The motion of the atars 



65 



7. In table III I put together the values obtained for the moments — Vy — 

 of the observed frequency table. In table IV I give the corresponding values of 

 the moments — Nij — of the correlation surface of the linear velocities. These 

 moments were found from the formulae (20) and ff above. The value of q used 

 was, as alread}^ remarked, 



q — 1.269B, 



which gives 



0 = = 0.6205. 

 Î 



This value of q was obtained from the formula 



q — e 



using the values 



Â; = 3 and = + 0.5. 

 As to the value of ^ I refer to I p. 40. The value = -|- 0.5 is provisionally 



used. 



The formulae (20) and ff give not directly the moments iVy but X iV^/. 

 For obtaining the moments themselves it is necessary to know the value of îJ-j, 

 h. e. the mean parallax of the stars. The value of this quantity is discussed beneath 

 in connection with the determination of the apex of the solar motion. 



The skewness and the excess of the correlation surface of the linear velo- 

 cities can be found without knowing the value of the parameter d-^ . I have given 

 their analytical expressions above ((25) and (26)), but owing to some misprints there, 

 I give here the correct formulae. We have 



o — 1 AT ■ N 



[o I 



^ ' Q — 1 TV • iV" '/--^ 



Oy "2'-^'03 • 02 > 



and 



- i;,, = (iv,, - 3iv,,^) : 8i^^,„^ 



' In tab. V the resulting values of S and E are given for the 48 squares. 

 Unlike the frequency curves of the proper motions in a and S we find, that 

 the frequency curves of U and V have, with very few exceptions, a negative excess. 

 As to the values of the skewness we find that they are more systematically distri- 

 buted in the frequency curves of Ü and F than in the corresponding frequency 

 curves of Aa cos 8 and AS. 



8. For evaluating the influence of the uncertainty in on the characteristics 

 of the correlation surface of U and V I have performed the computation of Nij, 

 assuming 



1, = 0a. 



Lands Uiiiv:s Årsskrift. N. F. Afd. 2. Bd 8. 



9 



