THE ORBIT OP URANUS. 



69 



^v = 2r.e sin g — e^i^ cos g 

 = -j- 2.3". 2 sin tj — 16". i cosg; 



Sp = — ^e cos g — e^o) sin g 



= — 12". 6 cos g — 8". 2 cos g. 



Perturhations of Saturn and Uranus. 



The following expressions include, with these corrections, all the perturbations of 

 Saturn and Uranus which can produce any appreciable perturbations of the second 

 order in their mutual action. In these expressions the initial letter of each planet 

 is put for its mean longitude counted from the perihelion of Uranus. 



Let us now resume the equation 



^ dp [L ' ' Z r^ 



