OP ARTS AND SCIENCES. 



199 



The star Piazzi xv. 176, has the following determinations of its 

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

 cession and proper s^'steraatic corrections : — 



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



a;_0.77i/ = 9".l Wt=l^ 



X _ 0.40 y = b.l 1 



X — 0.33 y = 4. 9 1 



a;_0.10y = 2. 2 f 



Taking the mean by weights, we have x — 0.461 y = 6".09, which ia 



the final determination of ic — 0.46 1 y. 



Hence, 



O.SOd y = — 3".0l 



0.061 y=z — O.Sd 



0.131 y = — 1.19 



0Mly = — 3.8d 



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=—r'.39 

 0.004 y = — 0.02 

 0.017y = — 0. 16 

 0.0975/ = — 1.05 



Adding " 0.260 y = —2.(j2 



y 



= _ io".08 hence x = 6".09 -f 0.461 X — 10.08= 1".44 



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 : — 



