STARS IN COMA BERENICES. 459 



and the residuals : 



Star 1. Star 2. Star 4. Star 5. Star 14. Star 15. Star 2I. Star 22. Star 23. 



In a —0.65 -I-0.25 -j-i.io -fo.69 — 0.47 — 0.21 4-0.67 — 0.35 -fo.36 

 In (5 +0-03 +0.18 — 0.23 -)-o-o6 — 3-26 +0-28 -I-0.37 +0.07 +0.06 



Both the residuals and the probable errors, it is true, are rather 

 larger than when the constants were obtained by the more 

 elaborate method. But considering the quantities themselves, 

 it will be seen, that both / and /& differ from the values previ- 

 ously obtained by more than the sums of the probable errors. • 

 In the latter case, the reason for this discrepancy is an unex- 

 plained systematic difference between Romberg's places, and the 

 positions of my standards. The discordance in p cannot be thus 

 explained. It is much more serious, as it affects, not the group 

 as a whole, but changes the relative positions of the stars. It 

 appears then, that the constants are by far the most unreliable of 

 all the quantities used in the reduction of the plates ; and it 

 would seem that any labor spent on them, outside of what is 

 absolutely necessary, is but poorly repaid. 



m 



True Scale-Value. — It has been stated that the computed 

 scale-value, 5 2". 87(1 +/), involves the effect of aberration. 

 It may be useful for future reductions of the Rutherfurd photo- 

 graphs to set down the true quantities. Although for accurate 

 work it will in general be necessary to perform the least square 

 solution for each plate, and thus independently to obtain the 

 scale-value, cases might arise, when a close approximation would 

 be sufficient, or when the number of available standards is so 

 small, that no reliance can be placed on the resulting constants. 

 Then, too, it is possible that a relation may exist between the 

 "focus " and the scale-value. 



To find the form of the correction to be added to 5 2''. 8 7(1 -|-/) 

 in order to eliminate the effect of aberration, we let 



(7 = the //'?/£' distance in seconds of arc, from the center to 



any star on the plate ; 

 n = the measured number of millimeters on the plate, from 

 the center to the star whose distance is a. 

 (119) 



