August 14, 1879] 



NATURE 



Z^7 



a converse cause) the gas surrounding the spherical space 

 will diminish in density to a corresponding amount. This 

 initial irregularity of density will cause an initial irregu- 

 larity of pressure, which will tend at once forcibly to re- 

 adjust itself, and will do so by the gaseous mixture within 

 the spherical space expanding,' and an exchange of energy 

 (or "heat") taking place between the two gases — which 

 abnormal state of things can only cease when the two 

 gases become uniformly mixed, and consequently the 

 dynamical conditions become symmetrical in all parts of 

 the mixture. Owing to the absence of dynamical equi- 

 librium in the case of two gases having different mole- 

 cular velocities, unless the gases are uniformly mixed, 

 there is therefore a forcible dynamical tendency to pro- 

 duce uniform mixture, and to maintain it against disturbing 

 causes, when once the mixture has become uniform. When 

 the molecules of the two gases possess unequal normal 

 velocities (attendant on inequality of mass), it is evident 

 that the distribution of velocities can be symmetrical 

 throughout the mixture, only in that case where the 

 mixture is uniform. If, on the other hand, the mole- 

 cules of the two gases possessed the same normal velo- 

 cities (due to equahty of molecular mass), there would 

 be no dynamical cause for any particular mixture more 

 than another, or every assigned mi.xture (regular or ir- 

 regular) would be equally probable : for the distribution of 

 the velocities would be symmetrical or uniform, whatever 

 the mixture might be. Taking our illustration of the 

 spherical portion of gas, and supposing the gas surrounding 

 it (though chemically different) to have equal molecular 

 velocity, then the exchange of molecules between the gases 

 would take place at the same rate, and consequently there 

 would be no disturbance of the equilibrium of pressure at 

 all, but one mixture would be as possible as another, and 

 the distribution of the velocities would be symmetrical 

 whatever the mixture might be.* In fact, it would re- 

 semble the case of the diffusion of two portions of one and 

 tlie same gas into each other. 



Thus it would appear that the fact of the molecules of 

 the constituent gases of the atmosphere possessing unequal 

 normal velocities (due to inequality of molecular mass) 

 tends, through the dynamic action of the molecules, to 

 produce and maintain forcibly a uniform mixture of these 

 gases, and to prevent those detrimental irregularities of 

 mixture that would inevitably occur (by a sufficient range 

 of time and space), if the constituent gases of the 

 atmosphere were of equal molecular masses, and conse- 

 quently diffusion were brought under the pure contin- 

 gencies of chance. 



I have ventured to call attention to this point from its 

 apparent importance, and as the passage above quoted 

 would have the appearance at least of treating the problem 

 as one of pure chances, or as if the influence of the in- 

 equality in molecular velocity had not been taken into 

 account, but I shall be glad to accept correction if I am 

 wrong. 



The fact of the two gases of the atmosphere possessing 

 unequal molecular masses would evidently seem to be of 

 importance as a means for scattering and thereby render- 

 ing harmless, noxious vapours and gases which are emitted 

 into the atmosphere. For even if the particular vapour 

 (in a rare case) happened to be of the same molecular 

 mass as one of the constituents of the atmosphere, it must 

 differ from that of the other constituent, and thus a dy- 

 namical cause for dispersion exists. The considerable 

 inequahty in molecular mass of the most prevalent dele- 

 terious ingredient emitted in combustion and in the 



* The expansion may be seen by inclosing the oxygen in any clastic porous 

 enveloix, capable of expansion, and through which dilTusion can freely take 

 place. It m.ay be observed tliat unmixed gases (of uneijual molecuhar 

 masses, of course) arc known to pojsess a capacity for ;work, which ceases 

 when the gases become uniformly mixed. 



» It is conceivable that although the mean velocities or masses might be 

 ths same, the mean length of path of the molecules of the two gases might 

 be slightly difTerenl. We must therefore cither suppose a case where it is 

 •the same, or if minute exactness be desired, take it into account. 



course of animal life (carbonic acid) thus ensures its dis- 

 persion. 



In a paper published in the Pliil. Mag. for April, 1875, 

 by Lord Rayleigh — '' On the Work that may be gained 

 during the Mixing of Gases "^ — it was pointed out that 

 work may be derived from gases in an unmixed state, and 

 a special method for effecting this end was described. In 

 two papers communicated by me to Nature (vol. xvii. 

 pp. 31 and 202), I, being at that time unaware of 

 Lord Rayleigh' s memoir, indicated a simple mechanical 

 means of deriving work from unmixed gases by the use of 

 porous diaphragms. If we imagine a cylinder, into the 

 piston of which a disk or diaphragm of some porous sub- 

 stance (say plumbago) is fixed, and that two gases of un- 

 equal molecular masses (oxygen and hydrogen,for instance) 

 are introduced into the opposite compartments of the 

 cylinder, then diffusion commences in the known manner 

 through the porous diaphragm. Owing to the inequality 

 in the normal velocities of the molecules of the two gases, 

 they pass through the pores of the diaphragm at unequal 

 rates, thereby entailing an inequality of pressure on the 

 two sides of the diaphragm. If then the piston (con- 

 taining the diaphragm) be suddenly released, it will be 

 driven towards the opposite end of the cylinder, and 

 work may thus be derived. [A simple automatic device 

 for continuing the work by a constant supply of gas was 

 described in Nature, vol. xvii. p. 204.] Although the work 

 is here derived in a self-acting manner, solely at the ex- 

 pense of the normal temperature heat possessed by the 

 gas, yet this would not apparently be out of harmony with 

 the second law of thermodynamics [as the writer at first 

 supposed] ; for it appears that for such to be the case, the 

 process would require to be a reversible one, or the gases 

 would require to be restored again to their original un- 

 mixed state. But if it were possible that the gases could 

 effect this themselves, or become unmixed by their mere 

 action upon each other, and the probability, that in any 

 assigned time we should find all the oxygen back again 

 in the one half of the cylinder, where it was originally, 

 and all the hydrogen back again in the other half, is one 

 which can be measured (however remote this probability 

 might be) ; then we should have a possible means of de- 

 riving work at the expense of normal temperature heat by 

 a process that was self-reversible. Hence this result to 

 which we are led would serve to confirm the above view, 

 viz., that when gases are of unequal molecular masses, 

 there is a forcible dynamical tendency to keep them 

 mixed, or to prevent the gases from becoming separated 

 again when once they have become mixed. 



There would seem to be another consideration bearing 

 directly on the above case. It was a law enunciated by 

 Dalton that when gases of different kinds are placed in 

 the same vessel, " each gas behaves to the other as if it 

 were a vacuum." This, when viewed by the light of the 

 modern dynamical theory, is no doubt true as regards 

 the fact that the total pressure on the sides of the vessel 

 is the sum of the pressures which each gas would exert 

 independently if placed by itself in the vessel. But if the 

 expression " that one gas behaves to another as a 

 vacuum" were taken to refer to the arrangement of the 

 gas in the vessel, then some modification would appear 

 to be required in the statement of the law in the case 

 where the different gases are of equal molecular masses 

 (as also where portions of gas of the same kind are 

 successively introduced into the vessel). For it ap- 

 pears from the above considerations that gases do not 

 necessarily become uniformly mixed by the action of 

 diffusion, excepting when the gases are of unequal mole- 

 cular masses. For portions of gas of equal molecular 

 masses behave to each other as portions of gas of the 

 same kind. If we imagine (merely for illustration) the 

 molecules of a portion of gas to be marked, and this por- 

 tion of gas to be introduced into a vessel where already 

 gas of the same kind exists, then it is evident that there 



