268 POOR 



xdy — ydx xdz — zdx ydz — zdy 



at ' dt ' dt 



Jii jyi _|_ (iz^ "I ydydz zdzdx 



^ , V k^ dy-^ -I- dz^ -| 



+ ^-^ + 



r//^ ' dfi 



k^ dx^ -\- dz'^ ~| xdxdy . zdzdy 

 "dfi '^~dfl 



Vki dx^ + dz^ -| 



where C, C , C",f,f', and a are the arbitrary constants of inte- 

 gration. The ordinary elements of an orbit are arbitrary con- 

 stants, and are, consequently functions of the above constants, 

 being given by the following formulas : 



tan i2 = — , 



tan I = - ' 



where / is the longitude of the projection of the perihelion on 

 the fundamental plane. 



In the special problem under consideration, k^, in the above 

 formulas, becomes the acceleration at unit distance due to the 

 force exerted by the mass of Jupiter. Using Newcomb's de- 

 termination of the mass of Jupiter, I have 



log /f2= 3.4510772. 



From the above formulas were derived the values for the three 

 constants of area, C, C , C" , and for the semi-axis major of the 

 comet's orbit about Jupiter, namely, 



log C =4.7477148 

 log C 1=4.6228470 ;/ 

 log 6'^''= 5.2999551 n 

 log a =8.9332651 n. 



and consequently the relative orbit was hyperbolic. 



