242 Prsesepe Group; Measurement and Reduction 



k = the number of seconds of arc of a great circle through which 

 the axes are to be translated in the direction of decreasing 

 right ascensions. 



c = the number of seconds of arc of a great circle through 

 which the axes are to be translated in the direction of de- 

 creasing declinations. 



The corrections to the rectangular coordinates arising from p 

 are then : 



For X, -\-p ■ X 



" y, +p- r 



On account of the orientation corrections, remembering that r 

 is small, we have the corrections : 



ForX, -\-r-Y 

 " Y, —r-X 



Finally, k and c give the corrections : 



For X, ,+ * 

 " Y, +c 



Combining all these corrections, we have : 



For X, -f p • X-\- r ■ Y + k 

 " Y, +p- Y—r-X+c 



Let us now compute n x and r? ] for each comparison star, from 

 the following equations : 



n x sec 8 Q = X sec 3 plus corrections for transformation and 



refraction, minus Aa. 

 n = Y plus corrections for transformation and refraction, 



minus Ad. 

 Then for each comparison star we have two equations of the 

 following form from which to determine p, r, k and c : 



pX-\-rY-\- k-\-n x = o 

 pY — rX-\- e+ % = o 



Owing to the way in which the coefficients of the unknowns 

 are repeated in these equations we do not need to make the least 

 square solution in the usual manner, but as Professor Jacoby has 

 pointed out,* we ma} r find the unknowns very simply. Thus, let 

 v = the number of comparison stars, and let us denote by square 

 brackets the sum of v quantities. 



* Monthly Notices of the Eoyal Astronomical Society, May, 1896. 



