THE ORBIT OF NEPTUNE. 



33 



= rMlsin (2 f I 71+ T) 



.72 sin (2 P I T) 

 + .16 sin (2 I' I 71!+ r) 

 + .15 sin (2 ? Z TI' T) 



2".98sin (4P 2Z T) 



0".0110 



l".ll cos (2 Z' Z n + T) 

 + .72 cos (2 P I n T) 

 + O.lGcos (2Z' Z 7t+ T) 



.15 cos (2 1' I rf T) 



2".98cos(4Z' 2Z T) 



+ 0".0001< 



16. Perturbations of the co-ordinates Comparison with PEIRCE and KOWALSKI. 

 The first column of the following tables gives the coefficients according to 

 Peirce (Proceedings of the American Academy, Vol. 1, pp. 287-291) ; and the 

 second, the values according to Kowalski (Recherches sur les mouvements de 

 Neptune, pp. 14-16). In the case of Uranus, Peirce's coefficients have been 

 increased by + 3*5-* ^ reduce his mass of Uranus to the adopted one. The 

 coefficients enclosed in parentheses are not comparable, as they include the effect 

 of terms now developed as perturbations of the elements, and therefore omitted 

 from the perturbations of the co-ordinates. The perturbations of the radiua 

 vector have been reduced to logarithms by multiplying by 



I. ACTION OF URANUS. 



c5 log r = 



