III. Method of Reduction. 



Having obtained in the manner explained in the preceding 

 section the measured coordinates of the stars on the plates, we 

 are in position to deduce from them the differences in right ascen- 

 sion and in declination to which they correspond. It is plain that 

 certain corrections must be applied before this can be accom- 

 plished. In the first place, a photograph is a plane picture of 

 the sky ; hence we must introduce the " Transformation Cor- 

 rections." Then the stars' positions are affected by refraction, 

 precession, nutation and aberration, and the measures must be 

 freed therefrom. We shall find, however, in the progress of 

 the work, that before we can apply these corrections to the 

 measured coordinates, we must reduce the latter into differences 

 of right ascension and of declination (except for the corrections 

 mentioned above) by means of certain constants to be dis- 

 cussed later. These are found by comparing the positions with 

 respect to a given origin of certain well known stars on the 

 plates with their measured coordinates, corrected for refraction, 

 etc. These constants being known, we shall find that by means 

 of simple formulae the measured coordinates can be trans- 

 formed into angular distances and at the same time freed from 

 the effects of refraction and errors of orientation. Adding these 

 distances to the known coordinates of the origin of measures 

 on the plate, we obtain the celestial coordinates of the stars ex- 

 cept for the transformation corrections. The latter are then ap- 

 plied to the means of all the observations on each star, and we 

 have the final right ascensions and declinations. 



Let us proceed to discuss these several steps. 



Transformation Corrections. — An astronomical photograph 

 may be regarded as a central projection on a plane of part of 



(98) 



