STARS IN COMA BERENICES. 453 



method, however. For, owing to the manner in Avhich n^ and 

 ;/ were obtained (namely, by using J« and Jo obtained from 

 catalogue positions), their weights are quite irregular. The 

 formulseof the general theory, therefore, had to be used. Each 

 equation was first multiplied by the square root of the weight 

 of the star on which the absolute term depended. This, al- 

 though not theoretically correct (since the weight should take 

 account of the uncertainty in the position of the central star, and 

 also of that of the measured photographic coordinates), was 

 found to be sufficiently accurate, owing to the minuteness of the 

 unknowns. For the same reason, no appreciable error was 

 committed by dividing the coefficients X and Y by lOO, and 

 retaining only the first place of decimals, while the arithmetical 

 work was greatly simplified thereby. The following set of ob- 

 servation equations was thus obtained : 



y'Jx k + V /i Xp' + V >; Yr' -f Vp\n^ = o 



y Pn C ^ Vp„ Yp' — 1 pa Xr^ -f 1 'A"i/ = O 



where ^'p is the square root of the weight, (// — i) is the num- 

 ber of standards used, /' = ioo/>, / being the scale-value desired, 

 and r' = lOO r. To find the unknowns, the following method 

 was used, a demonstration of which is given in Jordan, Hand- 

 Imcli del' Vennessungshtnde , Vol. I, p. 97 (4th edit.). Form 

 the two sets of normals : 



[Al'^'+EAA'i]/^ -^iP.Y.y -l-[A«.] =0 



lP^X,X{\p' + [AA-iK,]r^ + [A^V'a-] -o 



[A]^-+[A^2]A -lP^x.;\r^ +[A«.] =0 



ipi y-z y'l'] p' - [A^^2 y^Y + [a n«y] = o 



iP^x^x^y — lP^X^n,j-\=o 



where the subscripts ^ refer to the equations containing k, and 

 the subscripts ^ to those containing c. Now eliminate k and c 

 as usual, obtaining 



(113) 



