188 ■ THE ORBIT OF URANUS. 



(;U), 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: 



^ = _4".53 

 dt 



^'= + 5.43 + 0".387'. 

 dt ' ' 



^ = -5.17 



dt 



'^*'= —46 .78 + 0.127: 

 dt ' 



As a first approximation we have 



e=T = 73° 14' 8" — 3I69".27' 

 cj) = 46 20.54+ 2.48^ 



Substituting these values in (34) and integrating we find 



^ = <|), + 2".47 T + 0".13 T^ 

 a = 0„ — 3168 .427'+ 3 .00^- 

 T = To — 3168 .767'+ 3 .OOr- 



For tabulating we shall use, instead of 6 and t, the distance of the perihelion 

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

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

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

 the diff'erence of those quantities. We thus obtain for the values of the three 

 principal arguments : — 



fj = 220° 10' 10".35 + 1542574''.867'+^? 

 (0= 95 58.70+ 3168.767'— 3.00 7'^ 

 0= 73 14 8.00+ 1856 .827'+ 4.127'=' 



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

 have for the true anomaly 



/ = // + A?, 

 the argument of latitude will be 



"=/+«. 

 The reduction to the ecliptic will then be 



R = — (9". 37 + 0".01G7') sin 2«, 

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



;i = n + + 72, 

 and the sine of the elliptic latitude, 



sin /3o = sin <po sin u. 

 The perturbations of the latitude will be 



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



