II. The Limiting Magnitude of the Harvard Map. 



1. Definition of the Limiting Magnitude. 



The determination of the number of stars in any particular region of the 

 heavens has but a Uttle value if the magnitude of the stars included in the counts 

 is not known. The star density is in fact characterised by two quantities namely 

 the ntimhcr oj stars and ihc limiting magnitude. The first of these quantities have 

 been determined in the preceding pages, the latter will be the object of this chapter. 



If one part of a negative includes stars up to the wz"" magnitude, m is the 

 limiting magnitude of the part of the negative in question. 



Tliis quantity consequently indicates the limit in the brightness of the stars 

 included in the count. 



The considerable variation of the star density from one plate of the Harvard 

 Map to another and the decrease from the centre towards the margin is evidently 

 caused by an appreciable variation of the limiting magnitude of the Harvard Map. 

 The problem is now at first to determine the limiting magnitude on this set of 

 plates, and for the second to find the law of the variation of this quantity. 



2. Determination of the Limiting Magnitude. 



In order to determine the limiting magnitude I have solely used Hagen's 

 Atlas Stellariim Variabilium together with the photometric measurements of Pickering. 

 This atlas, containing charts of variable stars with the surrounding comparison stars 

 has previously been used by Prof. Chaelier to determine the limiting magnitude 

 of Cartes du Ciel. 



The atlas gives for every chart an index of the magnitudes of the comparison 

 stars in different scales. The scale used in this discussion is always the Harvard 

 Scale. I have proceeded in the following manner. When the part of the negative, 

 that corresponds to the Hagen chart is found, I have for each comparison 

 between chart and plate noted the magnitude of the star in the Harvard Scale and 

 the intensity of the photographic image of the same star, beginning with the brigh- 

 test. In this way I get two series, one giving the increasing magnitudes, the other 



