214 
ASTRONOMY: B. BOSS 
This last theorem is of interest in the method developed in recent 
years by Wilczynski for dealing with questions in projective differen- 
tial geometry. In fact, the coefficients of the transformed system of 
differential equations are what he has generally called seminvariants 
of the original system; the theorem affords a means for calculating 
these seminvariants in a purely mechanical way. In Wilczynski^s 
method, the geometric problem becomes the study of a completely 
integrable system of the kind we have been considering. 
The results outlined above have been developed at length in a memoir 
which is to appear in the Transactions of the American Mathematical 
Society, 
SYSTEMATIC MOTION AMONG STARS OF THE HELIUM TYPE 
By Benjamin Boss 
DUDLEY OBSERVATORY. ALBANY. N. Y. 
Received by the Academy, March 1, 19^ 
Several investigators using different methods and different material 
have shown beyond a doubt that the stars evidence a preference for 
motion in two opposite directions in the sky. This does not mean that 
all stars move in one of the two directions, but that there is a stronger 
tendency for stars to move in the favored directions than in any other. 
In such investigations the helium, or B-type, stars have presented 
considerable difhculties, since their motions are small, and since as a 
class they are situated at a great distance from the sun. It has seemed 
desirable, therefore, to devise a method whereby the preference of 
motion among the hehum stars might be determined with some degree 
of confidence. 
In the first place the zone in which all the hehum stars He was mapped 
off into twelve arbitrary divisions. For each division means were taken 
of the amount of proper motion in the two co-ordinates right ascension 
and declination, and these mean values were then subtracted from each 
proper motion. Thus the center of the velocity-figure was obtained. 
The rectangular co-ordinates were converted into polar co-ordinates and 
arranged in the order of their position-angles from the north pole. 
Then for thirty degree groups, 0°-30°, 10°-40°, etc., means were taken 
of the position-angles, and sums of the amount of proper motion. With 
the mean position-angles as abscissae and the sums of proper motion 
as ordinates, the results were plotted and smooth curves drawn to repre- 
sent them. Figure 1 shows how well the observations can be fitted by 
mooth curves. It will also be noted that there is more than one maxi- 
