The general Characteristics of the frequencyfunction of stellar movements 



25 



The second line contains the values of the function 

 p = Lu e-^-^fc 

 where oij = 0.429 



When computing the values of ll 3 and U i it will be found that approximative!)' 



n s =11* 



Consequently we take account of the correction by writing 



q = 0 88 é~~ (/ ' 2 fcS ~ °' 43) Xl (1 ~ h> 



and as before 



(50***) » s = *f [~q)* (S S) 



It is easily seen that q can not exceed the value 0.88 or, taking into account 

 the arbitrary character of the magnitude 3,0 as a lower limit, at least not much 

 exceed that value. Evidently the value q — 0.88 corresponds to the value \ — I. 

 As we have 



X. 



this requires that 



- 0, 



or that the absolute magnitude is the same for all stars apparently brighter than 6.0. 

 A value of X t only slightly smaller than 1 , however, does not necessarily require the 

 dispersion of the absolute magnitudes — cs 2 — to be very small, it only requires 

 that it is small compared with the dispersions Oj of the quantity y — — 5 log r. 



For the dispersion of the apparent magnitudes Charlier has for 12 regions 

 of the heavens found k = 3, having made use of counts of stars as far down as 

 to the magnitude 13.89. 



For the stars that have magnitudes smaller than 6. o we have put 



a[m) = K v e xm x = \ .i 



The general formula being 



_ (m— mop 



aim) = t== e 



k\/2K 



we see, as 



K x = a(0), 



that for magnitudes small compared to m 0 we must have 



m 0 ^ 



For m 0 we insert the mean of the values found by Charlier or 

 m 0 = 18.3, 



Lunds Univ:s Årsskrift. N. F. Afd. 2. Bd 11. 4 



