46 



Hans Henie 



The table contains 106 values of the limithig magnitude distributed on 40 

 negatives, and as the Harvard Map consists of 55 negatives there will be 15 nega- 

 tives of which no determination of the limiting magnitude has been possible by 

 this method. The reason why no determination has been made on these plates 

 is that no Hagen chart exsists for variables more southern than about — 30", 

 and as for the few northern the magnitudes in some cases are not given in 

 the Harvard Scale. However, these 15 plates have been treated in another man- 

 ner so that the limiting magnitude, as will be seen beneath, nlso in these cases has 

 been determined with a sufficient accuracy. 



The table of the limiting magnitude of the different negatives. Tab. VI, shows 

 in the cases, in which this quantity has been determined in a series of points 

 on the same plate, that the magnitude decreases from the centre of the plate towards 

 the margin. The problem is now to find the law of this decrease. 



An attempt to derive this law direct from the observations failed because of 

 the relative great probable eiTors in the determinations and because of the observa- 

 tions being too scattered. 



Consequently another method is to be applied. 



In each of the seven zones, into which I have devided the negative (page 37) 

 I consider the limiting magnitude as a constant, and only discuss its variation from 

 one zone to another. This variation may be discussed by help of the series of the 

 average values of the relative density of the zones given above. 



If, however, the variation of the limiting magnitude is to be derived from the 

 variation of the relative density, the connection between number of stars and magni- 

 tude of stars must at first be discussed. 



In SlelJnr Statitics I, prof. Chaklikr gives the number of stars a{m) of a cer- 

 tain magnitude, iv, in the form of an ordinary frequency function : 



Now the star density includes the stars from the brightest to the m'" magnitude. 

 We have accordingly, denoting the star density with A{in): 



3. The Star Density and the Limiting Magnitude. 



This may be written in another way if the integral of probability: 



is introduced. 



