At the suggestion of Prof. Tait, an attempt has been made in this paper to apply the method used by him in § 21 of his paper on “The Foundations of the Kinetic Theory of Gases” to a case of the question of the distribution of energy in a system of non-homogeneous impinging spheres.

The problem may be stated as follows:—Given a very great number of smooth elastic spheres, equal and like in all respects, whose centres of figure and centres of inertia do not coincide, and the sum of whose volumes is but a small fraction of the space in which they move, it is required to find the ultimate distribution of energy among the various degrees of freedom when by collisions the system has attained a “special state.”