20 Prof. Maxwell on the Motions and Collisions 
of the particles, and the distance between the centres of two par- 
ticles when collision takes place. We have at present no means 
of ascertaining either of these distances ; but certain phenomena, 
such as the internal friction of gases, the conduction of heat 
through a gas, and the diffusion of one gas through another, 
seem to indicate the possibility of determining accurately the 
mean length of path which a particle describes between two suc- 
cessive collisions. In order to lay the foundation of such inves- 
tigations on strict mechanical principles, I shall demonstrate the 
laws of motion of an indefinite number of small, hard, and per- 
fectly elastic spheres acting on one another only during impact. 
If the properties of such a system of bodies are found to cor- 
respond to those of gases, an important physical analogy will be 
established, which may lead to more accurate knowledge of the 
properties of matter. If experiments on gases are inconsistent 
with the hypothesis of these propositions, then our theory, 
though consistent with itself, is proved to be incapable of ex- 
plaining the phenomena of gases. In either case it 1s necessary 
to follow out the consequences of the hypothesis. 
Instead of saying that the particles are hard, spherical, and 
elastic, we may if we please say that the particles are centres of 
force, of which the action is insensible except at a certain small 
distance, when it suddenly appears as a repulsive force of very 
great intensity. It is evident that either assumption will lead 
to the same results. For the sake of avoiding the repetition of 
a long phrase about these repulsive forces, I shall proceed upon 
the assumption of perfectly elastic spherical bodies. If we sup- 
pose those aggregate molecules which move together to have a 
bounding surface which is not spherical, then the rotatory mo- 
tion of the system will store up a certain proportion of the whole 
vis viva, as has been shown by Clausius, and in this way we may 
account for the value of the specific heat being greater than on 
the more simple hypothesis. 
On the Motion and Collision of Perfectly Elastic Spheres. 
Prop. I. Two spheres moving in opposite directions with velo- 
cities inversely as their masses strike one another ; to determine 
their motions after impact. 
Let P and Q be the position * 
of the centres at impact; AP, Ve. am 
BQ the directions and magni- pa A 
tudes of the velocities before © TIS 
impact; then, resolving the ve- 
locities parallel and perpendi- 
cular to PQ the line of cen- 
tres, we find that the velocities purallel to the line of centres are 
impact; Pa, Qd the same after of 
