In the volume of the Arch. Néerlandaises for 1900, Dr Bryan discussed the investigation of the distribution of the velocities of a dynamical system for a stationary state from probability considerations.

He suggested the method of obtaining expressions for the second differential coefficients with respect to the time of squares and products of velocities such as enter into the expression for the kinetic energy, and finding from them equations of energy equilibrium, as well as conditions of stability for the stationary state.

He applied the method to a few simple examples, and indicated in these the preponderance of conditions for non-equipartition of energy.