P N E P N E 249 according to a power of the absolute temperature less than unity, but greater than one-half. His results in this respect are corro borated by those of Kundt and Warburg, Puluj, and other later experimenters. The 77 power is probably not far from the truth. Hence we may give as the final value for the viscosity of dry air the expression /*= -000185(1 + -00280). The following table gives the values for the different gases, as determined by the different investigators, the viscosity of air being taken as unity. Giahiim. Maxwi-ll. Meyer. Kundt and Warburg. Crookes. Air I OOO I OOO I OOO 1 000 I OOO Oxygen 1-112 1 095 1 119 Nitrogen 971 972 Carbonic: oxide 968 070 Carbonic acid 840 859 851 806 "920 Hydrogen 488 516 601 488 "444 We do not here enter into the question of the thermodynamics of gases ; enough to say that the relations between viscosity, diffusion, and thermal conductivity deduced by Maxwell from the kinetic theory have received remarkable corroboration from the experiments of Loschmicht, Stefan, Kundt and Warburg, and others. A discussion of the dynamical properties of gases would not, however, appear complete without mention of Crookes s so- called radiometer, even though these phenomena of high vacua are ultimately thermodynamics. nxess The typical form of the radiometer is a glass bulb, in which is id- hung a delicately poised arrangement of vanes. These, usually ier. four in number, are fixed at the extremities of two light horizontal cross-rods, which are supported so as to be capable of easy rotation about a central vertical axis. The vanes or disks are set in vertical planes passing through the axis ; and each has its one side bright, and the other blackened. For any rotation the motion of each vane is exactly alike ; that is, either the bright faces all move first, or the dark faces do so. If the pressure of the gas inside the bulb is reduced to a very low exhaustion, the vanes under the action of light or heat will begin to rotate. The mere bringing the radio meter out of a dark region into daylight is enough to set up this rotation. In ordinary circumstances the dark faces are apparently repelled, and the vanes move round with their bright faces in advance. The phenomenon is really a thermal one, as was demonstrated experimentally by Tait and Dewar. 1 Further, although it is most evident in high vacua (provided they are not too high), it can be produced in very moderate exhaustions by a suitable arrangement, as was long ago pointed out by Fresnel. Thus, if under the receiver of an ordinary air-pump a light disk be delicately poised near a parallel fixed surface, it will be apparently strongly repelled by this surface if the opposing surfaces are brought to different tem peratures. This may be effectively done by means of a ray of sunlight. In this experiment, the essential condition is (as shown by Tait and Dewar) that the surfaces be at a distance comparable to the mean free path of the gaseous molecules. In Crookes s radiometer the free path is very long, and hence there is apparent repulsion between the blackened surfaces and the walls of the bulb. The reason simply is that, under the action of the radiant energy directed in upon the vanes, the dark faces, absorbing more energy, become warmer than the bright faces. Hence an inequality of temperature is produced in the highly rarefied gas, and this brings into existence a stress which displaces the vanes. Liquid in the spheroidal state illustrates the same principle. That a drop of water may be supported over a hot surface without touching it requires an upward pressure. In other words, the vertical stress in the vapour and gas which separate the drop from the surface must bo greater than the ordinary gaseous pressure all round the drop. This stress exists because of the difference of temperature between the drop and the surface, so that the pressure in the thin layer of vapour and gas is slightly greater in the vertical than in any horizontal direction. A general notion of the manner in which this stress is sustained may be obtained from the following consideration. According to the kinetic theory of gases, the mean speed of the molecules is a function of the temperature the higher the temperature the greater the speed. Hence molecules, impinging upon a surface at a higher temperature, and in a direction more nearly perpen dicular to it, will rebound from that surface with increased momentum. The simultaneous motion of the surface, as if repelled, is then somewhat analogous to the recoil of a cannon when fired. The whole investigation of the question is, however, by no means simple. Maxwell has discussed it with characteristic lucidity in his latest contribution 2 to the dynamical theory of 1 Proc. Roy. Soc. Edin.. and Xaiure, 1875. 