702 Proceedings of Boy al Society of Edinburgh. [sess. 
distance becomes diminished to £. When I speak of atoms or 
groups moving “ rapidly,” I mean that the velocities are moderate 
as thus defined. 
§ 31. Let us consider what would follow if we had given at any 
time, scattered randomly but equably all through space, simple 
Boscovich atoms moving with velocities randomly equal in all 
directions. As we are supposing the masses of all the atoms 
equal, we may call the mass of each unity: thus v 2 for all the 
atoms in any part of space at any time, is the total of their kinetic 
energy. Both the number of atoms and their total energy we 
shall suppose to be equal in all very large equal volumes. 
§ 32. The result of a collision between two atoms is essentially 
the same as that of the collision of two equal balls supposed simply 
repellent at contact, as in the elementary kinetic theory of gases 
as worked out by Maxwell and Tait ; * but the size of the balls that 
would give the same result depends, for each collision, very com- 
plexly on the law of force, and on the velocities and lines of 
motion of the atoms before the collision. As long as there is no 
case of collision between more than two atoms, the average energy 
of the free atoms at any time, and the law of the distribution of 
energy among the multitude in their free paths between collisions, 
is not affected by this complication, and is the same as if the atoms 
were equal hard globes merely repellent at contact. It is only 
when the results of unequal distributions of density, of energy, or of 
components of momentum, are to be traced, and the laws of the 
relation of pressure to density, or of thermal conduction, or of 
viscosity are to be investigated, that we can take into account the 
law of force, and can find differences from what the results would 
be if we had merely the hard equal balls to deal with. 
§ 33. But now suppose, while two atoms are in collision, a third 
to come within their influential distance, so that three shall be in 
collision at the same time. All three may go clear, or two of them 
may remain in collision, or in other words, fall into combination, 
and one go free. It is scarcely possible that all three can remain in 
* Maxwell, Philosophical Magazine, 1860, and Philosophical Transactions, 
1867 and 1878 ; Tait, “ On the Foundations of the Kinetic Theory of Gases,” 
Trans. Roy. Soc. Edin., vol. xxxiii., read May 14 and December 6, 1886, and 
January 7, 1887. 
