692 CAVALLIN, SECULAR PEETURBATIONS. 



the modulas of all tlie roots are unity, so that by (23) 



Im 



Generally we may anticipate the possibility of determiniog 

 M as often as the equation (10) is possible to solve. Therefore 

 i t ought to be practicable to determine M, when the right mem- 

 ber of (6) consists of three terms with the aid of the Solution 

 nevvly found of a trinoraical equation. 



Integrating both members of (20) between the limits i = 

 and t = t and denoting by ö, , „ the value of i9j for if = O, we 

 obtain 



^, — ^n o (^7) 



t, t 



- CO t-r "* m 1 1 °o .r "' m -i 



^ ■*", n i '^^ n 



n=\ n=\ 



The series in the right member of (27) having a finite value 

 för all t we thus conclude 



lira^ = ilf. (28) 



Now let US introduce a new system of convergents to the 

 constants (3) by changing the convergents (4) into 



üb ÜL2 "I!^ (29) 



• m m ra 



and *•, and 6/, into r\ and fi\ . 



Besides we assume these convergents to be so accurate that 

 in accordance with (4) we also have 



m'j > m'2 . . . > m^ , 



and moreover we assume the convergents (4) to be maximi- and 

 the convergents (29) minimi-convergents, so that 



•in -y in<i I It 2 



^' "" m' ' m'^^^'^ m! 



m-v 









m 





^ 



9n 



^ 





m 









m! 



