THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 1Q5 



(o,)(i,i)-f.(j,)= 0.5002407 



(0,1) =+ 2.9986729 

 Sum =C"-t-b'=4- 2.4984322 

 Therefore C"'=+[0.3976676]&'. 



(o,j)(s 1 i)-j-(s,i)= 0.2370651 

 -(,i)=+ 2.9988729 

 Sum =G'"^-V=-\- 2.7616078 

 Therefore <7"=+[0.4411620]Z>'. 



Computation of E, E', E", and E'". 



(o,s)(i,2)-i-(i,s)=_ 1.818323 

 -(0,2)=+ 0.861707 

 Sum =E-^b"= 0.956616 

 Therefore E= [9.9807377J5". 



-(1,1)= 011.3147682 

 +(o,i)(i,s)^-(o,s)= 10.9347838 

 Sum = {0+22.2495520 j 



log. {(o.3)-i-(2,3)j = [8.9723624] 

 Therefore E'= j 0+22. 249552 1 X 



[8.9723624J&". 



-(3,3)= 017.5528645 

 +(o,s)(s,i)-i-(o 1 i)= - - 0.0045090 

 Sum = |0+17.5573735 1 



log. {(,i)-s-(s.i)} = [9.7501125] 



Therefore E"= \ 0+17.5573735 1 x 

 [9.7501 125J6". 



(o,i)(s,s)^-(3 1 i)=_10.89986 

 -(o,s)=+ 0.86171 

 Sum E'"^b"= 10.03815 

 Therefore E'"= [1.0016537J&". 



Computation of F, F\' F", and F'". 



(o.s)(i,s)-i-(i,j)=_ 0.01326047 

 -(o )3 )=+ 0.02798148 

 Sum =F-+V"=-\- 0.01472101 

 Therefore J P=+[ 8 - 1 679376]6'". 



(o, 1 )(2,s)j-(2,i)=_ 0.1677337 

 -(0,3)=+ 0.0279815 

 Sum =F--V= 0.1397522 

 Therefore F'= [9.1453586J6'". 



14 February, 1872. 



(,7X.)-K 8 - 7 )= 0.0773584 

 -(4, 5 )=+ 7.3963746 

 Sum =C-i-6,=+ 7.3190162 

 Therefore <7 3 =+[0.8644527]& 2 . 



(4,6)(7,6)-5-(7,6) = -. 0.0602795 



-(4,8)=+ 7.3963746 

 Sum =(7 4 -7-6 2 =:+ 7.3360951 

 Therefore (7 4 =+[0.8^54649]6 2 . 



Computation of E lt E 2 , E 3 , and E 4 . 



(4, 7)(j, )-!_(, 7)= 0.09722854 

 -(4,6)=+ 0.07576285 

 Sum E l -^-b 3 = 0.02146569 

 Therefore E l= [8.3317448]6 3 . 



(5,5) 018.5962129 

 (.OC < '. 7 )^-( 4 ' 7 )= 21.1694805 

 Sum = J0+39.7656934| 

 log. {(4, 7)^(8, ? ) I = [8. 74377 18] 

 Therefore^,= ^0+39.7656934| x 



[8.7437718]6 3 . 



(7,7)= 0.6479569 

 (,0( 7 .)-5-(*' a )= -- 0.00067458 

 Sum = 10+ 0.64863148| 

 log. I (4, s)-K,)| =[0.7242832] 

 Therefore^,= ^0+0.6486315 } x 

 [0.7242832]6 3 . 



6 )= 9.296196 

 -(4,6) +0.075763 

 Sum =E t -r-bf= 9.220433 

 Therefore E<= [0.96475 14]5 S . 



Computation of F^ F 2 , F s , and F+ 



(4,eX,)-5-(,)= 0.01871457 

 -(4, 7)=+ 0.02401693 

 Sum =F l -^b t =4- 0.00530236 

 Therefore J F 1 =+[7.7244692]6 4 . 



(4,6X.')-5-( 6 -0= 2.296302 

 -(4,7)=+ 0.024017 

 Sum =F 2 +b t = 2.272285 

 Therefore*^ [0.3564628]i 4 . 



