240 



Prsesepe Group ; Measurement and Reduction 



extra correction for orientation. (See note at the end of this 

 paper.) The formulas that I have preferred to use are those given 

 by Professor Jacoby ; * while these are not quite so simple as 

 those of Professor Turner, they take into account the orientation 

 correction mentioned. Let 



<p = the latitude, + 4o°44' in this case. 

 — a = the hour angle of the centre of the plate, from Table I. 

 £ = the declination of the centre, + 20°i3' 

 /?= the constant of refraction, computed in the usual way 

 and then multiplied by |f to allow for the increased refrangibility 

 of photographic rays.f 

 Now let us compute : 



tan N = cos (0 — a ) cot </> 

 G =cot {S + N) 

 S == tan (6 — a ) sin N cosec (<5 + N) 



N x = p\Q — tan <J ) HseeA 

 M,, = j3(G-{- tan 6 ) H cos rf 



N y = p{i + G*) 



Then the corrections for refraction take the form : 



Correction for X sec <5 = M x ■ X sec <5 + N z ■ Y 

 « " Y = M y ■ Xsc\-\- NyY 



The coefficients of X sec <5 and of Y m the second members are 

 constant for an entire plate. We may then construct Table "VII, 

 in which the number of the plate is the argument. 



Table VII. — Refraction Coefficients. 



Plate. 



Mx 



Nx 



My 



Ny 



I. 



O.OOG356 



0.000017 



0. OOOI 14 



O.OOO349 



II. 



0.000423 



0.000042 



0.000174 



O.OO0375 



III. 



0.000404 



0.000031 



0.000153 



O.OOO373 



IV. 



0.000523 



0.000086 



0.000255 



O.OOO424 



V. 



0.000357 



0.000015 



O. OOOI 10 



0.000354 



VII. 



0.000423 



0.000042 



O.OOOI74 



O.OOO375 



VIII. 



0.000491 



0.000074 



O.OOO233 



O.OOO404 



II. 



0.000377 



0.000023 



O.OOOI3 I 



O.OOO360 



All the coefficients are positive. 



* Astronomical Journal, No. 387. 



t Bulletin du Comite* Permanent, I, 464 ; and Scheiner and Eambaut, 

 Astron. Nach. 3255. 



