272 
MATHEMATICS: G. A. MILLER 
100 to less than 10 as the rod approaches saturation (H= 150 gauss) and to 
decrease thereafter asymptotically to zero. 
If p is the force per square centimeter of section of the rod and E Young's 
modulus, 
p = E(Al/D_ (1) 
regarding the magnetic stress as traction. 
Using the expression for the potential of a disc, the field 7^ in a narrow cre- 
vasse normal to F, between molecular layers of magnetic surface density of 
magnetization kH 
F = + H 
where k is the susceptibility of the metal. 
Hence the force per square centimeter should be p' = FkH, or 
p' = H'i^wk^ + k) (2) 
Equating p = p' m equations (1) and (2) 
A/ + k 
I ^ E 
If the data in figure 3 are taken above 800 gauss, supposing that these are far 
enough removed from the initial compHcations, the estimate would be {E — 
2 X 1012), ^ = 15; 
An order of mean susceptibihty of 1.6 (which seems not an unreasonable 
assumption) would thus account for the observed contractions. Naturally 
as k is essentially variable with H a better statement of the case might be given 
by postulating such a relation. 
1 London, PhiL Mag., 37, 1894, (131). 
2 Carnegie Inst., Washington, Pub., No. 149. 
3 These Proceedings, 5, 1919, (39). 
* These Proceedings, 4, 1918, (328). 
(3) 
GROUPS INVOLVING ONLY TWO OPERATORS WHICH ARE 
SQUARES 
By a. G. Miller 
Department of Mathematics, University of Illinois 
Communicated by E. H. Moore, May 2, 1919 
The abelian group of order 2^ and of type (1, 1, 1, . . . ) is completely 
characterized by the fact that all of it operators have a common square. 
When we impose the condition that the operators of a finite group G have two 
and only two distinct squares then G must belong to one of three infinite sys- 
tems of groups whose characteristic properties we proceed to determine. 
