276 OUTLINES OF NATURAL PHILOSOPHY. 



273. The inequalities of the small planets 

 Vesta, Juno, Ceres and Pallas, have not yet been 

 computed ; the disturbances which they must 

 suffer from Mars and Jupiter are no doubt con- 

 siderable, and, on account of their vicinity, 

 though their masses are small, they may some- 

 what disturb the motions of one another. Their 

 action on the other bodies in the system is pro- 

 bably insensible. 



As two of these planets have nearly the same perio- 

 dic time, they must preserve nearly the same dis- 

 tance, and the same aspect with regard to one 

 another. This offers a new case in the computa- 

 tion of disturbing forces, and may produce equa- 

 tions of longer periods than are yet known in our 

 system. 



. The action of Jupiter and Saturn on one 

 another, produces an inequality in the motion 

 of each, of considerable amount, and of a long 

 period, viz. 918.76 years. 



a. tin express a number of years reckoned from the 

 beginning of 1750, S the mean longitude of Sa- 

 turn, and I of Jupiter, reckoned from the same 

 time, then the great equation that must be applied 

 to the mean longitude of Jupiter, or to I, is 



+ (20W.5 n X 0".042733) X 

 sin (5 S 2 I + 5.34'.8" X 58".88) ; 



and 



