183 THE ORBIT OF URANUS. 



(34), correcting the data for the new mass of Neptune. We shall also use the 

 same motion of the ecliptic adopted on p. 95. We have thus : 



4P = __ 4 ".53 

 dt 



~dt ~ 

 dt' 



///7 



v \ f* Q I f\ 



dt = 

 As a first approximation we have 



/i 7*3 1 -t' S" 



<p = 46 20.54+ 2 AST 

 Substituting these values in (34) and integrating we find 



$ = $ + 2".47 T + 0". 13 T 2 

 = 3168 A2T+ 3 .00 T 72 

 r = TO _ 3168 .76 T 7 -}- 3 .007 72 



For tabulating we shall use, instead of and T, the distance of the perihelion 

 from the ascending node, or n r, and the value of 6 corrected for Struve's pre- 

 cession. Since the mean motion has been derived without making any distinction 

 between T and 0, it will be necessary to correct the motion of mean anomaly by 

 the difference of those quantities. We thus obtain for the values of the three 

 principal arguments: 



g = 220 10' 10".35 + 15425 74". 867'+ H 

 o= 95 58.70+ 3168 . 76 T 3.00 T 3 

 0= 73 14 8.00+ 1856.827 7 +4.127 72 



If we represent all the inequalities of the true longitude by A7, so that we shall 

 have for the true anomaly 



the argument of latitude will be 



W=/+G). 



The reduction to the ecliptic will then be 



/ J /O'' O T I f\ f f f\ "1 f* ^77\ " C\ 



A = (9 .61 + .016T) sin 2u, 

 the true longitude on the ecliptic referred to the mean equinox of date, 



a = u + + 72, 

 and the sine of the elliptic latitude, 



sin j3 = sin (> sin . 

 The perturbations of the latitude will be 



(Z>.c.O) + (&.c.l) cos g + (b.s.l) sin g + etc. 



