THE ORBIT OP NEPTUNE. 31 



ACTION OF JUPITER. 



The direct action of Jupiter is so nearly insignificant that the details of the 

 computation are omitted. The only terms in the longitude exceeding one hun- 

 dredth of a second, and not sensibly confounded with the elliptic elements of 

 Neptune, are 



0".278sin (% X) 

 + .019 sin 2 (tf A 



ACTION. OF VENUS, EARTH, AND MARS. 



The only appreciable effect of the attraction of these planets is found in the 

 relation between the radius vector and the mean motion. The coefficients of the 

 perturbative function which correspond to the case when both i' and i are zero 

 introduce changes as below into the secular variation of the longitude of the 

 epoch. Those which correspond to the term in which N=X o' introduce con- 

 stants as below into the logarithm of the radius vector. For the sake of com- 

 pleteness we include the similar perturbations produced by Jupiter, Saturn, and 

 Uranus, as already computed : 



de 



It 



Action of Venus, + 0".0403 11 



Earth, + .0444 12 



Mars, + .0059 2 



Jupiter, +15.3571 4240 



Saturn, +4.8687 1344 



Uranus, + 1 .1261 311 



Total, 21.4425 5920 



The principal term of y , and, indeed, the entire portion not multiplied by the 



at 



second power of the eccentricity, is 



while the principal term in 8 log r is 



8 lo r = 





The effect of these terms might, therefore, have been included in the mean 

 distance as a single term, without appreciable error. 



14. Perturbations of Neptune l>y Saturn throuyh the Sun. 



These perturbations, it will be remembered, have been omitted in the preceding 

 computations, from reasons already set forth. They have been computed by 

 formula) (16) (19), and are as follows: 



