The general Characteristics of the frequencyfunction of stellar movements 47 



There seems to be principally three possible explanations of this difference 

 between the results of radial- and proper-motions*. They are: 



l:o. If the stars out of the Galaxy have greater spread of motion than the 

 galactic stars. 



2:o. If the mean parallax t)- 1 is greater near the pole of the Milky Way 

 than in its plane. 



3:o. If the tangential components of motion parallel to the galactic plane 

 generally predominate over the radial components. 



The second explanation is decidedly the most simple and plausible one, but 

 it has the fault that the difference to be explained is too great. Indeed, it would 

 for q = 0.75 require a ratio of * 1 out of the Galaxy to & 1 in the Galaxy amounting 

 to about 2:1. Now for the stars brighter than the magnitude 6.0 it is not probable, 

 that the boundary of the stellar system being further away in the Galaxy than at 

 the pole, should have any effect on the mean parallax. Indeed, the variation must 

 principally come forth on account of the predominance of the early spectral class 

 stars in the Galaxy compared to the polar regions. The variation then cannot be 

 anywhere so great, In fact, as will be seen in a following chapter the proper 

 motions themselves make probable a ratio amounting to about 1.2. As a summary 

 it is only the more emphasized of how great an importance it is to study the 

 variation in & 1 and correct the axes for it. In a following chapter we will, in fact, 

 more carefully look into the thing, and we will there also procure a method of 

 correcting the characteristics for this variation. 



To explain the difference recourse must also be taken to one of the other hypo- 

 theses or both. To come to a decision it will perhaps be most expedient to com- 

 pute the ellipsoid separately from stars in the galactic and in the polar regions- 

 For the present I will, however, not go further into these questions, hoping to find 

 an opportunity to do so another time. 



19. The normal equations for the characteristics of the third order take the 

 following simple form: 









— 3.8512 7?' 



m $ 1 3 = -f- 1.3282 q" 6 — 0.5897 q'(l 



— q'*) + 0.1423(2 — 







13.9552 7i" 300 



0.1084 B" n 



V— 1.6878Ü" 



loa ^i 3 = + 0 bl8i q' s -f 0.6877 q'{\ 



— q' 2 ) — 0.0342(2 — 



3«' + q' 3 ) 



4- 



0.1084 



— 5.9383 



— 0.6209 



= — 1.5020 -j- 0.9243 



— 0.1210 







1.6878 



— 0.6209 



— 7.4710 



= — 0.6289 -f 0.1477 



— 0.1463 







13.7772 B" 030 



V+ 01084 B '\u 



V— 1.7438 i?" 



12 V= +10.7940 g' 3 4-20 1610 q'(l 



-q" 2 )+ 1.6458(2 — 



Sq 1 4- q' s ) 



4- 



0.1084 



— 5.9902 



— 0.5624 



= -j- 0.9566 — 3.6172 



-j- 0.0976 







1.7438 



— 0.1624 



— 7.4710 



= -j- 2.2416 — 7.2754 



-j- 1.5002 







11.1286 B" Q03 



V— 0.9627 B" 20 



V— 0.9545 B" 



21 -ô' 1 3 = — 4.9453 q' s -f 5.7262 q'(l- 



- q' 2 ) — 0.5677 (2 — 



3?' + q' 3 ) 





0.9527 



— 8.2352 



— 0.5904 



= — 3.6788 4- 3.5266 



— 0.3886 







0.9545 



— 0.5904 



— 8.2320 



= — 3.1457 4- 5.4148 



— 1.7464 





* On the whole all possible explanations of the difference between the results deduced from 

 the cross motions and from the radial motions must be sought either in a variation of the para- 

 meters &, and q' in different regions of the sky, or in the circumstance that the distribution of 

 the velocities is not strictly the same in all parts of the heavens. 



