of the Rutherfurd Photographs. 243 



Put 



^ = [xx] + [yr]-i([xp+[rp) 



c=[x-«,j + [F. % ]-l([x][»,] + [r][ % ]) 

 j 5 ;=[r.^]-[x.« i/ ]-I([r][n,]-[x][ % ]) 



Then we have 



g 



p = -, with the weight A. 



A 



A? A - 



k - 1 ( [X\p + [F] r + [**] ), with the weight, » - ^j] ^ [ ^ 



c = - I V (mp-tX]r+M), " » « ,-^m+OT. 



The following will be found a convenient check on the computa- 

 tions : the sum of the residuals for the right ascension equations 

 is equal to zero, and similarly for the declination equations.* 



The above method of solution is rendered still simpler in the 

 present case, as we are going to use the same comparison stars 

 for all the plates. Hence all the terms in the expressions for A 7 

 G and E are constant except those which involve r> or n . Thus, 

 selecting the coordinates of the comparison stars from an}^ plate 

 in Table Y, and multiplying them by 52.87 we have, with suffi- 

 cient accuracy : 





X 



F 



4 



— 1620" 



—1850' 



5 



— 1 140 



+1530 



15 











40 



+1370 



—1850 



44 



+1820 



+ 1390 



Consequently, for all the plates, 



* This is indeed a general check for any set of observation equations in 

 which one of the unknowns enters with a constant coefficient; if this unknown 

 is missing from some of the equations, then the sum of the residuals for those 

 equations in which it does appear is equal to zero. The theorem may be 

 easily modified to include the case of unequal weights. 



