OF ARTS AND SCIENCES. 



199 



The star Piazzi xv. 17G, has the following determinations of its 

 declination, reduced to the movable planes of 1875, by Bessel's pre- 

 cession and proper systematic corrections : — 



The equations to be solved by least squares will be : — 



x—0.77y = d".l Wt=:H 



x — 0A0y = 5.7 1 



X — 0.33 ij = A.2 1 



a;_0.10y = 2.2 f 



Taking the mean by weights, we have x — 0.461 y = G".09, which is 



the final determination of a; — 0.46 1 y. 



Hence, 



0.3093/==: — 3".01 



0.061?/ = — 0.39 

 0.131y = — 1.19 

 0.361 y = — 3.89 



with the same weights as before. Solving these equations by least 

 squares (a very easy process), that is, multiplying each by its coeffi- 

 cient of y and its weight, we get — 



0.142 ,y=—l ".39 

 0.0045/ = — 0.02 

 0.017 2/ = — 0.16 

 0.097y = — 1.05 



0.260 2/ = — 2. 62 

 hence x = 6".09 -f 0.461 X — 10.08= 1".44 



Adding 



y = —10"M 



since the declination for 1875 was 14°10'42'' -|- x, and the proper 

 motions in one hundred years y; I took for y in round numbers — 10" 

 and brought up the declinations with its help as follows : — 



