6S T H E R B I T F U R A N U S. 



These equations give 



ff 



^E = + 64.8 (Epoch, 1800.) 

 hi = + 0.268 

 ^e = + 12.6 

 ehoi = + 8.2 



— Substituting these vahics in the seventeen equations of condition we have the 

 following residuals, or excesses of theoretical over observed longitudes: 



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 rehable 

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



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 formute 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 Sv and 5^ 

 the terms 



