274 POOR 



LaPlace ^ expresses that part of the perturbative function 

 which depends upon the figure of Jupiter in the following 

 form : 



i?=i(/j — ^)(i— 3 sinM) —-^ 



where the factor (o' — 1^) depends upon the shape and speed 

 of rotation of the planet ; B is the equatorial radius of Jupiter, 

 and rand o are respectively the radius vector and jovian decli- 

 nation of the disturbed body. From investigations upon the 

 motions of the satellites the value of the first factor was found 

 by LaPlace ^ to be 



log (p— io) =^8.34047 



From the above expression for the perturbative function can 

 be found by differentiation the disturbing forces in the directions 

 of r and o ; and thence by resolving the latter into its com- 

 ponents, the disturbing forces R, S, and IV. The formulas for 

 this latter step are rather complicated, unless we first refer the 

 elements of the comet's orbit to Jupiter's equator as fundamental 

 plane, or else neglect the inclination of the latter to the ecliptic. 

 This latter may be done, in the present special case, without 

 introducing any appreciable error, for this inclination is but 3°, 

 while the orbit of the comet was inclined some 64° to the 

 ecliptic. The formulas as thus deduced are, L being an aux- 

 iliary angle : 



cot Z = COS « tan i 

 sin (5 = sin // sin / 



y?/= — (1— 3 sin2<5) - 



r'- 



where 



.V= —(sin 2(!cos L) ^ 



W^' = — (sin 26 sin Z ) — 



C=(p— \6) B^ 



'^ Mecnuiqtie Celeste, Livre VIII, Sec. I. 

 ^ Mecanique Celeste, Livre VIII, Sec. 27. 



