/ ASTRONOM Y: ADAMS AND S TROMBERG 
229 
to subject the spectroscopic method to a rigorous test of its appHcabihty to 
the stars of high luminosity and small parallax. The importance of this ques- 
tion is evident when we consider that the trigonometric method of measure- 
ment with a probable error which is nearly independent of the size of the 
parallax can give but approximate values of the absolute magnitude for stars 
of very small parallax. Thus if the measured parallax of a star of the fifth 
magnitude is +0^010 db 0''005 its absolute magnitude may lie anywhere 
within the limits — 1.5 and +0.9, and for smaller parallaxes the range is much 
larger. Since a great majority of the brighter stars in the sky have small 
parallaxes the use of the spectroscopic method in which the error is more 
nearly proportional to the size of the parallax is of fundamental importance for 
such cases. 
As a first step in the investigation a new determination of the constants of 
reduction for the intensities of the spectral lines was made in 1918 with the 
aid of the large number of measured parallaxes then available. The absolute 
magnitudes based upon this system have been divided into groups and com- 
parisons have been instituted with the values obtained from parallactic motion 
and all available measured parallaxes. In this way we can determine whether 
the absolute magnitude varies continuously with the line-intensity; and it is 
possible to use a large number of measured parallaxes including stars of dif- 
ferent proper motion and apparent magnitude. 
The results of the comparison are shown graphically in the accompany- 
ing figures. The spectroscopic absolute magnitudes are plotted as 
abscissae, the line-intensities being indicated on parallel axes. The absolute 
magnitudes derived from measured parallaxes and from parallactic motion 
are plotted as ordinates. The full-line curve represents the values computed 
from parallactic motion; the broken curve those from measured parallaxes. 
The wide break in the curves for the K4-K9 and the M stars are due to the 
well-known division 01 these stars into the giant and dwarf classes. 
It is at once evident that the computed absolute magnitudes vary continu- 
ously with the spectroscopic magnitudes quite as well among the stars of 
highest luminosity as among the fainter stars. In fact the largest discordance 
is found not among the brighter stars but among some of the faintest stars of 
groups A7 to Fg where the luminosities as computed from measured parallaxes 
show but little variation with line-intensity and for the very faintest stars 
appear to act in the wrong direction. It is to be noted that in this comparison 
the more accurate result for the more distant stars is given by the parallactic 
motion and for the nearer stars by the measured parallaxes. 
It is clear that if there are no systematic corrections to be applied to the 
spectroscopic absolute magnitudes used in this comparison the curves should 
consist of straight lines with an inclination of 45°. The results show that these 
corrections are relatively small and that the spectroscopic criteria hold through- 
out the range of magnitude investigated. 
