CS THE OR BIT OF URANUS. 



17.19& + 3Un 2.16e 3.15e&o = +1069.3 



0.04 +587 + 6.83 - 0.69 + 239.3 



2.14 +207 +21.58 + 2.19 + 208.1 



2.11 60 + 3.61 +19.66 + 53.8 



These equations give 



$e = + 64.8 (Epoch, 1800.) 

 n = + 0.268 

 to = + 12.6 



e&a = + 8.2 



Substituting these values in the seventeen equations of condition we have the 

 following residuals, or excesses of theoretical over observed longitudes: 



1 + 7.2 10 +10.7 



2 4.3 11 6.4 



3 -10.2 12 1.1 



4 +21.7 13 0.4 

 59.0 . 14 0.0 



6 7.1 15 + 3.7 



7 -11.3 16 + 4.1 



8 + 8.2 17 7.7 



9 6.4 



These residuals are much larger than they should be, and I scarcely know to 

 what cause to attribute their magnitude. The results are however amply reliable 

 for the purposes of the investigation, and lead to the following elements of Saturn : 



O '/ 



?t, 90 6 26 



f , 14 50 3.2 



0, 112 20 



$, 2 29 39.2 



, 43996.395 



e, .0560660 



log ( + &,), 0.979676 

 Epoch, 1850, Jan. 0, Greenwich mean noon. 



It will be seen that the adopted position of the plane of Saturn's orbit is retained. 

 It was corrected from observations before the perturbations were finally computed. 



Of the above corrections, those of the epoch and mean motion need not be taken 

 account of in the corrections of the co-ordinates, since the mean longitude remains 

 in the formulae as an arbitrary quantity to the end. The effect of the correction 

 of the mean distance is insensible. The corrections of eccentricity aud perihelion 

 are therefore alone to be retained. They are allowed for by adding to v and ^ 

 the terms 



