1166 



coefficient of / in t«r has been denoted bj •/. t<^ prevent confusion 

 with the known number -t. The quantity ^,, occurring in the different 

 coefficients, is a function of a, and q, determined by the relation ') 



^ -f ^-^ ^ - 3«' ; 



(5) 



here the constant teru» of a periodic function lias been denoted by 

 a stroke above the functional sign. The resulting development of po is 



/, is a constant, /^ = ; /,,.., I,„ . • • are functions of o^ and q. 

 3. Substituting the developments (3) and (4) in (2) we get: 



(6) 



R.= 



Ma' 



j. = C 



/'=« 



COS TiT H Af, COS pT -f sin 'W i; B^, sin pr 

 /,=0 ,,=i ■ 



(7) 



r=oo 



A — 12 A 11' 



■rip — ' ■"^i>,rl'- 1 



this formula can be written so : 



B^= 2: Bp,r!i' 



r=0 



m' e' +°° _ 



(8) 



where 



2 ' 



Ap-\rBp 



c,= 



C-,, 



P>1, 



(9) 



and 6), can be developed so 



c,' = 



7=0 



C/v•^t^ /?= — 00, . . , f 00 



(10) 



The coefficients .4^,,,, Z^^^, C),,,- are functions of Q^,<i^,q. 



The values of the coefficients C),,, and of tlie derivatives of these 

 coefficients, considered as functions of j>o,ö, and q, with respect to </ 

 have been collected in the next table. These values belong to the 

 numerical values of the coefficients of the developments (3) and (4), 

 deduced in the second chapter of the "Investigations". 



1) Investigations, Chapter II, § 8. 



