244 Prsesepe Group; 3Ieasurement and Reduction 



A = 20,080,000 



C = [X ■ nj + [ Y ■ %] - 86 [* J 4. 156 [n f ] 



.£= [ F • nx] - [X • % ] + 156 [«*] - 86 [«,] 



C 



p = ; weight, 20,080,000 



20,080,000 

 E 



20,080,000 



20,080,000 ' 



& = — 862?+ 156 r — 0.20 [?i x ]; -weight, 4.96 

 c = + 156^4- 36 r — 0.20 [w,,] ; " 4.96 



It now remains to show how the right ascensions and declina- 

 tions of all the stars may be computed. The constants of the 

 plate give rise to the corrections : 



For X sec rf , -\- p ■ X sec <J + r sec fJ • F+ k sec rf 

 " Y , +p ■ Y —r-X + c 



The corrections for refraction are : 



For X sec S , + M x - X sec rf 4. JV B ■ F 



" F , + My ■ A" sec <f + N„ ■ Y 



We have still to add corrections for transformation, which vaiy 

 from star to star, but are the same for different plates. Now let 

 us define a. x and d 1 as the projected right ascension and declina- 

 tion respectively of a star, the true right ascension and declina- 

 tion being given thus : 



a = a y plus the correction for transformation. 



3 = 8 1 plus the correction for transformation. 



Then collecting the corrections given above : 



a x = (1 -\-p 4- M x ) Xsec (\ 4- {N 4- r sec 6 ) Y-{- (a 4- h sec 6 ) 

 *i = (1 +P 4- N y ) Y +{M y — r cos 6 ) Xsec rf 4" Co + <0 



Hence, to get the projected right ascension and declination of 

 any star, the constants of the plate having been determined, we 

 need only compute the six coefficients in the parentheses and per- 

 form the simple operations indicated. These coefficients, it is 

 needless to remark, are constant for an entire plate. 



As an example of the above methods I have set clown the de- 

 tails of the computations for the constants of Plate VIII. 



