266 POOR 



The most convenient point to make the transformation to 

 Jupiter as center of motion is undoubtedly that given by 

 LaPlace's idea of the "sphere of activity." The radius of this 

 sphere, as given by LaPlace ^ is 



5/ 2 



p^rV hill' 



where >> is the radius of the sphere, 



r is the radius vector of the comet, 

 ]>i' is the mass of the planet. 

 Using Newcomb's value of the mass of Jupiter, I find 



log ^=8.73176 



and the date which most nearly satisfies this condition is Octo- 

 ber 26.5, 1886, at which time I find 



log ^ = 8. 72954 



31. From the osculating elements of the comet for October 

 26.5, as given in §29, were derived by the usual formulas of 

 elliptic motion the heliocentric rectangular coordinates and their 

 derivatives with respect to the time. The ecliptic of 1886.0 was 

 taken as fundamental plane ; the positive direction of the axis 

 of X being directed toward the Vernal Equinox. Thus were 

 found, 



log a- =r 0.7 1 27 116 « 

 log ;(/ = 0.1 394713 « 



log 2^8.6977660 

 log J^= 7-3948617 



log^ = 7.6680856 « 



dz 

 log ^ = 6. 833587 1 « 



The corresponding coordinates and velocities for Jupiter were 

 found as follows. The heliocentric position of Jupiter in 1886, 



^ Micanique Celeste, Livre IV. 



