32 



C. V. L. Charlier 



As is seen, rather distinctly from so small a statistical material, from Tab. 3 

 and still better from the (somewhat hypothetical) graphical curves, there is a fairly 

 constant difference between the BD magnitudes in Cj and amounting to about 

 _|_ O'^.si *). Furthermore the parabolic form of the curve H—BB is pretty well 

 developed. We get approximately the same form for the curve in both squares. 

 It is only transferred parallel to itself through the distance 0'".3i. It is easy to 

 get the equations of these curves, but it will be adviseable to postpone the deter- 

 mination of the analytical form of the curves till the other squares have been 

 examined. 



The comparison between BB and PG I here omit, because it cannot be 

 performed beyond the magnitude 7™. 5. It must liowever be borne in mind that 

 Messrs Müller and Kemppf, the both observers in Potsdam, have deduced a rather 

 considerable systematic difference between the Harvard and the Potsdam-magnitudes 

 dependent on the colour of the star, which difference, according to these observers, 

 must be ascribed to the Harvard measurements. It is declared to be a >^PwJcinje 

 effect» due to the mode of observation at Harvard. As the colour of the stars 

 fainter than 7™.5 is entirely unknown, we cannot for the present estimate the influ- 

 ence of this systematic difference, but we iriay assume tliat the magnitudes in HR 

 may be affected by a systematic error amounting perhaps to some tenths of a 

 magnitude. 



16. We have next to determine the limiting magnitudes of the C. du G. 

 As this determination is, however, still not accomplished I transfer this question 

 to the next lecture. We shall today examine how the parameters in a{m) can be 

 mathematically determined. 



Denoting with N the total number of stars in a cone determined by a certain 

 square we have 



N 2/t2 



(63) a(m) = — 7= e 



For determining the three parameters N, and Ic we may proceed in two 

 different ways. It is to be presumed that the parameter m.Q is rather great. Hence 

 writing (63) in the form 



, , , ™ avi—hirfi 



(63*) ffl(m) = Ce 



we may assvnne that, for small (or moderate) values of m, the term hn^, in the 

 exponent, is comparatively small as compared with the term am. In other words 

 we may assume that for small m the number of stars of the apparent magnitude 

 m can be approximatily expressed through the formula 



*) That the magnitudes of BD are dependent on the density of the stars has been found 

 by Sghönpeld and more fully stated by Scheiner and Seeliger. 



