of the Rutherfurd Photographs. 2*7 T 



constants of the plates would have to be changed so as to secure 

 the best possible agreement between the two catalogues. Bach 

 star gives two equations of the form, 



Xdp + Ydr + dk + da = o 

 Ydp — Xdr + dc + dd = o 



where <Za and dd are the uncorrected or direct differences in the 

 table. The least-square solution may be carried out in a manner 

 entirely similar to that previously used. The differences for stars 

 18, 20, 24 and 25 were not used because these stars were not in- 

 cluded in Schur's triangulation, but each was merely located by 

 position angle and distance from the nearest star in the triangula- 

 tion. Stars 19, 41 and 42 were also excluded in making the least- 

 square solution because of the small number of plates on which 

 they appear. The remaining stars, thirty-three in number, give 

 the following corrections to the contents: 



dp = + 0.000011 ± 0.000009 

 dr = -\- 0.000098 dz 0.000009 

 dk = 4- o // .047 ± o // .oi4 

 dc = — o // .667 ±o // .oi4 



The probable error of one equation is 



± o^.oSo 

 a quantity which speaks well for the accuracy of all three re- 

 searches concerned. The corrected differences in the table are 

 now obtained by adding to each uncorrected difference 



X-dp -j- Ydr + dk in the right ascensions, 

 and T-dp — Xdr 4- dc in the declinations. 



Prom the above value for dp we see that the meridian observa- 

 tions gave a scale-value which agrees very closely with that ob- 

 tained from the heliometer places; the largest effect that dp has 

 on either coordinate of any star is only about o // .02. On the other 

 hand the value of dr, or the change in the orientation constant 

 is quite large, corresponding to a correction of about o".20 in the 

 coordinates of outlying stars. The meridian observations which 

 we used to determine the orientation of the group, were also em- 

 ployed by Schur for the same purpose, and were found by him to 

 give results which practically agreed with those obtained by an 

 independent method. As we have adopted Schur's proper mo- 

 tions for the comparison stars, to reduce their places to the epochs 



