268 PHYSICS: J. A. ELDRIDGE Proc. N. A. S. 
culate it for the case t' = 0. For this special case of (12) the curva- 
ture is: 
, cor 
It appears from the calculations just made that the spacial geometry 
for the rotating system depends on the time and space co5rdinates of the 
point considered, and this is at first sight in contradiction with our ordinary 
ideas of rotating systems. The explanation of this fact is that for a system 
rotating with respect to a "stationary" system there is no separation into 
space and time which stands out as the natural one for the entire rotating 
system, and consequently for this system spacial geometry is only defined 
when our coordinates have been selected. Since the equations (9) depend 
on coordinates so chosen that when f = 0, the points on the radius vector 
6^ = 0 coincide with those on the radius vector 6 = 0, at / = 0 in the 
stationary system, it is based on coordinates "natural" to these space- 
time points ; in the sense that they are those of a stationary system coin- 
ciding with the rotating one at the space-time points considered. It will 
be noticed that for these points the curvature given by (13) is co^/c^. 
This shows that the curvature of the spacial cross-section at any space-time 
point in the coordinates "natural" to this point is constant; it is the square 
of the angular velocity of rotation in radians per light-second. ^ 
\ 
THE ENERGY LOSSES ACCOMPANYING IONIZATION AND 
RESONANCE IN MERCURY VAPOR 
By John A. Bldridge 
Department of Physics, University of Wisconsin 
Communicated June 28, 1922 
Much light has in recent years been thrown upon the constitution of 
matter, and upon the validity of the Bohr theory of atomic structure by 
the study of resonating and ionizing collisions of electrons in vapors and 
gases. There are, however, still a great many questions of a fundamental 
nature in regard to such phenomena which cannot be answered by the 
