ME. CLEBK MAXWELL ON THE DYNAMICAL THEOEY OE OASES. 
55 
this case the different centres may either be separated, so as to form a group of points, 
or they may be actually coincident, so as to form one point. 
Finally, if necessary, we may suppose them to be small solid bodies of a determinate 
form ; but in this case we must assume a new set of forces binding the parts of these 
small bodies together, and so introduce a molecular theory of the second order. The 
doctrines that all matter is extended, and that no two portions of matter can coincide in 
the same place, being deductions from our experiments with bodies sensible to us, have 
no application to the theory of molecules. 
The actual energy of a moving body consists of two parts, one due to the motion of its 
centre of gravity, and the other due to the motions of its parts relative to the centre of 
gravity. If the body is of invariable form, the motions of its parts relative to the centre 
of gravity consist entirely of rotation, but if the parts of the body are not rigidly con- 
nected, their motions may consist of oscillations of various kinds, as well as rotation of 
the whole body. 
The mutual interference of the molecules in their courses will cause their energy of 
motion to be distributed in a certain ratio between that due to the motion of the centre 
of gravity and that due to the rotation, or other internal motion. If the molecules are 
pure centres of force, there can be no energy of rotation, and the whole energy is reduced 
to that of translation ; but in all other cases the whole energy of the molecule may be 
represented by where /3 is the ratio of the total energy to the energy of transla- 
tion. The ratio (3 will be different for every molecule, and will be different for the same 
molecule after every encounter with another molecule, but it will have an average value 
depending on the nature of the molecules, as has been shown by Clausius. The value 
of (3 can be determined if we know either of the specific heats of the gas, or the ratio 
between them. 
The method of investigation which I shall adopt in the following paper, is to deter- 
mine the mean values of the following functions of the velocity of all the molecules of a 
given kind within an element of volume : — 
(a) the mean velocity resolved parallel to each of the coordinate axes ; 
(/3) the mean values of functions of two dimensions of these component velocities ; 
(y) the mean values of functions of three dimensions of these velocities. 
The rate of translation of the gas, whether by itself, or by diffusion through another 
gas, is given by (os), the pressure of the gas on any plane, whether normal or tangential 
to the plane, is given by (f 3 ), and the rate of conduction of heat through the gas is given 
b y M- 
I propose to determine the variations of these quantities, due, 1st, to the encounters 
of the molecules with others of the same system or of a different system ; 2nd, to the 
action of external forces such as gravity ; and 3rd, to the passage of molecules through 
the boundary of the element of volume. 
I shall then apply these calculations to the determination of the statical cases of the 
final distribution of two gases under the action of gravity, the equilibrium of tempe- 
