THEORBITOFURANUS. 83 



COS 2g, we may reduce the number of arguments to eight, and the number of tables 

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



— O.IOS sin (—fj-]- '2 S — J) —0.001cos{—g-\-2S — J) 



— 0.014 sin ( 2S — J} —0.012 cos ( 2S — J) 

 + 0.164 sin ( g-\-2S — J) —0.267 cos ( gJ^2S—J). 



These terms may be allowed for by adding to (w.c.O), (r.s.l), (I'.c.l), the terms 



(v.c.O) = —0.014 sin (2.?—/) — 0.012 cos (2^— J) 

 {v.s.\) = + 0.260 sin {2S — J) + 0.272 cos {2S—J) 

 (v.c.l) = + 0.056 sin {2S—J) — 0.274 cos (2S—J). 



From the perturbations of longitude and radius vector already given, we readily 

 find the following values of [v.q.O), (i'..s-.l), etc. 



Actiun of Jupiter. 



(v.c.0)=+53.064sin A, —0.004 cos A, 



— 0.277 sin 2.4, +0.036 cos 2^ 



— 0.025 sin 3.4i 



// // 



(«.c.l)=+ 2.226 sin J,— 0.090 cos .4, (r..s.l)=— 0.094 sin ^^ —4.764 cos A^ 



— 1.256 .sin 2^1+0.510 cos 2Ji —0.520 sin 2^ —1-108 cos 2^ 



— 0.006 sin 3^1 +0.016 cos 3^i 



— 11". 467' — l".22r 



(v.c.2)=+ 0.121 sin ^,—0.038 cos A, (w.s.2)=— 0.056 sin ^,—0.175 cos A^ 



+ 0.012sin2.4, — 0.014cos2^, +0.008 sin 2^i +0.042 cos 2.4, 



+ 0.029 sin 3.4i —0.034 cos 3^1 +0.034 sin 3^ +0.035 cos 3^1 



— 0".67 7' — 0".07ir 



(v.c.3)=— 0.04r (t;.s.3)=— 0.005 7' 



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

 + 4 cos 2Ai 



(p.c.l)=— 2 sin ^,+57 cos J, (p.s.l)=+108 sin J, + 2 cos Ay, 



+ lO sin 2^1 —23 cos 2.4, + 2i3 sin 2.4, +12 cos 2.4i 



+ 137" • -120^ 



(p.c.2)=+ 7cos A+1^ (p-«-2)=+ 7 sin A, —ST 



