Researches in Stellar Photography. 



197 



nary convention explained in " Mem. Roy. Astron. Soc," vol. 47. Bnt 

 it should from the first be understood that any other convenient light 

 ratio, and any other standard magnitude, might have been adopted. 

 It may properly be here repeated that the object of the research is 

 confined to the question whether a definite relation can be discovered 

 between measured photographic images and the ordinary conven- 

 tional magnitudes of stars. 



If this equation expresses the true relation between diameter of 

 image and magnitude, then an equation of condition for the deter- 

 mination of the numerical values of the constants becomes of the 

 form — 



log2/=log/*-| (1) 



the logarithms here being on the ordinary base 10 ; i.e., if D, D' be the 

 measured diameters of two stars on the same plate, and M, M' their 

 corresponding magnitudes, then — 



D-D=alog]J (2) 



From this it follows that in the equation of condition (1), (derived 



at 



from the original equation to the curve, viz., y=Ae~a ), the constant fi 

 is the magnitude of the faintest star at all impressible on the plate 

 for the exposure in question (or whose photographic diameter is zero), 

 and 8 denotes the diameter of that star whose magnitude is the tenth 

 part of that of this zero star on that plate, this particular number 

 (10) being necessarily introduced by the adoption of the Briggean 

 system of logarithms. 



With regard to the relation (2) 



D-D' = S{logM'-log M}, 



it is noticeable that it is in analogy with the fundamental relation 

 existing between light and magnitude — 



M-M'=K{logL'-logL} (3) 



We now proceed to the numerical computation of the constants (fi) 

 and (£), and consequently to the comparison of the resulting computed 

 magnitudes with those instrumentally obtained by the Wedge Photo- 

 meter. 



The results of the present research are confined to the discussion 

 of three plates of a portion of the Pleiades, exposed for 7, 12, and 

 15 minutes respectively on February 11 and April 2 of the present 

 year, at the respective altitudes of 51° 57', 23° 49', and 21° 50'. The 

 stars selected for measurement on these plates are twenty-four in 



