August 16, 1907] 



SCIENCE 



205 



of this motion is one of the fundamental 

 quantities to be determined. If the mean 

 parallax of any sufficiently extensive group 

 or class of stars was known we should have 

 at once means for a direct determination 

 of the velocity of the sun's motion in space ; 

 or if, on the other hand, we can by inde- 

 pendent methods determine the sun's 

 velocity, then the mean parallax of any 

 group of stars can be determined. 



DETERMINATION OP STELLAR MOTION IN THE 

 LINE OF SIGHT 



Science owes to Sir William Huggins the 

 application of Doppler's principle to the 

 detei-mination of the velocity of star-mo- 

 tion in the line of sight. The method is 

 now so well known, and such an admirable 

 account of its theory and practical develop- 

 ment was given by its distinguished in- 

 ventor from this chair at the Cardiff meet- 

 ing in 1891, that further mention of that 

 part of the matter seems unnecessary. 



THE VELOCITY OP THE SUN's MOTION IN 

 SPACE 



If by this method the velocities in the 

 line of sight of a sufficient number of stars 

 situated near the apex and antapex of the 

 solar motion could be determined, so that 

 in the mean it could be assumed that their 

 peculiar motions would disappear, we have 

 at once a direct determination of the re- 

 quired velocity of the sun's motion. 



The material for this determination is 

 gradually accumulating, and indeed much 

 of it, already accumulated, is not yet pub- 

 lished. But even with the comparatively 

 scant material available, it now seems 

 almost certain that the true value of the 

 sun's velocity lies between 18 and 20 kilo- 

 meters per second;^' or, if we adopt the 

 mean value, 19 kilometers per second, this 



" Kapteyn Ast. 'Nach., No. 3487, p. 108; and 

 Campbell, Astrophys. Joum., XIII., p. 80. 



would correspond almost exactly with a 

 yearly motion of the sun through space 

 equal to four times the distance of the 

 sun from the earth. 



Thus the sun's yearly motion being four 

 times the sun's distance, the parallactic 

 motion of stars in which this motion is 

 unforeshortened must be four times their 

 parallax. How this number varies with 

 the amount of foreshortening is of course 

 readily calculated. The point is that from 

 the mean parallactic motion of a group of 

 stars we are now enabled to derive at once 

 its mean parallax. 



This research has been carried out by 

 Kapteyn for stars of different magnitudes. 

 It leads to the result that the parallax of 

 stars differing five magnitudes does not 

 differ in the proportion of one to ten, as 

 would follow from the supposition of equal 

 luminosity of stars throughout the uni- 

 verse, but only in the proportion of about 

 one to five.^" 



The same method can not be applied to 

 groups of stars of different proper motions, 

 and it is only by a somewhat indirect 

 proof, and by calling in the aid of such 

 reliable results of direct parallax deter- 

 mination as we possess, that the variation 

 of parallax with proper motion could be 

 satisfactorily dealt with. 



THE MEAN PARALLAXES OP STARS OF DIF- 

 FERENT MAGNITUDE AND PROPER 

 MOTION 



As a final result Kapteyn derived an 

 empirical formula giving the average 

 parallax for stars of different spectral 

 types, and of any given magnitude and 

 proper motion. This formula was pub- 

 lished at Groningen in 1901.-" Within the 



^' Astron. Nachrichten, No. 3487, Table III.; 

 and Ast. Joum., p. 566. 



^ Puhlioations Astron. Laboratory Groningen, 

 No. 8, p. 24. 



