Til K ORBIT OF URANUS. 



The computation of these terms liein^ extremely complex, a clieck upon their 

 accuracy is desirable. In tin- < -:IM- of the secular variations of the coefficients, the 

 coefficients of the time are easily obtained by substituting in the integrated per- 

 turbations the variations of the eccentricity uud perihelion of Saturn. Thus I 



have found 



// a 



&v = +0.010:} t sin (>>g 0.0094 1 cos (2? f) 

 +0.0027 / sin (Xj O 0.01:38 1 cos (3</ f) 



'1'be greatest discrepancy is found in the coefficient of sin (3# f),nmi it amounts 

 t,. n .0():>v, or about 0".4 in a century. But, owing to the great period of this 

 term, nearly l!0() years, this difference, during any one century, will be nearly 

 eliminated through the mean longitude and mean motion. 



It may also be remarked that in this case the terms derived from the pertur- 

 bations of the elements are undoubtedly the correct ones, and will therefore be 

 employed. 



The terms which the preceding integration fails to give, owing to the constant 

 terms introduced into &Q and >?6@, are found by (22). 

 \\ e thus have 



HS/jJt? = + 0".36 

 n2 q u k>? = -f .27 



r*Sp = Mnt 1 J0".36 sin g 0'.27 cos g\ 

 a* = \ Mi? } 0*.36 cos g + 0".27 sin g \ 



t l |0*.0000038 cos*/ + 0". 0000029 sin g\. 



The greatest effect of these terms amounts to less than one-twentieth of a 

 second in a century. They may therefore be neglected in the present theory. 

 The other terms containing the square of the time are yet smaller. 



Applying the terms of the second order thus found to the terms of the first order 

 depending on the corresponding arguments, the perturbations of Uranus by Saturn 



become 



T here represents the time counted in centuries from 1850.0. 

 The other terms remain the same as given on page 50. 



Perturbations depending on tJte product of ffie masses of Jupiter and S'lturn. 



The values of ^D',/2, 



r)R 



, and 

 <3v 



. 

 op 



, depending on the products of the masses 



