u 



H. JACOBT, 



of course precede the former, and it will be carried 



in the following way. Put: 



% = *' — «, 



n, = it' — tz 



' y 



Then n and w are known, being of course computed with the approximate 



9 



values of g, yj, etc. We then have from each known star a pair of equations 

 of the form : 



sin B je cos B j j A „ « 



»sinl" * psial" J # . /ox 



; (3) 



p dm — to cos B d% — to sin B dr\ -+- w = 



From a solution of these by least squares the most probable values of 

 d|, dt\ 9 da, and dA can be found. It is interesting to note that dA occurs 

 only in the right ascension equations, and tito only in those derived from 

 the polar distances. From the nature of the case, this could not be 

 otherwise. 



We also notice that in the solution of equations (3) by least squares, 

 the equations derived from the right ascensions must not receive the same 

 weight as those derived from the polar distances. It is evident that in order 

 to make the weights of all the equations alike, it is necessary to multiply 

 those derived from the right ascensions, whose numerical term is n x , by 



the quantity: 



pto sin 1 



rr 



If we perform this multiplication, and write: 



a = — to sin B, b = — to cos B, 

 dA' = to sin l" dA, n' x =p<*} sin l"n , 



equations (3) take the form: 



adfc-*-b d-f\ -h-pdA' -4-^ = 



b dc, -+- a dr\ -+- p d to -+- n = 



if 



(4). 



The rigorous least square solution of these equations can be obtained 

 by the aid of the following very simple formulas, in which the square 

 brackets denote the summation of as many quantities as there are stars in 

 the solution. 



$H3.-MaT. CTp. 44. 4 



