  Once Perrin was able to calculate the mean kinetic energy of the Brownian particles he could support the most basic assumptions of kinetic theory without a need to complicate matters by adding additional hypotheses. From the point of view of the kinetic theory, systems are in equilibrium when the mean kinetic energy of the molecules in those systems are equal, with particle collisions being the mechanism by means of which equilibrium is reached. Brownian particles constitute a system that differs from the molecules constituting a gas only quantitatively, not qualitatively. If a system of Brownian particles is in thermal equilibrium with a gas at some temperature, T, then, from the point of view of the kinetic theory, the mean kinetic energy of the particles must be equal to that of the molecules of the gas. By measuring the mean kinetic energy of Brownian particles from the observable density distribution at temperature, Tr, Perrin had in effect measured the mean kinetic energy of the molecules of a gas at that temperature. That knowledge enabled him to calculate Avogadro's number. As Perrin (1990, 104) remarked, it was with ‘the liveliest emotion’ that he found that number to be in accord with previous, more indirect, estimates of Avogadro's number.