The electron, its isolation and measurement and the determination of some of its properties

If there is one single molecule at rest in a cubical space 1 cm. on a side, the chance that another molecule which is shot through the cube will impinge upon the one contained is clearly in which is the mean diameter of the two molecules. If there are contained molecules the chance is multiplied by , that is, it becomes . But on the average the chance of an impact in going a centimeter is the number of impacts actually made in traversing this distance. The mean free path is the distance traversed divided by the number of impacts made in going that distance. Hence This would be the correct expression for the mean free path of a molecule which is moving through a group of molecules at rest. If, however, the molecules are all in motion they will sometimes move into a collision which would otherwise be avoided, so that the collisions will be more numerous when the molecules are in motion than when at rest—how much more numerous will depend upon the law of distribution of the speeds of the molecules. It is through a consideration of the Maxwell distribution law that the factor is introduced into the denominator (see Jeans, Dynamical Theory of Gases) so that equation (54) becomes