68 Rutherfurd Photographic Measures of 



scale-divisions. The clock was then again made to run long 

 enough to permit the formation of another image of the central 

 star. The line joining this last image with the central image was 

 used as the origin of the position-angles. Angles so measured 

 were made in the present paper to conform to the custom of count- 

 ing from the north point towards the east by addition of 270 ° to 

 the observed readings, as seen in Table VI. 



Of course the position-angle of this last impression of the prin- 

 cipal star is not exactly 270 , however, unless there has been ab- 

 solutely no shifting of the telescope in declination during the 

 formation of the trail, or when clamping in the clock for the final 

 image. It is a priori probable that such shifting did occur ; but 

 with such alterations in the balance-weights of the tube, in the 

 pointing of the telescope, and in the other conditions of exposure 

 of many plates during the course of several years, we may fairly 

 assume, on the other hand, that such shifting in declination is not 

 S3'stematically in the same direction ; that, consequently, the 

 mean of the position-angles of a given star as determined from all 

 the plates is its most probable value. Hence, if all the stars were 

 found on all the plates, it would be unnecessary to apply a cor- 

 rection for error of orientation. But such is not the case. Fur- 

 thermore it is desirable to use the individual measures separately 

 for a determination of the parallax. 



This correction may be deduced from standard stars by taking 

 from the mean of all the angles of all the plates the angle meas- 

 ured on each plate separate^, and regarding the residual as the 

 orientation variation of that plate. For any particular star such 

 residuals would not, however, be the true correction ; for it would 

 contain the effect of both the proper motion and the parallax of 

 the central star. Several stars should, therefore, be selected as 

 standards ; and they should be so distributed in distance and 

 angle as to eliminate both parallax and proper motion from the. 

 mean of their residuals for each plate severally. Since the prob- 

 able error of measures of angle vary inversely as the distance, 

 these means should be taken by weight proportional to the square 

 of the distance. 



Expressed symbolically these conditions are : 



A. 

 B. 



Sff 2 ^ 



2cr 2 



SS-j = 0. 





