THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



43 



The following calculation of A A must serve as an example for the computation 

 of all similar quantities. 



AEZJ[HE= 



[I72][T^][oTs] fi -5-JT3 = 



Sum of last three terms of AX{^= 

 Sum of terms = AA= 



Computed 

 Corrected 



— 0.06093580.0+ 0.33942S00 

 0.02543896.0+ 0.33254241 



+ 0.00258360 

 + 0.28269800 



— 0.08637476.0+ 0.95725201 

 A=rf— 40.22178322.0+193.3335643 

 A=(f— 40.30815798.0+194.2908163. 



If we proceed in like manner with A', A", &c, we shall obtain the following 



3 



system of fundamental equations for ^=+- 



3 



Fundamental Equations for (iz= - ; or for the case where rn= 



A =f— 40.30815798.0 +194.2908163; 

 A'=f— 23.17005142.0 + 98.2867801; 

 A"=g 3 — 18.28711570.0 + 70.37498708; 

 A l= f— 14.59391880.0 + 45.9791766; 

 A 2 =f— 10.00778683.0 + 6.35429409 ; 

 A 3 =f— 26.183106514.0 + 82.92120064; 



D =0 2 — 48.18393767.0 +708.16361 ; 

 X»'=0 2 — 55.19689421.0 +661.210840; 

 D"=f— 31.64052859.0 +246.9639388 ; 

 D x =f— 48.09965699.0 +201.477187; 

 D 2 =f— 51.05291057.0 + 34.3823000; 

 D & =f— 3.4187088566.0+ 1.7319493752. 



B= 1 9—34.6955039 \b ; B = [g— 17".578882777 j b 

 B'= |0—12 ,71500846 \b 



C = J 23.7687432 — 0J[9.176399O]6'; 

 C = 1 17.59363918— 0J [8.8694654]?/; 



C"=— [0.24459 ny/ ; 



C"=— [0.2654598]6'. 



E =+[9.6231944]Z>"; 



E'= [24,4151946 — 0J[8.5847O28]Z>"; 



E"= |17.56579106— 0j[9.6375865]6"; 



£'"=+[0.9518913]//'. 



F =— [7.6499091]//"; 



F' =+[8.9577383]//"; 



F"= j 14.07473753— 0J [0.8407439]//"; 



F m = ) 37.6032551 — 0J [9.4809266]//". 



B l = )0— 4.7867994 } &,; B 2 =\g— 0.6795721937 \ 6, ; 

 B 3 = J0—18.66558O712 \b 



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