THE ORBIT OF URANUS. 



81 



Action of Jupiter, 

 Action of Suturn, 

 Action of 



-f ISTcos g 

 +98TC080 

 + 67V 



-fir cos 20 

 -f 7 J cos 20 



The secular variation of the longitude of the perihelion is 



Action of .Iiipitrr, + 122.17* 



Action of Suturn, 4-118.47* 



Action of Neptune, -f 51.17* 



Total, * = +291.67* 



The effort of this secular variation on the longitude and radius vector is 



Action of Jupitrr, 

 Action of Saturn, 

 Action of Neptune, 

 Total, 



11.461^080 

 11.11 7" cos 

 4.80 T cos g 

 27. 37 T cosy 



0.671 TCOS 20 

 0.651 T cos 20 

 0.281 T cos 2y 

 1 603 T coa 20 



0.0473" cos 30 

 0. 039 T cos 30 

 0.01 6 T cos 30 

 0. 102 r cos 9g 



Action of Jupiter, 

 Action of Saturn, 

 Action of Neptune, 



Ml, 



120 T sin 



inrsitl 



50 T sin 



8 T sin 20 

 STsiu 20 

 3 T sin 20 



For the purpose of conveniently tabulating the perturbations, we shall express 

 them in a form similar to that adopted in the theory of Neptune. Let us select, 

 from the terms of the periodic perturbations produced by any planet, all those in 

 which the difference between the indices t and f is the same. For example, in 

 the perturbations of the longitude produced by Jupiter, let us consider the terms 



8t> =-fl.2G9 sin ( 



3.495 sin (2^ 

 -f 1.182 sin ( 20 

 + 0.074 sin (3g 21) 



0.005 sin (2g 37) 

 + 0.0 11 sin (4j 30 



These terms may be expressed in the form 



+ 0.002 cos ( I) 



0.092 cos (2/7 

 + 0.515 cos ( g 20 



0.005 cos (30 20 



0.001 cos (4$r 30 



= smg X 



C09-7 X 



+ 0.094 sin (g I) 

 + 0.520 sin 2(7 



-2.226 sin (g 



+ 1.256 sin 2(^ 

 + 0.006 sin 3(jr 



4. 764 cos (7 



- 1.108 cos 2(0 



+ 0.016 cos 3(<7 



-0.090 cos (<j 

 + 0.510cos2(-7 



11 M.y, 1873. 





