284 

 and consequently 



U=z — - — = «„l/m.a (19) 



«0 



Here again «^ and m being constant, a is variable. We find further 

 U \/\—e' = G -V ^y^ (20) 



Case 111. II = «0 const., ii = /?„ cotist. 



The third linear element V is now a function of ö. Therefore 

 Ö0 d(f Ö0 d(f rdR ihf r 



Consequently, if we wish to have 



V zz=f= true anomaly 

 we must take 



dV 



do ^ 



and therefore 



Vz= V^- Ö \/m. 

 Now we can introduce a new variable v by 



ö\/m z= -^ i\/m — v). 



Putting then 



V, = -^ = ^,]/m.\/a = aym.a, .... (21) 



we find 



V='^^- = ^^v)/a = a,va (22) 



In this case, «„ and /?„ being constant a is also constant, by (10), 

 and V is variable. We have now 



vyY^' = G + é[/7n=G -^ V^— V. . . . (23) 

 The energy H is in the three cases : 



a'/^a, \l /2G \ 1 f 



2 y 1/771 y r Vk ^ / 2^ I 



///. //=_< + i^o^-^- _.. (^- F„)(2^,^+r- F) J^ _ ^ 

 2 r w ' 2r'' 



Here r must be understood to be written for- brevity's sake instead 

 of its expression in function of the elements. 



