146 
MATHEMATICS: G. A. MILLER 
Proc. N. A. S. 
crease in visibility and that with further observation some estimate can 
be made of the diameter of these stars. 
Assuming that the effective wave-length of a Orionis is 5.75 X 10 5 cm. 
and that the value of d is 121 inches (306.5 cm.), the angular diameter of 
a Orionis from the formula a = 1.22 \ proves to be 0.047. An esti- 
mate of its linear diameter may be made by using a mean parallax of 
0".018, 3 which gives a diameter of 240 X 10 6 miles, or slightly less than 
that of the diameter of the orbit of Mars. 
Corrections to this value will be derived by an experimental determina- 
tion of the value of X for this particular star ; by a more accurate setting of 
the mirrors, for the uncertainty of this measure is at least 10 percent; and 
by further determination of the parallax. The angular value given above 
is that corresponding to a uniformly illuminated disk. A darkening to- 
ward the limb, equal to that of the sun, would require an increase in the 
diameter of about 17 percent. 
We wish to express our obligations to Director Hale both for his en- 
couragement and for placing the resources of the observatory at our dis- 
posal, and to Mr. J. A. Anderson for his checking of the measures on the 
night of December 13. 
iThese Proceedings, 6, 1920 (474-475). 
2 Mount Wilson Contributions, No. 185; Astroph. J. Chicago, 51, 1920 (263-275). 
3 The weighted mean of Adam's spectroscopic parallax, 0.012 and the trigonometric 
parallaxes of Elkin, 0.030, and Schlesinger, 0.016. 
AN OVERLOOKED INFINITE SYSTEM OF GROUPS OF 
ORDER pq 2 
By G. A. Miller 
Department oe Mathematics, University of Illinois 
Communicated April 28, 1921. 
The determination of all the possible abstract groups of order pq 2 
p and q being distinct prime numbers, was considered by Cole and Glover 
in an article published in the American Journal of Mathematics, vol. 15 
(1893), p. 191 and by O. Holder in a long article published in the Math- 
ematische Annalen, vol. 43 (1893), p. 301. In a subsequent article, pub- 
lished in volume 46 of the latter journal, Holder directed attention in 
foot-note on page 323 to the fact that the enumeration of these groups 
contained in the former of the two articles mentioned above was incom- 
plete. 
The main object of the present article is to establish the fact that .there 
is an infinite system of abstract groups of order pq 2 which was overlooked 
not only by the authors already mentioned but also by others, including 
W. Burnside who gave an incomplete list of these groups in both editions 
of his well known and meritorious work entitled, "Theory of Groups of 
