18 PRESIDENT’S ADDRESS. 
the comparatively scant material available, it now seems almost certain that 
the true value of the Sun’s velocity lies between 18 and 20 kilometres per 
second ;! or, if we adopt the mean value, 19 kilometres per second, this 
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 universe, 
but only in the proportion of about one to five.” 
The same method cannot 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 determination as we 
possess, that the variation of parallax with proper motion could be satis- 
factorily dealt with. 
The Mean Parallaxes of Stars of Different 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 published at Groningen 
in 1901.3 Within the past few months the results of researches on stellar 
parallax, made under the direction of Dr. Elkin, at the Astronomical Ob- 
servatory of Yale University, during the past thirteen years,‘ have been 
published, and they afford a most crucial and entirely independent check 
on the soundness of Kapteyn’s conclusions. 
In considering the comparison between the more or less theoretical 
results of Kapteyn and the practical determinations of Yale, we have to 
remember that Kapteyn’s tables refer only to the means of groups of a 
large number of stars having on the average a specified magnitude and 
proper motion, whilst the latter are direct determinations affected by the 
accidental errors of the separate determinations and by such uncertainty 
as attaches to the unknown parallaxes of the comparison stars—parallaxes 
which we have supplied from Kapteyn’s general tables. 
The Yale results consist of the determination of the parallax of 175 
stars, of which only ten had been previously known to Kapteyn and had 
1 Kapteyn Ast. Nach., No. 3487, p. 108; and Campbell, Astrophys. Journ., xiii. p. 80. 
2 Astron. Nachrichten, No. 3487, Table Lil. ; and Ast. Jowrn., p. 566. 
3 Publications Astron. Laboratory Groningen, No. 8, p. 24. 
4 Trans. Astron. Observatory of Yale Univ., vol. ii., part 1. 
