18 
ASTRONOMY: KAPTEYN AND ADAMS 
case of the K stars, and we hope in the course of a more extended dis- 
cussion to describe it in detail, as well as to obtain similar expressions 
for the stars of other types. A very brief summary of the method used 
is as follows : 
1. All of the stars between the hmits X = 60° and X = 90° were 
selected from Campbell's catalogue and arranged according to amount 
of radial velocity. This selection was made in order to eliminate the 
effect of stream motion so far as possible. The appKcation of Maxwell's 
law to this material at once showed a large preponderance of high veloc- 
ities. Thus there are 17 stars with velocities above 40 km. per second 
where Maxwell's law requires less than one-third of this number. 
2. A satisfactory expression for representing the observed distribution 
of velocities was found in the sum of two Maxwell equations with differ- 
ent moduli. A peculiar feature of this result is that if all of the stars 
are used, and not alone those on which the stream motion has Httle 
influence, the exponential constants remain essentially unchanged. 
3. With the aid of this expression the relationship was determined 
between the average radial velocity and the component of the linear 
velocity at right angles to the line of sight. 
4. The stars were then divided into groups, each within a narrow 
range of proper motion, so that they may all be regarded as at the same 
distance. The components of the Hnear velocities at right angles to the 
line of sight were then computed by the aid of the parallaxes given in 
Groningen Publications No. 8. A factor was applied to the parallaxes such 
as to make the total average hnear velocity for all of the stars equal to 
the total average radial velocity p. Table II shows the final results for p. 
It appears from these results, therefore, that our assumption c is quite 
adequate to explain the variation of radial velocity with proper motion. 
There remains, however, the possible effect of a or h, which we may 
designate briefly as the effect of distance or of absolute magnitude. 
With more extensive data it might perhaps be possible to separate these 
two effects. As it is we shall suppose the distance effect to be neghgible 
and try to determine the absolute magnitude effect. 
For stars of approximately the same distance we shall assume that 
p = a -\- h M, where M is the absolute magnitude derived from the 
formula,^ M = m -\- S -\- S iogx. In general we have kept the same 
groups used in Table I, the variation in distance not being excessive, but 
in a few cases consecutive groups have been combined. These groups 
were then further divided according to apparent magnitudes, an attempt 
being made to keep the numbers of the stars in the extreme subdivisions 
about equal. The values of the parallax tt were then taken from Gronin- 
