194 



NA TURE 



\^Dec. 27, I < 



It is this chapter which will excite the most general 

 interest, for although the fact of this still very incomplete 

 theory being found consistent with observed gaseous 

 phenomena would not afford a crucial test of its fitness to 

 explain the phenomena of solids and liquids, still its 

 failure to explain the phenomena of gases would appear 

 to be crucial as regards its unfitness as an atomic theory. 



The fair and cautious spirit in which Mr. Thomson 

 discusses his results cannot be too much admired, 

 although we may not bo quite able to realise the truth 

 of his reasoning. 



The most general and important phenomenon of gases 

 is that sometimes called ]5oyle's law — that the product of 

 the volume and pressure of any fixed weight of gas varies 

 directly as the amount of heat, /.(■. kinetic energy, in 

 a gas. 



Accordingly Mr. Thomson calculates the product of 

 the pressure and volume which would result in the case 

 of a vortex atom gas. This he finds equal to two terms, 

 one being the kinetic energy multiplied by a constant, the 

 other a certain quantity which involves the squares of 

 the velocity of the medium at the boundary surface. To 

 fit Boyle's law this second term must vanish or nearly so. 

 Mr. Thomson argues that it does so vanish, because the 

 surface being at rest the velocity of the fluid at it must be 

 small. This argument we entirely fail to follow, possibly 

 owing to some misapprehension on our part ; but it seems 

 to us that a vortex being near a solid surface is no reason 

 for supposing the tangential velocity of the fluid small, 

 while if the gas consists of vortex atoms so must the solid 

 surface, and there is nothing to show that the mean 

 square of the velocity within the solid and at its surface 

 will be less than in the gas. 



Passing on from Boyle's law, with the explanation of 

 which he is satisfied, the author next turns to the pheno- 

 mena depending on the velocity of the gaseous molecules. 

 As this seems to us the most interesting part of the dis. 

 cussion, we quote the passage in full : — 



"According to the vortex atom theory, as the tempera- 

 ture rises and the energy increases the mean radius of 

 the vortex rings will increase, but when the radius of a 

 vortex ring is increased its velocity is diminished, and 

 thus the mean velocity of the molecules decreases as the 

 temperature increases ; thus it differs from the ordinary 

 kinetic theory, where the mean velocity and the tempera- 

 ture increase together. It ought to be remarked, how- 

 ever, that though in the vortex atom theory the mean 

 velocity decreases as the temperature increases, yet the 

 mean momentum increases with the temperature. 



" The difference between the effects produced by a rise 

 in temperature on the mean velocity of the molecules will 

 probably furnish a crucial experiment between the vortex 

 atom theory and the ordinary kinetic theory of gases, 

 since all the laws connecting the phenomena of diffusion 

 with the temperature can hardly be the same for the two 

 theories. In fact, if we accept Maxwell's reasoning about 

 the phenomenon called ' thermal effusion ' we can see at 

 once an experiment which would decide between the two 

 theories. 



" The phenomenon is this, if we have a porous dia- 

 phragm immersed in a gas, and the gas at the two sides 

 of the diaphragm at diflerent temperatures, then when 

 things have got into a steady state the pressures on the 

 two sides of the diaphragm will be different, and Maxwell, 

 in his paper 'On Stresses in Rarefied Gases' {Phil. 

 Trans. 1879, pa^t '• P- -55), gives the following reasoning 

 to prove that, according to the ordinary theory of gases, 



the pressures on the two sides are proportional to the 

 square root of the absolute temperatures of the sides. 



He says : — 



"'When the diameter of the hole and the thick- 

 ness of the plate are both small coinpared with the length 

 of the free path of the molecule, then, as Sir W. Thomson 

 has shown, any molecule which comes up to the hole on 

 either side will be in very little danger of encountering 

 another molecule before it has got fairly through to the 

 other side. 



" ' Hence the flow of gas in either direction through the 

 hole will take place very nearly in the same manner as if 

 there had been a vacuum on the other side of the hole, 

 and this whether the gas o 1 the other side of the hole is 

 of the same or of a different kind. 



" ' If the gas on the two sides of the plate is of the same 

 kind but at different temperatures, a phenomenon will 

 take place which we may call thcr>na[ effusion. The 

 velocity of the molecules is proportional to the square 

 root of the absolute temperature, and the quantity which 

 passes out through the hole is proportional to this velocity 

 and to the density. Hence, on whichever side the pro- 

 duct of the density into the square root of the temperature 

 is gieatest, more molecules will pass from that side than 

 from the other through the hole, and this will go on till 

 this product is equal on both sides of the hole. Hence 

 the condition of equilibrium is that the density must be 

 inversely as the square root of the teiuperature, and since 

 the pressure is as the product of the density into the 

 temperature, the pressure will be directly proportional to 

 the square root of the absolute temperature.' 



"If we were to apply the same reasoning to the vortex 

 atom theory, we should no longer have the velocity pro- 

 portional to the square root of the absolute temperature, 

 but to some inverse power of it, and the above reasoning 

 would show that if p and p' be the pressures, t and t' the 

 temperatures on the two sides of the plate, pip' = (tji')'", 

 where in is a cjuantity greater than unity. Thus accurate 

 investigations of the phenomenon of thermal effusion 

 would enable us to decide between the vortex atom and 

 the ordinary kinetic theory of gases. These experiments 

 would, however, be difficult to make accurately, as we 

 should have to work with such low pressures to get the 

 mean path of the molecules long enough that the pressure 

 of the mercury vapour in the air-pump used to rarefy the 

 gas might be supposed sensibly to aft'ect the results. In 

 the theoretical investigation, too, the effects of the boun I- 

 ing surface in modifying the motion of the gas seem to 

 have scarcely been taken sufficiently into account to 

 make the experiment of the crucial test of a theory ; and 

 it is probable that the theory of the dift'usion and viscosity 

 of the gases worked out from the laws of action of two 

 vortex rings on each other, given in Part II. of this essay, 

 would lead to results which would decide more easily and 

 more clearly between the two theories. 



" The preceding reasoning holds only for a monatomic 

 gas which can only increase its energy by increasing the 

 mean radius of its vortex atoms ; if, however, the gas be 

 diatomic, the energy will be increased if the shortest dis- 

 tance between the central lines of the vortex cores of the 

 two atoms be diminished, and if the radius of the vortex 

 atom is unaltered the velocity of translation of the mole- 

 cule will be increased as well as the energy ; thus for a 

 diatomic molecule we cannot say that an increase in the 

 energy or a rise in the temperature of the gas would 

 necessarily be accompanied by a diminution in the mean 

 velocity of its molecules." 



With the argument here used we have no fault to find, 

 but it does seem to us that the author has fallen into some 

 confusion between the experimental phenomenon of 

 thermal transpiration through porous plugs and the theo- 

 retical idea of " thermal effusion." It has probably 

 escaped Mr. Thomson, but the experiment he suggests 



