ôô 



Sven Wicksell 



teristics given in tables XIV and XV for q = Ü.62 with the two-stream hypthesis 

 would be hopeless. 



32. In the paragraphs 35" and 36 of his work Charlier makes some ex- 

 cedingly interesting remarks regarding the bearing of the law of Maxwell for the 

 molecules of a gas on the distribution of stellar velocities. The law of Maxwell 

 requires that taking out particles (stars) of the same mass the distribution of their 

 velocities in any one direction shall be of the normal form. What would then be 

 the distribution when particles (stars) of different masses are mixed? Assuming the 

 logarithmus of ithe mass to be normally distributed with the dispersion L, Charlier 

 finds that the skewness should be zero and the excess given by 



E= 3 / 8 (e i2 — 1), 



or taking the luminosity to be proportional to a constant power c of the mass 



(87) #== B Y 8 (e*V— 1), 



where 



_ 0.921034 



c 



and a 2 is the dispersion of the absolute magnitudes. 



To get an opinion of the order of magnitude of this excess we will proceed 

 as follows: 



Assuming for a moment the density of the stars to be of the form used by 

 Seeltger 



D = y v-' 



we should find from the equations of paragraph 11 



and by equations (47) and (47*) * 



(50*) » s (m) = (j) 



and here q has the form 



q' = e -m»\ 



By computations similar to those performed in § 12 we should find that for all 

 stars brighter than 6.0 we have to take 



q = 0.88 e-'''-' Ä . 



* It has already been pointed out by Chakliek that the assumption of Seeligek regarding 

 the density function will give rise to the expression (50*1 for ft s . 



