1857 and by
Clerk-Maxwell in 1859.

The considerations that led Clerk-Maxwell to take up the computations
may be stated in his own words, as formulated in a paper "On the Motions
and Collisions of Perfectly Elastic Spheres."

"So many of the properties of matter, especially when in the gaseous
form," he says, "can be deduced from the hypothesis that their minute
parts are in rapid motion, the velocity increasing with the temperature,
that the precise nature of this motion becomes a subject of rational
curiosity. Daniel Bournelli, Herapath, Joule, Kronig, Clausius, etc.,
have shown that the relations between pressure, temperature, and density
in a perfect gas can be explained by supposing the particles to move
with uniform velocities in straight lines, striking against the sides of
the containing vessel and thus producing pressure. It is not necessary
to suppose each particle to travel to any great distance in the same
straight line; for the effect in producing pressure will be the same
if the particles strike against each other; so that the straight line
described may be very short. M. Clausius has determined the mean length
of path in terms of the average of the particles, and the distance
between the centres of two particles when the 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 successive
collisions. In order to lay the foundation of such investigations on
strict mechanical principles, I shall demonstrate the laws of motion
of an indefinite number of small, hard, and perfectly elastic spheres
acting on one another only during impact. If the properties of such a
system of bodies are found to correspond 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 explaining
the phenomena of gases. In either case it is necessary to follow out
these consequences of the hypothesis.

"Instead of saying that the particles are hard, spherical, and elastic,
we may, if we plea