18 



SECULAR VARIATIONS OF THE ELEMENTS OF 



Substituting the values of (0,1), (0,2), (0,3), &c, given in §7, in equations (26), 

 we shall get the following values of | o,g| , |i,i| , 1 3 , 2 | a &c. : — 



[J77J=0— 5".5702558 

 [TTT1=«7— 11 .3147682 

 ri7?1='<y— 13 .0721730 

 [T^1=g— 17 .5528645 



\TZ\=g— 7".5123754 

 [7771=0—18 .5962129 

 [7771=0— 2.7662522 

 \ry\= g — 0.6479569. 



These give 



\EMhl\=g 1 .— 16.8850240.0+ 63.02615319170556 

 {n\\HI\=9 1 — 18.6424288.0+ 72.81534747185340 

 [ZJ]\TJ\=(?— 23.1231203.g-i- 97.77394528773910 

 [771 [7721 =/— 24.3869412,(7+147.90860736529860 

 QTT] GlI]=£ 2 — 28.8676327.0+198.60659306350890 

 [|3 [Ml=# 2 — 30.6250375.0+229.45408138955850 



[13 E3=^ 8 — 26.1085883.0+139.70173232312266 

 \M\{EI}=9' 2 — 10.2786276.0+ 20.78112497747588 

 14,4117,71 =^— 8.1603323.#+ 4.86769547582026 

 E3[H3=^ 2 — 21.3624651.0+ 51.44181484629338 

 [777] [TTT] =0 2 — 19.2441698.0+ 12.04954446242401 

 [H3(IZ]=^— 3.4142091.0+ 1.79241220013018 



[7^11 1 , 1 1 1 2 , a I r?Ti1 =0 4 — 47.51OO615.0 3 +8O9.584727769664.0 2 \ 



-5804.515976137376.0+14461.60808412039 



]=0 4 — 29.5227974.0 3 +23O.634324285266. 

 —523.768277980466.0+250.403089395286 



[IT*] [JTJJ [77JJ [777] =0 4 — 29.5227974.0 3 +23O.634324285266.0 2 1 



(67) 



(68) 

 (69) 

 (70) 

 (71) 

 (72) 

 (73) 



(74) 

 (75) 

 (76) 



(77) 

 (78) 

 (79) 



(80) 



(81) 



13. We shall now give the computation of equations (31 — 50), and also of (53) 

 and (54) in full, because we can then readily correct them for any assumed changes 

 in the adopted masses; and observe at the same time that the coefficients in 

 equations (55 — 64) are independent of the masses of the planets, and consequently 

 are not affected by their supposed variation. 



Computation of A. 

 [775] |-77i1 =ff-— 18.642428800.0+ 72.815347472 



— [J7J][T7JJ[27JJ. 

 — [2771(7771 [77+ 

 + [7JFJ[^[|7JJ-[77i] = 



-+E3E3& 



-\m\EB 



Sum of terms 



■[J7J]= —21.562395123.0+120.10805649 

 [7771= — 0.016959303.0+ 0.22169494 



+ 0.1803729465 

 [77?]= + 0.01596936 



= — 0.00787688 



A= 0-— 40.22178322.0+193.3335643 



