Group of the Pleiades. 275 



In the case of the distances it is also possible to deduce a sys- 

 tematic correction for each plate. But the result upon the mean of 

 the measures is nil, as before. Let x and y be the coordinates of 

 the central star in a system whose origin is at the corrected posi- 

 tion of the same, and whose axes of X and Y are directed toward 

 the North and East. Then each measured distance requires the 

 correction 



x cos p -j- y sin p. 



If we let o be the mean from all the plates of a measured dis- 

 tance g, and put 



d = 6 — (j, 



then every star on the plate yields an equation of the form 

 x cos p -j- y sin p = d 



for determining x and y. Forming normal equations, and solving, 

 we get : 



[sin 2 p] [d cos p] — f[sin 2p] \_d sin p] 



— J[sin 2pf -j- [ sm2 i>] [cos 2 p] 



_ J[sin 2/)] [d cos p~] — [cos 2 p] [d sin p~] 



— [sin 2 p~\ [cos 2 p2 -J- £[sin 2£>] 2 

 Now if we put : 



[2)] = the sum of all the values of d for any particular star from 

 all the plates, we shall have 



[*>] = [•.-•] = o , 

 consequently 



l[d cosjo]]' = [[-D] cos p] = o 



[id sin p-]] = [[Z>] sin p] = o , 



and therefore 



[a?] = o 



[2/] = o. 

 The sum of all the systematic corrections for any particular star is 

 then also zero : for 



[x cos p -f- y sin p~] = [a?] cos p -\- \_y~\ sin p = o 



Consequently the mean of all the measured values of <j would not 

 be changed by the application of the corrections. 



