281 



fp r= tl\ and tbr the variables (j; he talies O, G and h. In order 

 to get a more general point of departure I take for the function 

 <l> which serves to define the new variables 



s r 



^=0x0^ \ Qds + I Rdr, 



(5) 



where 



Q' = G' 



O' 



cos' *• 



2/^- y- 



R'' = m{ — a' ~^~ ~ 



r r' 



(6) 



We have thus 



d<D , d<P d<I* 



Or OS Ow 



a' ^'~k /G' \ 1 



and therefore 



^=-y + '— ^-h(--yM^-« • • . . .(7) 



Ó r \m J 2 r' 



I will now for two of the variables qi take O and G, for the 

 third I take either «, [^ or y, or a function of one of these parameters. 

 We have thus in all cases 



^ = -^=''- -^^^^ (8) 



If now we introduce the auxiliary angle S' by 







and then construct the right-angled spherical triangle of which the 



sides next to the right angle are $' and s, it is easily seen that in 



d^' dQ 

 this trianele we shall have — ==r~— if we put 



ds oG '^ 



& =1 G cos i, 



where i is the angle opposite the side 6'. Consequently i and x> are 

 the inclination and node of the instantaneous orbital plane, i. e. the 

 plane which contains the origin of co-ordinates and the velocity of 

 the body P. Introducing now the argument of the latitude ^, i. e. 

 the angle between the line of nodes and the radius-vector, or the 

 side .opposite the right angle in the above mentioned triangle, we 



