THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



105 



(o,»)( 3l i)-^(a l8 )=— 0.5002407 

 _(o,i)=+ 2.9986729 

 Sum z=C"-r-V=-t- 2.4984322 

 Therefore G'"=+[0.3976676]Z/. 



(o,a)(j,i)-i-(s,a)=_ 0.2370651 

 _(o,i)=+ 2.9988729 

 Sum =C""-^b'=-\- 2.7616078 

 Therefore C""=+ [0.441 1620] V. 



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



(0,3)(l,2)H-(l,3) = — 1.818323 



— (0,2)=+ 0.861707 

 Sum =E+b"=— 0.956616 

 Therefore E=— [9.9807377J6". 



—(1,0=—^— 11.3147682 

 +(o,i)(i,3)-^-(n,3)= —10.9347838 

 Sum =— { g -\- 22.2495520 } 



log. |(o,3)-h(2,s) } =[8.9723624] 

 Therefore £'=—{£+22.249552] X 

 [8.9723624]6". 



—(3 , s)=— £— 17.5528645 



+(o,3)(3,i)^(o,i)= — 0.0045090 

 Sum =—{£+17.5573735] 



log. J(o,i)^-(2,i)« = [9.7501125] 

 Therefore E"=— \ ^+ 17.5573735 1 x 

 [9.7501125J6". 



(o , i)( 3 , 2 )-f-( 3 , i)=— 10.89986 

 —(o,2)=+ 0.86171 

 Sum =E m -±-V=— 10.03815 

 Therefore E m =— [1.0016537]6". 



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



(o,2)(i,3)^-(i,2)=_ 0.01326047 

 —(0,3)=+ 0.02798148 

 Sum =F+-V"=+ 0.01472101 

 Therefore jP=+[8.1679376]&"'. 



(o, 1 )(2,3)-^(2,i)=— 0.1677337 

 —(o,3)=+ 0.0279815 

 Sum =F-=-&"=— 0.1397522 

 Therefore F'=— [9. 1453586] 6'". 



14 February, 1872. 



(4,7X«,»)-f-(6,7)=_ 0.0773584 

 — (4,«)=+ 7.3963746 

 Sum = <^6 a =+ 7.3190162 

 Therefore (7 s =+[0.8644527]6 a . 



(4,g)(v,5)-^(7,o)=_ 0.0602795 

 — (4,*)=+ 7.3963746 

 Sum =C' 4 -f-i 2 =+ 7.3360951 

 Therefore £ 4 =+[().8<354049]& 2 . 



Computation of E^ E 2 , E 3 , and E t . 



(4,7)(8,«)-^( s ,7)=— 0.09722854 

 — (4,c)=+ 0.07576285 

 Sum E l ^-b s =— 0.02146569 

 Therefore E 1= =— [8.3317448]i 8 , 



—(5,5)=—^— 18.5962129 

 (4,«Xi,»)-f-(4.T>= —21.1694805 

 Sum =—{£+39.7656934] 

 log. |(*.0-H«.»)i = [8.7437718] 



Therefore£' 2 = — l^r+39.7656934 J x 



[8.7437718]6,. 



— (7,7)=—^— 0.6479569 

 («, 7)(7, e )-h(4 I 6)= — 0.00067458 

 Sum =— {£+ 0.64863148] 

 log. {(4, «)-=-(«,«)] =[0.7242832] 



Therefore£' 3 =— {£+0.6486315 ] x 

 [0.7242832]6 3 . 



(4, 5 X7,6)-^(7, S )=— 9.296196 

 —(4,6)=+ 0.075763 

 Sum =E^b z =— 9.220433 

 Therefore E,=— [0.9647514]6j. 



Computation of F x , F 2 , F s , and F t . 

 (4,6)( 5 ,7)-^( 5 ,6)=_ 0.01871457 

 —(4,7)=+ 0.02401693 

 Sum =F l +b i =+ 0.00530236 

 Therefore ^=+[7. 7244692]6 4 . 



(4,e)(6,7)-^(e, S )=— 2.296302 

 —(4,7)=+ 0.024017 

 Sum =F a -hb t =— 2.272285 

 Therefore!^— [0.3564628]6 4 . 



