1880.] under the gravitation of its own parts. 11 



Three integrals of these equations are 

 e + v' = L-~^ 



where L, M, iV are constants. 

 Therefore 



© , -pSy« | u- | w 



j?35 K<V + n 2 ) iff + ,«) - (n^ + n iV y 



(<z 2 + c 2 ) 



(a' + c'fl ' V, 2c* c» 2c 



and therefore £ is an elliptic function, either the en or dn, of the 

 time t. But if c 2 = 3a 2 , then £ is a trigonometrical function of t. 



Again, put H x = 12 cos </>, D 2 = — O x sin <£, 



so that Q* = M+— ( ^V; 



then 



at a c M + ac^ 



zc 



