The distribution of the stars to the eleventh magnitude 



53 



6. Connection between the Limiting Magnitude and the Time of 

 Exposure. 



The time of exposure of the negatives of the Harvard Map is in most 

 cases approximately one hour. P'or some of the plates, however, it differs considerabely 

 from one hour, so that the extreme values are 56"" and 74". (I exclude the plate 

 no. 1. which according to circular 71 has a length of exposure of 39"'. This value 

 seems to be too small ) This collection of plates consequently is not fit for a 

 discussion of the connection between time of exposure and limiting magnitude. 



It would, however, be of interest to see liow much a variation of the time of 

 exposure between the extreme values might influence the limiting magnitude. 



For this purpose I make use of the »blacken law» given by Schwaezschild 



Supposing one star, with the magnitude exposed for t^ minutes, anotlier 

 , for minutes, the law above mentioned gives the following relation, if the in- 

 tensity of the images is to be the same: 



m, — 2,5 p . log — w., — 2,5 p . log 



or 



»Wj — w«2 = 2,5 27 . log ^ . 



This may be directly applied on the limiting magnitude. For sensitive plates 

 2) has the mean value 0,76. Accordingly the increase of the limiting magnitue, Am, 

 is given by 



1,9 log 



Giving and f.-, the extreme values of the Harvard Map we have 



74 



Am = 1,0 log ^= 0,23 



The table VIII seems to show a slight increase in the magnitude, when the 

 duration of exposure is augmented. Taking together the negatives having approxi- 

 mately the same length of exposure I get the following average magnitudes. 



length of exposure lim. magn. 



< (31 11,25 ± 0,108 



eT— 65" 11,25 + 0,126 



65 — 70 11,28 ± 0,334 



> 70 11,66 + 0,236 



As can be seen, the mean errors are rather considerable. The augmentation 

 is, however, of the order, which might be expected according to Schwarzschild's 

 theory. 



