167 



For the fnrthei" developments of this paper ihe value of the 

 coefficient 6o,i 'S required. 

 We have the equation : 



1 /'=«> 

 M 2 ^y.i cos PT = 



l>=0 





Q. + 



dö 



^ + 



'^1 

 bd 



6, + [h\,S>,, (11) 



[], being an abbreviation for [ ]p=oo,j=<ro,9=^)- 



The right member of this formula is an even periodic function 

 of t; if we replace t by jx — t, q^, a^ {:=()), 0^ and i2j change their 

 sign, their coefficients remaining unaltered; thus the left member is 

 an even periodic function of t, changing its sign if we replace t by 

 jr — T ; then 



Ai,,i =0. p = 0, \, . . .■ 



and 



Co,i = ^o,i=:0 . (12) 



4. As regards rf<9 ') the solution of the equations (1) is: 

 'be a.'j èObol rdfdR, do rdtrdR.do or, da 



drt, dq 



(W = 



1 rdt OR, do r, 



d(7, d^ dq dögjj A dr dr J ^[_dq do, 



+ 



+ 



+ 



(13) 



^) Investigations, 111, § 1. 



