THE ORBIT OF URANUS. 



e (in sec.), 9678".69 



n, 15425.752 



log , 1.2829072 



log a u 1.2831044 



Log ! includes, as before, the constant term in the perturbations of the logarithm 

 of the radius vector which, with the corrected mass of Neptune, is -J-.0001972. 



To find the corresponding elements at any other epoch, the following secular 

 and long-period perturbations are to be applied. Those produced by Neptune are 

 derived from the expressions in Chapter III by correcting them for the new mass 

 of Neptune, and for the change in the value of the small divisor 2' n produced 

 by the correction of the elements of Uranns. The logarithms of the factors for 

 correction are, 



Correction of mass of Neptune 9.93598 



Correction of divisor 0.00051 



Log. factor for B 9.93496 



Log. factor for &, &r, 5 9.93547 



Including the perturbations of the second order just found, we have, by putting 



N=W-y, 



= 113 30' 46".0 4 8 26' 51".9r, 



Z = ( 2850".41 4- 0".32r) sin N+ (387".67 6".377 7 ) cos ft 

 4- 112 .72 sin 2iY 47.28 cos 2^ 



7 .72 sin 3N + 4.33 cos 3N 



4- .55 sin 4JV 0.46 cos 4JV 



.037 72 _83".787 7 + 2811".41. 



M = -- 412".18 sin JV-f- (14".03 Q".86T~) cos N 

 4- 29 . 20 sin 2N- 6 .09 cos 



3 .11 sin 3^+ 1 .19 cos 



4- 0.28 sin 4iV- .13 cos 4JV 

 4- 14.767 7 +398.33 



Ms = 411".53 cos y (13".65 W.86T) sin N 

 4- 29 .33 cos 2^4- 6.17sin2JV 

 3. 12 cos 3^- 1.21 sin 3N 

 + 0.29 cos 4^4- 0.13 sin 4^ 



5.453T 7 -124.7^ 

 5x> (in units of the 7th place of decimals). 



= 1963 cos N+ 103 sin N 



+ 15cos3JV+ 6s 

 4-511.0. 



The perturbations of ebn and h are here replaced by those of h and Ic, defined 

 by the equations 



h = e sin (n 7t ) 

 4 = e cos (n 7t ) 



