16 THE ORBIT OF NEPTUNE 



10. That portion of the perturbative function which is due to the action of 



the inner planet on the sun is 



r' 



-5 cos V 



r 



V being the angular distance between the planets. Developing it in a series of 

 terms of the form 



cos (m + 



\JL 

 f* 



h will be of the form -# c being a numerical coefficient, multiplied by powers of 



GC- 



the eccentricities and mutual inclinations. 



From this development, and the equations (3), (4), (5), (7), and (8), I have 

 computed the following analytical values of the coefficients for the perturbations 

 of the longitude, latitude, and logarithm of radius vector. 



a 



Vft 



:^ 25 



a 





6 ^ 3 2 



(17) 



2 Vu 3 



=e 



= e 2 ( \l v, + V ^ 9 



