THE ORBIT OF URANUS. 



165 



In the equations of condition ten years has been adopted for the unit of time, 

 in order to make the general vahie of the coefficients as nearly equal as possible, 

 and the time lias been counted from the epoch 1830.0, in order to have the posi- 

 tive and negative values of t in the equations more nearly balanced. To distin- 

 guish these values of he and hi they are marked with an accent. This unit of 



2 

 time gives O.SOli for the value of "'- in arc, whence 



3/i 



on ol 



The equations of condition are now formed by putting in the preceding equa- 

 tions for heliocentric lonnjitude and radius vector 



ll 





6?. 



cU 



e-x. 



dX^ 



^^+^:^-+.i^'^+i2-^^ + rv 



ov 



oe 



ed:i 



6n 



fp = ' ds -f- ,, m-l- '- ie 4- -^^- ebn. 

 ^ OS en de edn 



87. 



For the coefficients — ■" have been taken one-hundredth the perturbations of 



longitude produced by Neptune, as given in the heliocentric ephemeris at the end 

 of C'liaptcr V. The corrected mass of Neptune will then be 



17000^ ^100/ 



Finally, 1 remark that all the preceding comparisons are made with the helio- 

 centric ephemeris as printed, without the correction indicated in the column 

 adjoining it, but in the following equations this correction is for the first time 

 introduced. 



Equations of condition (jivcn hj the Corrections in Longitude. 



