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 |Q.Q|, [_'.i| [~.'-|, &c. : 



[o7o]=0 5".5702558; 

 [7771=0 11 .3147682 ; ; 

 rr1=g 13.0721730; 

 HTTI =017.5528645; 



[I7T]=0 7".5123754; 

 [7a1=<y 18.5962129; 

 [77jf]=0 2.7662522; 

 [777] =0 o .6479569. 



These give 



(67) 



[oTo]QTr]=0 2 16.8850240.0+ 63.02615319170556 ; 

 [oTojjTTJ =0 2 18.6424288.0+ 72.81534747185340 ; 

 [073 [373] =0 2 23.1231203.0+ 97.77394528773910; 

 [777] pm =0 2 24.386941 2.0+ 1 47.90860736529860 ; 

 [77JJ[37j]=:0 2 28.8676327.0+198.60659306350890; 

 [I7?1 [77^=0* 30.6250375.0+229.45408138955850; 



]=0 2 26.1085883.0+139.70173232312266; 



]=<7' 10.2786276.0+ 20.78112497747588 ; 

 [J77]=0 2 8.1603323.0+ 4.86769547582026; 

 [T7J]=0 3 21.3624651.0+ 51.44181484629338 ; 

 [7JJ=0 2 19.2441698.0+ 12.04954446242401 ; 



]=0 3 3.4142091.0+ 1.79241220013018; 



]=0* 47.5100615.0 S +809.584727769664.0 2 ) . 

 -5804.515976137376.0+14461.60808412039 j ; 



]=0 29.5227974.0 3 +230.634324285266.0 2 ) 

 523.768277980466.0+250.403089395286 j ' 



(68) 

 (69) 

 (70) 

 (71) 

 (72) 

 (73) 



(74) 

 (75) 

 (76) 

 (77) 

 (78) 

 (79) 



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. 



Sum of terms 



Computation of A. 



=g a - 18.642428800.0+ 72.815347472 

 = 21.562395123.0+120.10805649 

 [:];]= 0.016959303.0+ 0.22169494 

 = + 0.1803729465 



!!B ' 4- o.oi596936 



0.00787688 

 = <f 40.22178322.0+193.3335643 



