Astro-Photographic Catalogue Plates. 10 5 



Nx = w^t 



My = W4 t 



from which a table of i^, etc., may readilj' be written down with 

 the help of Crelle's tables. The details of the demonstration of 

 these refraction formulae will be found in the Astronomical 

 Journal (Vol. XY., No. 14). 



II. Correction for scale-vahi^, orientation, and error of centre vf 

 the plate. 



jpX sec c^+iV r sec rf F-f-js ^ sec <^, for X sec S 

 — 15 r cos (5 X sec cJ+pF+ c, " F 



The values of r, p, k and c are found from the known stars 

 on the plate. We compute from the known right ascensions and 

 declinations by means of tables formed from the expansions given 

 above, the values of x sec 8 and y ; we then have from every 

 known star a pair of equations of the form 



15 nx cos i^-\-iSpX-\-rY-\-h = ) , . 



ny-^pY— 15 rX+c = 



in which n^ and n^ are computed by the following formulae 



Ux = {X—x) sec (i+ifx Xsec (5+iVx F 



(2) 



Y—y+My X sec S-^Ny Y 



M^, etc., being as before the refraction coefficients. 



These equations can be solved by least squares or otherwise, 

 and make known the values o? p, r, etc. 



If the solution be carried out by least squares, it is by no 

 means necessary to form and solve the normal equations in the 

 usual way. For the equations possess the following peculiarity : 

 Each coefficient of r in the equations derived from the right 

 ascensions appears as the coefficient of p in the corresponding 

 equation derived from the declination. And each coefficient of 

 p in the right ascension equations appears in the corresponding 

 declination equation, with its sign changed, as the coefficient of 

 r. On account of this peculiarity the rigorous least square solu- 

 tion can be effected in the following very simple way: 



