ÖFVBRSiaT AF K. VETENSK.-AKAD. FÖRHANDLINGAR 1899, NIO 7. 673 



(IX) 



f 1 e 



2V = IS" y. -;r- cos £ ^ 



12 2 



,„ cos cp . 

 W — ^ sin £ 



: = Q COS w sin £ — p (cos £ — e) 



cos I -" ^ ^ ■ ' 



where we tlnis need no furtlier integrations. 



After this sliort exposition of the method for finding the 

 periodic terms, we pass to the essential part, th^ determination 

 of the constants of integration. 



One whichever of the differential quotients 



dB dY dW 



C?£ ' rffi ' t/£ 



dp da , . , .,, , • -1 dFrii . n ■, n 



-r- or ~, which we will design with ~ — , is or the torm 

 de de ^ ds 



dFr, 

 de 



= /",„ + ^2a-^{i i' c) cos (ie — i'Xm)->r22a^(i i's) sin {ie — i'X^ (1) 



— in the foUowing we always suppose rn to be odd — 

 where 



Fm = .^«1(0 i' 6) cos i' Xni — .^aj(0 i's) sin i'X^ i (2) 



this is valid for 



n 7t 



inn — — ^ £ ^ 'W5Tr + — ; 



(3) 



instead of the variable £ we will hare introduce a new variable 

 X with the following relation existing between £ and X: 



^ + A ; ^<l<^Tc . 



(4) 



The reason of this process will be evident after the integrations 

 have been performed. The equation (1) noAv beconies 



dF„ 



, — Fm +^.^fl](^^'c)cos 



+ .2'^a,(^^'s)sin 

 and thus 



Fm=-Fm'X + Sra + .32'^, (^ i' c) COS 



+ 2^^l(^■^V)sin 



iWiiTC — 3 I + ik — i'X,, 



+ 



% I niTC — ^^1 ■\- il — iXi 



(5) 



i mrt — — + U — i'X„ 



1 1 niTt — — I + il — i'Xj^ 



+ 



(6) 



