THE ORBIT OF URANUS. 



*o 



Again, the error of the standard is not necessarily constant, but may contain a 

 terra proportional to the time, arising from erroneous proper motion.s of the 

 standard star.s. Therefore, instead of supposing the residual constant, we shall 

 suppose it of the form a ~\- ht. Each observed correction to the theoretical latitude 

 will then give the equation, 



sin uhip — cos uq)hO -f- a -|- i 7'= f5/?. 



To facilitate the solution of these equations they have been divided into groups, 

 each group usually comprehending three oppositions, and combined into a single 

 equation multiplied by such a factor as would make its probable error half a second. 

 The factor by which the correction of the latitude is multiplied in the eqnatitm is 

 the same with the coethcient of a. The year 1840.0 is taken as the epocji for h. 

 Tluis we liave the following: 



Treatin" these equations by the method of least squares, we find the normal 



equations 



63.60,^+ 0.45(^^0— 52.10a— 1.0S& = -f 28.33 



6.45a<^ + 69.51^0 — 52.60(1 — \\:1^> = + 111.02 



-52.105<?) — 52.60<|)^3 -j- 133.50^ + 8.956 = — 76.55 



- 1.08^<^ — 14.25(|)^0 4- 8.95(1 + 4.496 = — 23.69 



