THE ORBIT OP URANUS. 



83 



cos 2</, we may r. -diu-c tin- iiunil)cr of arguments to ci^'lit, ami the number of table* 



to seventeen. Consider, for instance, the terms of the second series, 



it 



- 0. 108 sin ( y + 2S J) - 0.007 cos ( g + 2S J) 



-0.014 sin ( 2SJ) -0.012 cos ( 2S J) 



+ 0.164 sin ( g + 2S J) 0.267 cos ( g + 2S J). 



These terms may be allowed for by adding to (r.c.O), (.*.!), (v.c.l), the terms 



// a 



(r.c.O) = 0.014 sin (2S J) 0.012 cos (2S J) 

 (v.a.l) = + 0.260 sin (2S J) + 0.272 cos (2S J) 

 (v.c.l) = + O.OG6 sin (2^ J) 0.274 cos (2SJ). 



From the |>crturbutions of longitude and radius vector already given, we readily 

 find the following values of (p.c.O), (.#.!), etc. 



Action of Jupiter. 



(rr.O)=-J-53.064sin A t 0.004 cos ^, 

 - 0.2778^2^1, +0.036 cos 2A l 



0.025 sin 3 J, 



/' // 



(r.r.l)=_(- 2.226 sili A, 0.090cos A t (..!)= 0.094 sin A, 4.764cos 



1.256 sin 2A t +0.510 cos 2A l 

 0.006 sin 3 J, 



-ir.467 7 



(v.c.2)=+ 0.121 sin 4, 0.038 cos A l 

 -j- 0.0128^2^1, 0.01 4 cos 2 J, 

 + 0.029 sin 3^1, 0.034 cos 3 J, 

 -(r.677 1 



(c.c.3)= 0.047 



-0.520 sin 2A l 1.108 cos 2A, 

 -f-0.016 cos 3A l 

 -r.22T 



(r.. 2)= 0.056 sin A l 0.175 cos J t 

 +0.0088^2^+0.0420082^1, 

 +0.034 sin 3^, +0.035 cos 3^, 

 Q'.QIT 



(..3)= 0.005 T 



(p.c.0)=+1127cos 4, 

 + 4 cos 2 Jj 



(p.c.l)= 2 sin At +57 cos A { 



+ lO sin 2A l 23 cos 2J, 

 +137 7 



(p..l)=+108 sin A l + 2 cos 

 + 26 sin 2J, +12 cos 

 -120T 



(p.c.2)=+ 7cos A l +17* 



(p..2)=+ 7 sin J, 8T 



