452 KREIZ. 



k = the correction in seconds of arc of a great circle to be 



added to the assumed right ascension -of the center ; 

 c = the correction in seconds of arc of a great circle to be 

 added to the assumed declination of the center. 



Then the measured coordinates in seconds of arc of a great 

 circle, A'' and Y, will require the following corrections : 

 Due to erroneous scale-value, 



Correction to X = -)- pX 

 Correction to V=:'^-pV; 



Due to orientation error", remembering that r is small, ■ 



Correction to A' = -[~ 7'V 

 Correction to y= — rX ; 



Due to errors in the assumed position of the center. 



Correction to X = -\- /e 

 Correction to F= -f- r. 



It is evident that if we add the sum of these corrections to 

 X and Y corrected for refraction and for transformation errors, 

 we should obtain J« cos o^ and Jo respectively. We have, 

 therefore, from each star, two equations of the form 



/& 4- J>X -\- rY-\- Hx^ v■^ 

 cA^p V— rX + ihj = V, 



where the z's, as usual, are the residual errors due to inaccuracy 

 of the observations. 



Let us now form, for each plate, equations like the above for 

 every standard measured ; we shall get a set of observation equa- 

 tions, from which the constants can be determined by the method 

 of least squares. Usually, when all the ;/s have the same weight, 

 or when the weights of corresponding equations in the two coor- 

 dinates are equal, it is possible to abridge the labor considerably 

 by means of certain formula deduced by Professor Jacoby.^ As 

 given by him, they apply to the case of equal weights only, but 

 they might easily be generalized. I could not niake use of this 



ijNionthly Notices, May, 1896, p. 424. 



(112) 



