194 W. A. Norton— Theories of Heat. 
atomic heat-vibrations, may be derived from the consideration 
that the rapid subsidence of the supposed vibrations, both of heat 
and light, when their inciting cause is no longer in operation, 
implies a degree of resistance to the rapidly moving atoms, from 
the ether to which the living force of the vibrations is communicated, 
fur greater than can be admitted to exist. short calculation 
will serve to make this evident. According to the experiments 
of MM. F. Lucas and A. Cazin,* the duration of a spark from 
an ordinary electrical machine does not exceed 4 millionths 
of a second. In this minute interval of time, then, a large frac- 
tion of the living force of atomic light-vibrations, incited by 
the electric discharge, is communicated to the surrounding 
ether. Now let us allow that the extent of the vibrations is 
8 ;a's7 of an inch (which is undoubtedly much above 
its actual value). The average number of undulations per sec- 
ond, in the waves of the different colors that make up white 
light, is about 550,000,000,000,000. In one second, then, each 
the vibrating atoms will have traversed, in successive vibra- 
tions, the space of 0-001 x550,000,000,000,000 in. = 8,680,555 
miles. This exceeds the velocity of the earth in its orbit 
(18°18 miles per second) in the ratio of 477,478 to 1. Now we 
will suppose that in the interval of 4 millionths of a second 
the average velocity of the atomic vibrations is only reduced 
by a small fraction, say ;';, instead of being entirely taken up, 
and that the retarding force of the ether remains sensibly con- 
stant while this small reduction takes place. Denote this retard- 
ing force, for a single atom, by p; the initial average velocity of 
vibration, above given, by v; and the interval of time in which 
a constant retarding force, of the intensity p, would be capable 
of bringing the atom to rest byt. then v=pt. Also let v’=v— 
> and ¢’ the interval of time in which the same retarding 
force would destroy this velocity; then v’'=pi’. Hence v—v'=p 
v—yv @ v : 
(¢—?’), and ¢t—-’=—__- = 10= —_._ This is then the expression 
P Pp 10p 
for the interval of time in which the velocity v should be 
ced ;';. The retarding force of the ether, at the velocity of 
T—T’ to be the interval of time in which this force should re- 
duce the velocity (V), equal to that of the earth in its orbit, 
by ;'5- Then, as before. 
* Philosophical Magazine, Oct., 1872, p. 319. 
