THE OEBIT OF NEPTUNE. 



21 



The values of those constants which depend on the ratio of the mean distances 

 are as follows, using the notation of the Mecanique Celeste : 



I— URANUS AND NEPTUNE. 





{») 



cZi« 



,^^'i' 



."^^ 



^d%^l 



i 



h 



da 



da? 



da} 



" da^ 







2.26969 



0.72903 



1.8326 



6.4384 



35.17 



1 



—1.68379 



6.05279 



—13.0023 



65.5556 



—259.42 



2 



0.37751 



0.95867 



2.1283 



6.7135 



35.99 



3 



0.20310 



0.72530 



2.2389 



7.4924 



36.95 



4 



0.11422 



0.52446 



2.1024 



8.2270 



39.52 



5 



0.06593 



0.36954 



1.8319 



8.5192 



43.00 



6 



0.03870 



0.25606 



1.5157 



8.302 



46.01 



7 



0.02299 



0.17533 



1.2085 



7.679 



47.57 



8 



0.01379 



0.11900 



0.9365 



6.804 



47.27 



9 



0.00832 



0.0802 



0.7100 



5.818 



45.18 



.0 



0.0051 



0.054 



0.533 











(t) 



dh^^ ' 



d^h^'^ 







i 



™§ 



da 



. «^J 







o' 



• —0.8966 



26.5493 



2.80 







1 



3.2907 



11.9366 



60.92 







2 



2.4710 



11.0760 



59.76 







3 



1.7806 



9.6115 



57.07 







4 



1.2524 



7.9427 



52.59 







5 



0.8668 



6.3301 



46.80 







6 



0.5931 



4.9065 



40.34 







7 



0.4023 



3.7215 



33.83 







8 



0.2711 



2.7738 



27.69 







9 



0.1817 



2.0381 



22.20 





It will be observed that in iP^, ah^f, and their differential coefficients, we have 

 included those multiples of — which are introduced by the action of Uranus on 

 the Sun. It seemed less laborious to do this than to make a separate computation 

 of the terms produced by this cause. But for Saturn and Jupiter -^ is so large 

 that it will be better to use the developments previously given. 



