478 
PROFESSOR J. J. THOMSON ON SOME APPLICATIONS OF 
Now, the kinetic energy corresponding to y 1 is 
that corresponding to y z is 
2 5 
i 1 ^ 2 “. 
The ratio of these is X 3 Lo/L 1 ; this is a quantity depending only on the configuration 
of the circuits, and, if the molecules are geometrically similar, will be the same for each 
molecule ; thus the ratio of the mean kinetic energy corresponding to y x to that corre¬ 
sponding to y 3 is A 2 L a /L 1 , and, by properly choosing the configuration of the circuits, 
this quantity may be made to have any positive value we please, whereas, if 
Boltzmann’s theorem were true, the ratio ought always to be equal to unity. Hence 
we conclude that Boltzmann’s theorem is not true. It ought to be noticed that in 
this case the ratio is constant, though not unity, and this is all that is assumed by 
Clausius. 
The consideration of the collision of two vortex rings, according to the vortex ring 
theory of gases, would, I think, lead us to the conclusion that the energy corre¬ 
sponding to each mode of vibration is, when the gas is in a steady state, a function of 
the mean translatory energy of the molecules of the gas, the function being of such 
a kind that, the higher the mode of vibration, the smaller the ratio of the corre¬ 
sponding energy to the mean translatory energy. 
The application of the Second Law to the case we have just discussed, which is the 
one investigated by Szily and Clausius, does not include the application to the case 
(almost the only one of importance in the applications of the Second Law) when the 
system absorbs or expends work when heat is communicated to it. It would not 
include, for example, the case when heat is applied to a gas at constant pressure. 
Let Pj, P 2 , . . . be the external forces of type p x , y> 3 , respectively, acting on the 
system, and let the points of application of these forces move through S p x , Syn . . . 
Then, if SQ be the quantity of undirected energy supplied to the system, that is, 
energy that is not supplied by moving the system against definite external forces, ST 
and SV the increments in the kinetic and potential energies of the system, 
SQ = ST + SV -Pj Sjq - P 3 S p 2 .(G) 
Thus, for example, in the case of a gas contained in a cylinder with a movable 
piston, 
SQ = ST + SY + p Sx, 
where p is the total pressure on the piston, and x the distance of the piston from the 
bottom of the cylinder. 
