where A has the value A = 1.203, which was found to be the same in all the series of observations, we find for the four temperatures of the observations 25.1°, 32-6°, 35°, 40-3° the nearly agreeing values 0.870, 0.876, 0.875, 0.877, respectively for e, the mean of which is ε = 21 (n1/n2) = 0·874, from which further follows so that the ratio in this case only slightly exceeds that resulting from the other calculation [viz. 0·631 in the mean]. We further obtain the following values of 7, from the values given before for B: and on reducing these to 0° C. by division by 1 + a9, we get for 10 m, the values 121, 124, 127, 124 respectively. These give values of 7, that are somewhat smaller than the former mean value 0.000130, but they do not vary very much from their mean value ทา = 0.000124. From this follows for the coefficient of viscosity of the gas at 0° when all its molecules are double, or C,O,, the value n2 = 0·000192 which agrees perfectly with the mean (0·000194) of the numbers found for it from the other formula. After this multiplied confirmation of our formulæ we can scarcely still doubt that the theory of viscosity in partially dissociated gases which we have developed corresponds to the reality in all essential points. The deviations which occur between calculation and observation will doubtless be completely explained and made to disappear when the calculation is made with more exactness and generality. A first improvement that is desirable has already been named; it consists in the introduction of a law of dependence of the density on the pressure, which embraces both the liquid and the gaseous states of the substance. A second possibility of improving the theory lies in the consideration that, in addition to single molecules CO, and double ones CO, in the gas, there may also be present triple molecules CO, quadruple ones C,O,, &c. 3 The want of the necessary leisure alone prevents me from carrying out these calculations. 92. Transition into the Critical State In the combination of the simple molecules of a gas or vapour to form larger masses we must doubtless see an approximation to the liquid state in which all particles are joined together into one cohering mass. If, now, the viscosity increases when the density rises by aggregation of the molecules, as in the theories and observations we have before discussed, we shall have to conclude that the viscosity of a vapour attains its greatest value when the vapour has attained the saturated state. But an experiment of Lothar Meyer's,1 on the viscosity of the vapour of benzol, seems to contradict this. He allowed saturated benzol vapour to pass through a capillary tube into a space where the pressure was less; the vapour was here condensed by cooling, and the mass of vapour which had traversed the capillary tube in a given time was determined by weighing the liquid. From this weight the coefficient of viscosity of the vapour was calculated by Poiseuille's law. Calculation gave the value of this coefficient (which is constant for gases) to be the smaller the higher the back pressure at the exit of the capillary tube. We may therefore also say that the friction seemed to be the smaller the larger the mean pressure was in the tube; but this is the exact opposite of the theoretical conclusion, that the viscosity of a vapour is the more considerable the nearer the vapour is to the saturated state. Lothar Meyer has explained this apparent contradic 1 Wied. Ann. 1879, vii. p. 531. tion in an easy way, by recalling attention to the fact that the saturated vapour which enters the tube cannot, with a high back-pressure, expand so much as still to follow with sufficient exactness the gaseous laws, while, with smaller back-pressure, it is brought by expansion still more nearly. into the state of a perfect gas. Schumann,' who had taken part in carrying out these observations, followed up this explanation still further by saying outright that the originally saturated vapour must, during its expansion, form drops of liquid which it carries on with it, and that thence it follows that the mass transpired comes out as too great, and consequently the coefficient of viscosity as too small. To make this explanation of the process perfectly clear and convincing we have only to remember that a saturated vapour which expands must cool thereby, and consequently partially condense into a liquid. The capillary tube used in Lothar Meyer's experiments was, of course, contained in a tube surrounded by the vapour of benzol of the same pressure and temperature, so that it seemed to be ensured against cooling. But if we consider that the thick wall of a fine capillary tube offers a considerable obstruction to the passage of heat, it in no way seems improbable that a slight lowering of the temperature might have occurred within the capillary tube, and that, therefore, a slight amount of vapour might have been condensed. This mass of vapour precipitated in the form of drops will then settle on the walls. of the tube, and spread over them as a thin liquid layer. That the transpired mass becomes greater by means of this disturbance of the experiment follows at once from the fact that the density of the liquid is very much greater than that of the vapour. But we might raise the objection that the friction which the liquid experiences as it flows along the bottom of the tube is also much greater than that which the vapour undergoes. This objection is, however, answered by the fact that the coefficient of friction of a substance is not by any means so greatly altered by the passage from the vapour into the liquid state as its density is. Thus, for instance, the coefficient of friction of water in the liquid 1 Wied. Ann. 1884, xxiii. p. 393. state at mean temperatures is only about 120 times greater than that of water-vapour, while the density of the liquid water is about 1,000 times greater than that of water-vapour under atmospheric pressure. From this example we easily understand how a wet vapour seems to have a smaller viscosity than a dry saturated vapour. This behaviour substantially occurs also in the case of mercury vapour, the viscosity of which has been determined by Synesius Koch. Since the mercury vapour entered into the capillary tube in a saturated state in Koch's experiments, we must assume that, in these measures too, some of the vapour condensed in the tube into little drops, and that, consequently, the transpired masses came out too large, and, therefore, the values of the viscosity too small1; and, indeed, they will have come out the smaller the nearer the vapour was to condensing, and, therefore, the lower its temperature. Hence the consequence would be that the observations would give a greater variation of the viscosity with temperature than the theory could explain. The same might, in like manner, occur with many others of the vapours mentioned in § 87. 1 Compare also § 108. 247 CHAPTER VIII DIFFUSION OF GASES 93. Observations By diffusion we understand the slow mixing of two liquids or gases which were previously separated. Such mixing may be effected by processes of different kinds which, though closely connected, are yet so materially different from each other that it is well to give them different names. In this the terminology of Graham is satisfactory. When the two substances are separated by a solid wall which contains one or more narrow openings, the mixing is caused by effusion, the laws of which have already been discussed in Chapter III. § 37. This mode of mixing must be distinguished from that which takes place through the pores of a natural or artificial membrane, a porous pot or the like, which for liquids is called osmose, and for gases transpiration; the slowness with which this transpiration is carried on is a consequence of the internal friction of the gas, dealt with in Chapter VII., which is active within the narrow channels of the porous partition. A process which essentially differs from the last is that which occurs when the substance of the partition is capable of absorbing either one or both of the gases, so that it takes the gas in at one side and gives it out at the other; this process can also be explained by the kinetic hypothesis, but as it is conditioned, not only by the state of motion of the gaseous substance, but also by the movements of the molecules of the liquid or solid partition, we cannot treat of it here. What we have here to describe, viz. diffusion in the narrower sense of the word, is the mixing together of two liquids or gases which directly touch each other without being |