CHAPTER V 



The moments of the second order from p oper motion and radial 

 velocity observations. 



55 In this chapter I will make a short examination of the moments of the 

 second order. 



When examining the velocity distribution as derived from proper motions, we 

 have to consider the formulae which express the angular mean velocities in linear 

 measure '. 



V# 200 = V 2no?' — 0 — ?'K 2 > 



(51) V^o 2 o=v 02û2 '-(l- (i ')î/ 0 2 , 

 V #uo = v iio i — (1 — Q) *o Vo- 

 liere q is the fundamental constant in the star density function, whose 



numerical value we are now going to determine. 



56. At first we may from the proper motion observations regard the velocity 



distribution as expressed through the ellipsoidal hypothesis. 



For this purpose we have to determine from the formulae (51) the parameters 



in the expressions (30) page 33 which characterize the ellipsoidal surface 2 . 



It is, however, not necessary to treat the expressions (51) in their present 



form. Using in the calculations the observed moments 



V 200 > V 020 > V 110 



we get a determination of the velocity distribution of the so called »apparent 

 cross-motions». 



The values of the moments v 200 , v 020 , v 110 as well as of v 002 , computed about 

 the mean observed, are tabulated in the table XX. 



1 See Chaelier cited memoir. 



2 The solution from the first two formulae of (51) I have given in meddelande No 59. The 

 complete solution, however, including also the third equation of (51) is deduced by S. Wjckselt, 

 and published by him in Meddelande No 60. 



