442 W. A. Norton—Force of Effective Molecular Action. 
that each elementary part of the surface will be occupied by one 
such atom, and so will be a center of radiation of wave-impulses 
propagated to O (p. 486). Now let w be the maximum velocity 
of pulsation of the ethereal atoms in any wave, at the point O; 
m the mass of ether effective in the pulsation; s the minute 
space (equal to half the length of a wave) over which m moves 
while the velocity is increasing from zero to u, or decreasing 
from u to zero; and p, the mean impulsive force taking effect 
over thé space s. Then for the wave impulses propagated along 
‘the normal at O, p,x2s=mu?. Let n, denote the number of 
successive waves in the space, 1, and take for the unit of time 
the interval employed by the wave in traversing the distance, 
1; and we have ™=5, and PiX2sX sg = Nymu?, orp, X1l=nymu?. 
tion inclined under any angle g’ to the normal, the normal 
impulse will be p’ cos g’, need 
around the normal, form an elementary zone of the hemisphere, 
whose breadth is dg, and altitude, in the normal direction, 
d cos ¢, or sin gdg. it then n represent the number of molecules 
in the entire hemisphere, n':n:: sin gdg:1; and n’=n sin gdg. 
us 
wT 
7 : cos? p\2 
: 0 
nn,mu* nn mu? nn mu? 
ees Gp 2 
Now 
is the entire living force, or energy, of all the ethereal waves 
occupying at any interval of time the space unity on all the 
lines radiating from O; or included within a hemisphere trac 
around O with the radius 1. Calling this E, we have p=3E. 
But the hypothesis, which has been tested by quantitative deter- 
minations (p. 487), that the repulsive term in equ. (1) varies 
inversely as the cube of the distance, 2’, teas the centers of 
the molecules, gives the same law of variation for the impulses 
received at O; and accordingly if T denotes the value of E, 
ti . 
when a’ =1,p=3-,=4y; in which V is the volume occupied 
_ by a given number of molecules, N, in terms of the volume, 1, 