2 Phil. Trans., 1879. gases. He finds that, when inequalities of temperature exist at a given point in a gas, the pressure is not the same in all directions. Its value in any given direction, in so far as it depends upon the temperature inequality, is proportional to the space-rate of change of the space-variation of the temperature in that direction that is, to the second differential coefficient of the temperature with respect to the given direction. Hence the pressure will be greatest along the line for which this differential coefficient is a maximum. It appears that the pressure so called into existence by a possible temperature inequality is very minute at ordinary hydrostatic pressures, but becomes considerable when the pressure of the gas is made very small. If the inequality of temperature throughout the gas is due to the presence of small bodies, whose temperatures differ from the temperature of the gas at a distance from them, then the small bodies will be acted upon by the stresses set up, provided they are of the same order of smallness as the mean free path of the molecules. In the case of two such small bodies, there will be apparent repulsion between them if the bodies are warmer than the air at a distance from them, and attraction if they are colder. If one is warmer and the other colder, the action may be either attractive or repulsive, according to the relative sizes of the bodies and their exact temperatures. These results are obtained by considering only the stresses normal to the solid surfaces. When the tangential stresses are taken into account, then it appears that inequality of temperature, when the flow of heat becomes steady, cannot produce other than equilibrium in the material system immersed in the gas. Hence Maxwell believes that the explana tion of Crookes s phenomenon must depend ultimately upon the slipping of the gas over the solid surface. If such slipping be permitted, its effect will be to diminish the tangential stresses acting on the solid surface without affecting the normal stresses ; and hence the equilibrium will be destroyed. In attempting to express the conditions to be satisfied by the gas at the solid surface, Maxwell is led to the consideration of the phenomenon discovered by Osborne Reynolds 3 and named thermal transpiration. This phenomenon consists of a sliding of the gas over the surface of an unequally heated solid from the colder to the hotter parts. Maxwell considers the particular case of the slow steady flow of gas along a capillary tube of circular section, the temperature of which varies steadily from point to point. The amount of gas which passes through any section depends both upon the rate of change of pressure and the rate of change of temperature in passing along the axis of the tube. If the pressure is uniform there will be a Mow of gas from the colder to the hotter end. If there is no flow of gas, the pressure will increase from the colder to the hotter end. The case of uniform temperature is the ordinary case of transpiration through capillary tubes, as discussed experimentally by Graham, Meyer, Puluj, and Kundt and Warburg. The experi mental investigation of the first two cases seems at present hopeless, on account of the minuteness of the quantities to be measured. Reynolds experimented, not on capillary tubes, but on the passage of the gas through a porous plate, the temperatures being different on the two sides. (C. G. K.) PNEUMONIA, or inflammation of the substance of the lungs, manifests itself in several forms which differ from each other in their nature, causes, and results, viz., (1) Acute Croupous or Lobar Pneumonia, the most common form of the disease, in which the inflammation affects a limited area, usually a lobe or lobes of the lung, and runs a rapid course ; (2) Catarrhal Pneumonia, Broncho-Pneu monia, or Lobular Pneumonia, which occurs as a result of antecedent bronchitis, and is more diffuse in its distribu tion than the former ; (3) Interstitial Pneumonia or Cir rhosis of the lung, a more chronic form of inflammation, which affects chiefly the framework or fibrous stroma of the lung and is closely allied to phthisis. Acute Croupous or Lobar Pneumonia. This is the disease commonly known as inflammation of the lungs. It derives its name from its pathological characters, which are well marked. The changes which take pkce in the lung are chiefly three. (1) Congestion, or engorgement, the blood-vessels being distended and the lung more voluminous and heavier than normal, and of dark red colour. Its air cells still contain air. (2) Red Hepatiza- tion, so called from its resemblance to liver tissue. In this stage there is poured into the air cells of the affected part an exudation consisting of amorphous fibrin together with epithelial cells and red and white blood corpuscles, the whole forming a viscid mass which occupies not only 3 Proc. Roy. Soc., 1879.
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