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.

The modern system of analytical geometry of three dimensions originated with Clairault, and received its final form from the hands of Monge. Descartes, it is true, had remarked, that the orthogonal projections of a curve anyhow situated in space, upon two given rectangular planes, determined the magnitude, species, and position of that curve; but this is, in fact, only an appropriation to scientific purposes of a principle which must have been employed from the earliest period of architectural delineation—the orthography and ichnography, or the ground-plan and section of the system of represented lines. Had Descartes, however, done more than make the suggestion—had he pointed out the particular aspect under which it could have been rendered available to geometrical research—had he furnished a suitable notation and methods of investigation—and, finally, had he given a few examples, calculated to render his analytical processes intelligible to other mathematicians;—then, indeed, this branch of science would have owed him deeper obligations than it can now be said to do.