118 Reduction of Stellar Photographs. 



this it is necessary to compute the eflfect of aberration upon the 

 value of p derived from the known stars in the manner explained 

 above. We find that the quantity which must be added to the 

 value of p so derived, to reduce it to what it would have been if 

 there were no aberration, is given by the following formulae : 



7i = — (tane sincJ + sin a cosrf) sin i" 

 y^ = COS a COS S sin i " 

 Corr° = C7i + Dj^ 



In these formulae s is the angle between the equator and eclip- 

 tic, and C, i), are the usual Besselian day numbers given in the 

 Berlin Jahrbuch. 



Since each plate has four overlapping plates, it is clear that a 

 rigorous application of the above method of adjustment will give 

 us a series of equations involving twenty unknowns, four for each 

 of the plates under consideration. The solution of such a series 

 of equations for each plate would ofier insuperable difl3culties, on 

 account of the excessive labor involved. Even the application of 

 the process to two overlapping plates with the necessary eight 

 unknowns would be too much trouble. Except in very special 

 cases, therefore, we shall have to substitute some approximate 

 method of adjustment for the above rigorous one. Various ap- 

 proximate methods readily suggest themselves, but it will not be 

 possible to decide on the best one until a considerable fiumber of 

 plates have been measured and preliminarily reduced. We shall 

 then have material which will enable us to deal with the question 

 practically. 



