Sronry—-Of the Kinetic Theory of Gas. 309 
or indirectly influence the motions of molecules in their journeys 
between their encounters. If, accordingly, there be any events of 
the kind which we have termed Be events, they and the forces 
concerned in them may be kept outside the theorem, and may 
exist and involve any amount of energy; which energy is, however, 
additional to that which in the theorem is regarded as the total 
energy, which is to be understood as the total of the energy of the 
events with which the theorem is concerned. 
The following mechanical illustration, which is that usually 
employed, will enable us better to grasp the meaning and appreciate 
the value of these remarks. In it I will suppose the gas to be of 
one kind, with molecules that are all alike, and that the number 
of molecules and the average duration of a journey are what they 
are in atmospheric air at the surface of the earth. 
The simplest way of fulfilling the condition that the expression 
for the energy shall be a sum of squares, is to provide a mechani- 
cal model in which the whole energy is kinetic; and the simplest 
way of securing this is to suppose each molecule to be a rigid elastic 
body, with a frictionless surface. The expression for the energy 
of the molecule will then take the familiar form— 
T=3(M (w+ +w’) + Aw’ + Bo? + Cw;"] 
where the letters have their usual meanings. Here each term in 
the expression corresponds to one of the six degrees of freedom of 
the rigid body, and the theorem states that the time-integrals of 
the several terms of this expression are equal, and that the average 
value of 7 is 1/NV of the total energy in the gas, V being the 
number of molecules; in other words, that the molecule exhibits 
one-sixth of its share of the total energy in each of the following 
ways, viz.:—1°, in its journeyings east and west; 2°, north and 
south ; 3°, up and down; and 4°, 5°, 6°, in spinning on each of 
its three principal axes. ‘To simplify the conception as much as 
possible, we may suppose our model of a molecule to be a smooth 
ellipsoid of uniform density. 
Let us next represent the molecules by ellipsoids of revolution. 
The full expression for the energy of such a body is— 
(I) P= 3 [I +0? +0) + Aus + Bor + wx)), 
