(22) 



THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 5 



It will manifestly be unnecessary to compute b ( V separately, since it is already 

 included in the value of & (0) . Therefore taking logarithmic coefficients of equations 

 (19) and (21), we shall have the two following working formulae for the computation 

 of b m and b ( V. 

 &<>= a 4 ^ 0.625 [9.1938200]a 2 [8.3876400]a* [7.9317080]a 8 



[7.6026493]a 8 [7.34301 19]a 10 [7.1278964]a 12 



[6.9439800]a u [6.7832222]a 16 [6.6403720]a 18 



- [6.51179S9]* 20 [6.3948844]a 22 [6.2876743]a 24 



- [6.1886714]a 20 [6.0967014] x 28 &c. } 



&(i> = _ a \ 1 [9.0969100]a 2 [8.1938200]a 4 [7.6886700]a 6 



- [7.3296480]a 8 [7. 049 80 7 3] a 10 [6.8201332]a 12 

 -[6.6252212]a 14 [6.4558633] x 1G [6.3061010]a 18 



- [6.1718509]a 20 [6.050 1898]a 22 [5.9389523]a 24 



- [5.8364888]a 20 [5.7415133]a 28 [5.6530038]a 30 &c. 



Then we shall have 



3 



c.o= - 



. (23) 



5. To reduce the preceding formulae to numbers we shall assume the following 

 values of the invariable elements of the eight principal planets. 



Invariable Elements of tlie Eight Principal Planets. 



