It is the object of this paper tor establish with numerical exactness the following law of the Diffusion of Gases:“The diffusion or spontaneous intermixture of two gases in contact, is effected by an interchange in position of indefinitely minute volumes of the gases, which volumes are not necessarily of equal magnitude, being, in the case of each gas, inversely proportional to the square root of the Density of that gas.”These replacing volumes of the gases may be named equivalent volumes of diffusion, and are as follows: Air, 1; Hydrogen, 3.7947; Carbureted hydrogen, 1.3414; Water-vapour, 1.2649; Nitrogen, 1.0140; Oxygen, 0.9487 ; Carbonic acid, 0.8091; Chlorine, 0.6325, &c.; numbers which are inversely proportional to the square roots of the densities of these gases, being the reciprocals of the square roots of the densities, the density of air being assumed as unity.