126 

 But 



PROFESSOR G. H. DARWIN ON THE INTEGRALS OF THE 

 </- = 1 - <f = I ( l + P + 4 /8~), and thence 



This value of g will be found to give the correct value for g^. 

 Then fg K = (f )~ (1 + 5/3 + V P), 



and /yV = (I) 4 ( 1 + 1 0/3 + ^ 2 ). 



Introducing this into the value of L A (cos), we find 



L (cos) = 



G/3+150*) ....... (41) 



agreeing with the result on p. 549 of " Harmonics" for i = 3, ,s = 0, type OEC. 

 Airain in " Harmonics" I defined 



s 8 0*)= 157>3 ( /i ) + P 3 2( /t ) = 15Bintf[l-f/8-(l- |/3) sin^] . (42). 

 To make the former definition agree with this we must take 



fa* =-15(1- P), >- 3 = - 15 (1 - |/8). 

 In the present case 



,/ = i [4 - ^ + ^(1 - ^ + 4^)] = 1 - ^ + f/c'* + -.V, 



Omitting the term in /3 3 we find, with this value of <f, 



fo= 15(1 ^/J 3/8 2 ), and that the second equation is satisfied. 

 Again 1 defined 



Hence to secure agreement we must take 



Now * = 1 - 



^= -2(1+0)*. 



s = (1 - - 10 + |/3 2 ), and therefore 



The second equation is satisfied. 



