:u4 



ON THE STABILITY OF THE MOTION OF SATURN'S RINOS. 



Let us put 



, / 

 = S 

 \ 



sin'0 

 sin 2m0 cos 



sm0 



4sin 



cos 6\ 

 in'0 ) 



- r 

 = 



.7 = 2 



sn 1 



sin' 



sin 



(8)*, 



where the summation extends to all the satellites on the same side of P, 



x 



that is, every value of 6 of the form - IT, where x is a whole number less 

 than . 



The radial force may now be written 



P = - R {K+ LA cos (ms + a) - MB cos (ms + ft)} 



(9). 



* The following values of several quantities which enter into these investigations are calculated for a 

 ring of 36 satellites. 



=24-5. 



4342 



3287 



e 



4' 



