi successively for a, and adding, we get 



/cos/td) e ^dip^fj'^e'^ + n I dae + jj / rfae ' = \'o" 

 "V W 2 J o A^ u 



since the last terms destroy each other. 



(f)2 (p (T)2 



CO .. x CO / ~4~ d ^ d ty \ 



Also / (f>cosn(be 2 d(b = il <pdd>(e 2 +e 2 ). 



/o /o \ / 



Now /"' 



=aA e 2 T between limits ; 



_ 

 (/6 2 da 



) 



