56 



H. JACOBY, 



twist, or some similar derangement, is really the thing most to be feared. 

 Moreover, we have already mentioned that the present method has the 

 powerful advantage of substituting the precision of micrometric measures 

 for observations of transit times, and of multiplying enormously the quantity 

 of material obtainable in a single fine night. 



"We shall take as our point of departure equations (12). If we combine 

 the n pairs of equations of this form into a pair of mean equations, we get 

 for each star: 



u s -t-p s d A r -*-sin B 0iS d x-i-cQS B^ s d y -+- f , , = 

 v s -+-P s d o w — cos ^o, s do x -+- sin B 0jS d y -t- f = 



. .(16) 



It will therefore be necessary to determine d x and d y in order to 



arrive at values of: 



u' -+■ p s d A' and v -*- p d co . 



To do this, we subtract the mean equations (16) from equations (12), 

 and thus obtain for each exposure and for each star a pair of equations of 

 the form: 



p s \A' -h sin B 0i9 A n x -t- cos B^ s A n y -h A n l\ s == 

 Ps A n w - cos B o, s '%*& sin B 0iS A n y + A n Z' njS == 

 In these equations, as already stated: 



. .(17). 



A n x = d n x—d x, A n 't ^==1 „,, — <; 0>- , 

 \y==d n y — d oyi A n ^, = f^ — f 0f f , 



etc. etc. 



Equations (17) are solved easily by least squares, and make known 



the values of: 



\ A '> \<*> \ x > \y- 



Now from equations (11) we obtain: 



d n *= cos AJ d n x— sin Ajdv 



If we put: 



d n n = — sin Aj d n x— cos Ajd n y. J 



(18) 



d n l= cos AJ A n x— sin AJ A n y, 



<'/] = — sin A n 0A n x— cos A n bA n y, j 



(19) 



d' n I and d' n t\ become known quantities, and we have : 



4'ii;i.- Msit. crp. 56. 1 6 



