ee Us 
LXX. The Persistence of Molecular Velocities in the Kinetic 
Theory of Gases. By J. H. Juans, IA., Fellow ‘of 
Trinity College, Cambridge *. 
§ 1, | i the Kinetic Theory investigation of the pheno- 
mena of viscosity, conduction, and diffusion of 
gases, it is usual to assume that a collision may be supposed, 
so to speak, to wipe out the whole previous history of a 
molecule, so that the ‘‘ expectation” of any quantity which 
can be associated with a molecule is the mean value of that 
quantity at the point at which the last collision occurred. It 
will be shown in the present paper that this assumption 
cannot be justified. Ifa molecule now at P is supposed to 
have last collided at Q, it will be shown that on tracing back 
the history of the molecule, the probability is that it will be 
found to have come initially from a point beyond Q in the 
direction away from P, so that the ‘expectation ” of any 
quantity to be associated with the molecule will not be that 
appropriate to the point Q, but will be appropriate to some 
point beyond Q. 
We may begin with a theorem due to Maxwellt. If two 
molecules collide with velocities such that their centre of 
gravity is at rest before collision, and therefore of course 
after collision also, then all directions are equally probable 
Fig, 1. 
for the velocity of either after collision. From this it follows 
that if two molecules collide in any way, the “ expectation” 
of the velocity of either is exactly equal to the velocity of 
the centre of gravity of the two. In figure 1, let OP and 
* Communicated by the Author. 
+ Collected Works, i. p. 378. 
