114 Beduction of Stellar Photographs. 



These results signify that if we have computed x and y from 

 the known right ascension and declination of the star, using a 

 and 8 as the right ascension and declination of the centre of the 

 plate, and if the true right ascension and declination of the centre 

 of the plate are : 



a -\- da 6 -\- d(\ 



then the true values of x and y will be : 



X -\- dx y -\- dy. 



We shall therefore have the following equations, in which p 

 and r indicate the scale value and orientation constants, as be- 

 fore, and X and Y are the observed co-ordinates : 



x^dx^X^pX+rY ^ 



y -^ dy=Y + pY—rX \ ^^ ' 



The constants k and c do not appear in these equations, be- 

 cause up to the present I have assumed that an imaginar}^ line 

 passing through the optical centre of the object-glass, and cut- 

 ting the sky at a point whose right ascension and declination are 



a -^ da, S -^ dS 



will cut the plate at a point whose co-ordinates x and y are both 

 o. If such a line cuts the plate at a point whose co-ordinates are 



— X, ■ — f 



equations (/) become : 



x+dx = X-{-pX+rY+ X I (. 



y -^dy =Yi-pY — r X+i' i ^^' 



I shall now impose upon the above imaginary line the further 

 condition that it be perpendicular to the plate, which condition 

 at once assigns definitive values to / and (p, and for a given posi- 

 tion of the telescope, to dx and dy. This is equivalent to defining 

 the sight line of the telescope as a line drawn through the optical 

 centre of the object-glass, and perpendicular to the plate. In 

 this way we avoid the question of a possible inclination of the 

 plate to the sight line of the telescope. 



We now substitute in equation (cj) the values of dx and dy 



