302 



18 



II = ^ I/- al + 2 (m Ne^- a^) + 2 m a, f ^ - meFf ^ 

 öS _ ] 



ÔS 



V—al + 2(miVe^ + a^)yj+ 2maif meFf 



a.. , 



(44) 



where and «3 are two integration constants. According to (6) the quantities /, 

 and will now be given by 



V-al-\-2 (m Ne^ - 03) f + 2 maj^— meF'$' 



L = 



[a,'d,p, 



+ 2 (m ATe^ + a,) + 2 m «1 mePrj 



(45) 



where in the expression for and the integration is to be extended twice be- 

 tween the roots of the integrands. Expanding after powers of F. and expressing the 

 a's as functions of the /'s, we find 



J^n'U'j^ m 3F 

 1,-1, 



à", 



(46) 



In these formulae o' is a small quantity containing the second power and higher 

 powers of F, while d" is a small quantity containing the first power and higher 

 powers of F. The term in the expression for the energy a, which is proportional 

 to F is of large importance for the determination of the frequencies occurring in 

 the motion of the system, but, since in the calculation of the coefficients C occur- 

 ring in the trigonometric scries representing the molion we shall, as mentioned, 

 neglect small quantities proportional to F and higher powers of F, we may neglect 

 this term, as well as the terms 0' and o". In this way we find, by introducing (4(î) 

 in (44), for S expressed as a function of ~, vj, ip, I,, I.^, I^, 



where we have introduced the abbreviations 



(4 



