26 



Sven Wicksell 



from which we see that the stars brighter than 6.0 will best fit into a normal 

 frequency curve having the dispersion 



I = 4.1. 



Indeed, by more recent computations performed at the Lund Observatory taking 

 account of the results arrived at by Henie for the distributions of the stars to the 

 eleventh magnitude, it has been found questionable if the dispersion k should not 

 have a value more near to four than to three. As in the following we shall make 

 use of a q amounting to 3 A it will be of interest to see what should be its bearings 

 on Xj and a 2 . 



By the equation for q of page 25 we find for k = 4 



a 2 



3] = 3.9 % = 1.0. 



Taking k — 3 we find l 1 = 0.87 which gives 



o, = 2.8 a 2 - l.l , 



by which it is seen that for q = 0.76 the value adopted for k will not have much 

 influence on o 2 . 



The unities are for 



r : 1 Siriometer = 10 6 . the mean distance of the sun, and for 

 M : the same unit as for m, 

 so that M corresponds to the magnitude of a star when placed at the distance 

 1 Siriometer. 



The parallax is 



7C = - 0". 206265, 



r 



from whith it follows that 



M(n) — ^.0". 206265. 



Of course, as y and M are logarithms, a x and a 2 are independent of the units 

 chosen for the distance and the luminosity. 



12. Now, to find the moments of the linear motion in the region considered, 

 we have 



(54) *i s JVô = .î' V,(S, 7 s) # 



and using the equations (45) (45*) (45**) for vjj; and N'y we find 



