Concerning the Abstract Groups of Order k ! and ½k ! Holohedrically Isomorphic with the Symmetric and the Alternating Substitution-Groups on k Letters

Abstract

On the Abstract Groups of Order k! and $1, 8fc. 357spheres, the change of direction of the relative velocity clue to collision, and therefore XV-\v of Art. 20, depends only on 0 and f», and not on the magnitude, of V.In the case of the molecules being centres of repulsive force, let c be the distance at which when two molecules approach each other that force first becomes sensible, and call c the diameter of a molecule, and define 0, f as in Art. 17.It is then easy to see that the change of direction of V between the beginning and end of an encounter depends on V as well as on 0 and 0; whence we may infer that, in this and in all cases whore finite forces act between molecules, & and D are functions of h t i.e., of the temperature, as well as of the density.It seems reasonable to expect that D = 0, the point at which the mathematical formula ceases to be applicable, would, if we could solve the problom, express that relation between density and temperature at which the gas changes its form and becomes liquid.