The general Characteristics of the freqnencyfunction of stellar movements 23 



we have 



cc 



(47) a(m)= f ' dy \{y) <p 0 [m + y) 



00 



(47*) a{m) ih{m) f dy \{y) 'f 0 (wi + y) e hy , 



— GO 



where •&.<(?») is the mean of -i- for the stars having the magnitude m. 



Regarding the density function & 0 {y) and the luminosity curve <p 0 {M) Charlier 

 and others have found that they can he expressed by 



(48) ?0 (M) = e 2V 



(y — w,) 8 



(48*) A 0 (y) — -= e~ 2o >* 



o t |/2« 



by which he also finds from (47) and (47*) 



t 



(49) a(m) 



k V2n 

 ^ = 0* + % 



and 



(50) », (m) = K 



where 



m 0 = w 2 — w?, , 

 6X. i« 



Finally putting 



(50**) 



— 6«jfc*X,(l- 



he finds 



(50*) » s (m) = »*(m) 



12. In the present investigation we do not use stars of a certain magnitude 

 m, but all stars brighter than m = 6.0. 



The question is now: can the equation (50*) be used even in this case? 

 Charlier seems to have been of the opinion that, taking stars brighter than G o, 

 equation (50*) is still valid. 



By numerical calculations I have come to the same opinion except on one 

 single point, I find that equation (50**) should be written 



