ON AN ELLIPSOID. 



Thus we get the relations 



91 



lh -m/=0 



mg - Jch = ) 



A B l[A B\ 



Hence, > = 1 = 7 T f ) > 



w/ mg h\l k) 



and consequently 



.(19). 



A B^ 



similarly, 



C A 

 9 ~m I 



(20). 



* k m* 



By means of (18) and (20) the equations (17) become 



(21); 



which, restoring their values to w, v, w } may be written 



V ktf 



Put y -2 = m; .'. 



It & 



, &C. 



,(22). 



, and then we get 



f= m r-v 



with similar equations for the projections on the other co-ordi- 

 nate planes. This result is identical with the known one in 

 Leroy, p. 304, or Hymers, p. 201. 



It is hoped that the novelty of treating symmetrically a non- 

 integrable equation in three variables, will be admitted as an 

 excuse for the length to which this paper has extended itself. 



