THE ORBITS OP THE EIGHT PRINCIPAL PLANETS. 



27 



15. We shall now give the computation of N 1 , N", &c., for the root g. Using 

 #=5".46370645, we get # 2 =29.8520882. Substituting these in equations (98-109), 

 we get the following values of A, A', &c., D, D 1 , &c. 



A=+ 3.425636; 

 A'=+ 1.390983 

 A"=+ 0.5599336 

 A!= 3.9055338 

 J 2 = 18.472552 

 J 3 = 30.285419 



log. 0.5347412; 

 " 0.1433218; 

 " 9.7481365; 

 " 0.5916804n; 

 " 1.2665269n; 

 " 1.4812336; 



D =+468.78628 

 #=+385.91263 

 Z>"=+103.10436 

 D 1 =~ 31.473166 

 A= 214.70366 

 Z> 3 =+ 12.899760 



log. 2.6709749 ; 

 " 2.5864890 ; 

 " 2.0132764; 

 " 1.4979404n; 

 " 2.3318394n ; 

 " 1.1105816. 



Substituting A, A', A", D, D, B', in equations (84-86), and neglecting/,/', &c., 

 we shall get the following computation of N',N", and N'". 



Computation of N' & N". Computation of N' & N'". Computation of N" & N'". 



constant log. 0.3624135 



constant log. 0.8236010 



constant log. 1.1305346 



The computation of these quantities is thus seen to be correct, since independent 

 formula give the same values. We may now use these values of N\ N", and N m , 

 in equations (119), and we shall obtain the following values of J,, & 2 > b& an( l ^4- 



^=+0.0001151786^ 

 ^=+0.000007234609^ 



J 3 =+0.0000003080273^ 

 6 4 =+0.00000004087918JV 



Equations (114-117) will now give, 



^=+0.00007796538^ 

 _B 2 =+0.0005510300JV 

 3= 0.001520571^V 



(7 1= 0.00000152882^" 

 <7 2 = 0.00000525886^ 

 ^=0.0000348856^ 

 C t = 0.0000349058^ 



^=+0.000000002067JV 

 ^=+0.000000187594^ 

 E 3 = 0.00000855646^ 

 ^=+0.00000358228JV 

 ^=0.0000000000442^ 

 ^=+0.000000076558^ 

 ^3= 0.00000653946^ 

 ^ 4 =+0.000000238018^V 



log. 96.0613718; 

 " 94.8594150; 

 " 93.4885892; 

 " 92.6115022; 



95.8919018; 



96.7411752; 



97.1820068; 



94.1843555w; 



94.7208918n; 



95.5426467; 



95.5428974n; 



91.3153615; 



93.2732190 ; 



94.9322943; 



94.5541593; 



89.6454496n ; 



92.8839917; 



94.8155417n; 



93.3766095. 



