The general Characteristics of the frequencyfunction of stellar movements 57 



B t00 = Vs n x n 2 {a. 2 — a 2 2 ) 2 — - '/* " t « 2 — M a) ( a i 2 ~~ a 2 2 ) ( w i " "'s) 2 + 



+ Vs4 «j n 2 {\ — 6»j ?? 2 ) (vHj — m 2 ) 4 

 #220 = #202 = #022 = V* »j w 2 (a, 2 - a 2 2 ) 2 



^040 = #004 = 78 »! »2 K' — «2 2 ) 2 



# 3l0 = Jl Mn = B yw = B 103 = B 031 = B 013 = 0. 



Now, firstly, as the ellipsoid is three axial the condition 2V" 020 == iV 002 is not 

 fulfilled. 



For q - 0.75, however, the conditions ß 030 = B 003 = B 210 = B 201 = 0 are 

 nearly fullfilled. 



The conditions B 310 = B 301 = B 130 — B 103 = B 031 = B 013 = 0 cannot be said to 

 be fulfilled, and B 220 , 2? 022 and B 202 are not as is required positive. B QOi is, ho- 

 wever, positive. 



Before going further we will take a look at the values found by Eddington 

 for the characteristics of the two drifts. From his new hook »Stellar movements 

 and the structure of the universe* I find that he has found 

 a. v — a., n x — 0.6 n 2 — 0.4 



and taking the square dispersion transverse to the relative stream direction as half 

 the unity 



n x a x 2 -j- d 2 a,, 2 — 0.5 11^ — m 2 = — 1 .87. 



Hence we obtain from our formulae 



2V 200 = 1-34 2V 020 = 2v~ 00 . 2 = 0.5 



#300 = — °- 105 ß 4oo = — °- 0B38 



and all the other characteristics zero. 



As the unities differ from ours we compute the ß-characteristics which are inde- 

 pendent of the unity. We find 



Psoo = - 0.033 ß 400 = - 0.030 



and the others zero. 



For q = 0.75 we obtain from our figures 



ßsoo = — ° 028 ^400 = — ° 047 



which is a very pretty agreement. 



To my opinion the results cited from Eddington principally constitute a de- 

 termination of the skewness and the excess in the vertex direction *, and the above 

 small calculation is, indeed, a determination of the constant q being strongly in 



* To avoid misapprehension I once more call attention to the fact that the results of 

 Eddington, being based on a study of the position angles of the proper motions do not necessa- 

 rily represent the true distribution of the linear velocities. More strictly they may be said to 

 characterize the distribution of movements in a constructed system of stars giving rise to the ob- 

 served directions of motion on the sky and as far as then possible having the two-stream property. 

 The results of Eddington are thus s true » in a similar sense as our results if we adopt a value 

 of q' only on account of it making the deviations from the normal distribution as small as possible. 



Lunds Universitets Årsskrift. N. F. Afd. 2. B 11. 8 



