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 DIFFUSION photography, contact prints being taken on collodiochloride of silver or other dry plates. Reflecting gratings can be copied by pouring collodion or gelatine over the grating and stripping off the films thus formed. The latter warp, however, and destroy the definition to a great extent. The grating always produces a brighter spectrum in the violet than a prism. In the green the reflecting speculum metal grating may be brighter than a prism spectroscope of five prisms, and for higher dispersion it surpasses the prism spectroscope both in definition and brightness in all portions of the spectrum. To produce the pure spectrum from flat gratings, two telescopes are generally used, as in Fig. 1. The telescopes are fixed, and the grating is turned on its axis to pass to different portions of the spectrum. As the glass of the telescopes absorbs the ultra-violet light, this portion of the spectrum is cut off entirely, unless quartz lenses are used. The concave grating avoids this trouble, and produces a spectrum without the aid of lenses, the lines being ruled on a concave surface instead of on a flat one. Such a grating, properly mounted, produces what has been called a normal spectrum, and is specially adapted to photographic purposes (Fig. 2). A special form of grating of great defining power has

Fig. 2.—Method of using Concave Grating. A, source of light; I>, slit; L>, grating mounted in beam C, movable along the ways E, E; F, camera-box or eye-piece. been invented by Professor Michelson of the University of Chicago, called the “ echelon ” spectroscope (see Spectroscopy). It is, however, of very limited application. See an article on “Gratings in Theory and Practice” in Astronomy and Astro-Physics, 1893, xii. p. 129. (h. A. R.) Diffusion of Gases.—When two gases are contained in different parts of the same vessel, at the same pressure and temperature without any currents being set up between them, a gradual mixing takes place which is called diffusion. Diffusion may also occur if the gases are separated by a thin membrane; it is then usually called osmosis or transpiration, and may give rise to differences of pressure on the two sides of the membrane. In the diffusion now considered such differences would cause the gas as a whole to move from the region of higher to that of lower pressure, hence the pressure of the mixture must be the same everywhere. By Dalton’s law, the pressure of a mixture of two gases is the sum of the partial pressures of the components, or, in other words, the sum of the pressures which each would exert separately. The sum of the partial pressures of the two gases is thus uniform. If then one gas is moving by diffusion in one direction, say from A to B, its partial pressure will be decreasing at A and increasing at B. Hence the partial pressure of the second gas must be increasing at A and

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decreasing at B,—that is, it must be moving from B to A. Thus diffusion may be regarded as consisting of two streams of gas flowing in opposite directions. Now it is natural to assume (at any rate as an approximation) that the rate of flow of either gas is proportional to the rate at which its partial pressure decreases in the direction of flow, or, as engineers term it, to the “ pressure gradient ” in this direction. This again is proportional to the rate of decrease of the density of the component in the same direction. We may define the coefficient of diffusion as the ratio of the total mass of either component which flows across a unit surface per unit time to the rate at which the density of that component decreases in a direction perpendicular to the said unit surface. The equations of diffusion given in Clerk Maxwell’s article Diffusion {Ency. Brit. 9th ed., vii. 216) need not be repeated here. According, however, to Meyer, Tait, and others, the coefficient of diffusion depends in general on the proportion of the two components contained in the mixture, and thus varies from point to point. The diffusion equation then becomes dvffit — (dffl7:){Y)dv1ldx), an integral of which has been found by Boltzmann. The equation of diffusion when gravity is taken into account has been integrated by Des Coudres. Natanson has reduced diffusion and other irreversible phenomena to particular cases of a general principle which he calls the “thermokinetic principle,” and which includes as a particular case the principle of least action of reversible dynamics. The “ dissipation function,” or expression for the rate at which heat is dissipated by diffusion is calculated, and from it are deduced equations similar to those in Maxwell’s article. The discovery by Lord Rayleigh of an unpublished memoir “ On the Physics of Media that are composed of free and perfectly elastic Molecules in a State of Motion,” which paper had been deposited in the archives of the Royal Society, shows that much of the kinetic theory of gases, including the view that the temperature of a gas is proportional to the square of the molecular velocity, was first established by J. J. Waterston in 1845. The kinetic theory, in its general aspect, is supported by modern experiments in high vacua. In many of Dewar’s experiments with liquid air a glass bulb placed in a mercury vacuum becomes coated with mercury in a surprisingly short time. The rate of deposition agrees fairly well with the formula for the total mass of molecules falling on a unit of area per unit time, viz., where p = density, q = mean molecular velocity. Sir William Crookes’s observation, that if two unequally exhausted vacuum tubes are connected by a fine capillary tube, equalization of pressure takes place very slowly, accords with what we should naturally expect in a rarefied gas consisting of molecules moving in straight lines, and rebounding from the sides of the vessels with but rare collisions with each other ; for the molecules would rarely chance to strike on the opening of the tube. The cathode rays have been attributed to a stream of molecules or particles projected by the cathode, and the fact that they only exist in high vacua accords with the view that at ordinary pressures the molecules of gas would collide with and obstruct them. In 1899 J. J. Thomson demonstrated the existence of such particles (“corpuscles” or “electrons”) having masses much smaller than those of atoms ; a similar conclusion was arrived at in connexion with the Becquerel rays by M. and Mme. Curie. The presence of certain gases in the atmospheres of some planets and their absence from others admits in some cases of a ready explanation according to the kinetic theory, to which may be attributed in particular the absence of atmosphere from the moon. Those molecules wThich are moving away from a planet with velocity greater than that due to the planet’s attraction tend to escape from the planet’s atmosphere. Hence we should expect