32 



NATURE 



{Nov. 8, 1877 



suddenly released, it will be driven by the excess of pres- 

 sure in the direction O H, and in that act the gas in O will be 

 chilled and the gas in H heated, which is contrary to the 

 second law of thermodynamics, since in this process work 

 is derived from matter all at a uniform temperature, or 

 work is derived by cooling a portion of gas below the 

 coldest of surroundzns^ objects. In the same way the 

 piston might have been connected to some external 

 mechanism, and so part of the work be done externally 

 (in a self-aciing manner). 



3. There can be little doubt that such work is done in 

 natural processes (in the animal and vegetable world) 

 since plants and organic tissues are distinguished fjr 

 their porosity, 3ind such tissues are permeated with the 

 various gases of the atmosphere, carbdnic acid, &c. It 

 may be observed that even without any porous diaphragm 

 at all, or when two gases whose molecules possess dif- 

 ferent velocities are allowed to diffuse into each other, 

 there is invariably a transferenr e of heaf, which is con- 

 trary to the second law of thermodynamics, which law 

 assumes that heat cannot pass between two bodies origi- 

 nally at the same temperature, or heat cannot pass from 

 a colder to a hotter body. Yet it is evident that as soon 

 as the heat has begun to pass from one of the diffusing 

 gases to the other, the one from which the heat com- 

 mences to pass is already the colder. 



4. Such a principle is evidently capable of an enor- 

 mously wide application in nature. It is only necessary 

 for example for the constituents of the universe to be 

 diverse, to get any amount of work by diffusing them 

 together, even if all originally at the satJte temperature. 

 The principle Gi the tendency to the uniform diffusion of 

 Matter, is capable of completely overthrowing the tendency 

 to the uniform diffusion of Etiergy ; for even if energy 

 were uniformly diffused, the uniformity could be upset by 

 the diffusion of matter {i.e. provided matter were not 

 already all uniformly diffused or homogeneous) : and, as 

 we have seen, the quantity of work to be derived by the 

 diffusion of matter is limited only by the quantity of 

 matter at disposal.^ In order that all capacity for work 

 might cease in the universe, it would be necessary not 

 only that there should be a uniform diffusion of energy, 

 but also a uniform diffusion of matter. Heterogeneity 

 confers a capacity for work, as well as inequality of tem- 

 perature. Heterogeneity, as far as is known, is one of the 

 distinguishing characteristics of the material universe. 

 Any dissimilarity of molecular mass, which (by equality 

 of temperature) is necessarily attended by dissimilarity of 

 molecular velocity, confers a capacity for work. The dis- 

 similarity of velocity is evidently the efficient cause in 

 determining the work, and therefore in the exceptional 

 case where dissimilarity of molecular structure is not 

 attended by inequality of mass (and consequently not by 

 inequality of velocity), work could not be derived. We 

 may note, therefore,. that inequality of molecular velocity, 

 as well as inequality of molecular energy, confers a 

 capacity for work, and in order that all capacity for work 

 should cease, not only must molecular energy, but also 

 molecular velocity be uniformly distributed, or the mole- 

 cules of matter which (by equality of temperature) possess 

 unequal velocities, must be uniformly diffused. 



5. We may observe that gravity which does not inter- 

 fere with the uniform diffusion of energy, does interfere 

 with the uniform diffusion of matter. Thus, for ex- 

 ample, the energy (heat) of the atmosphere, tends to be 

 uniformly diffused throughout a vertical column of the 

 atmosphere, in spite of the action of gravity. But the 

 uniform diffusion of matter {i.e., the uniform mixture of 

 the gases of the atmosphere through each other) is pre- 

 vented by gravity. For by the well-known law of Dalcon 



' Since the first draft of this paper was written, I have been informed that 

 the question ot the quantity of work to be derived by diffusing gases has 

 been treated of by Lord Rayleigh (^Phil, Mag, April, 1875;, but he does 

 not apparently mention the bearing of the case on the sec6nd law bf thermo- 

 dynamics. 



(>vhich accords with the result of the kinetic theory 

 of gases), each gas arranges itself as a layer upon the 

 earth's surface, precisely as it would do if no other gas 

 were present. Thus (as is known), owing to s^the fact 

 that a greater quantity of nitrogen exiss in the atmo- 

 sphere than oxygen, the nitrogen consequently rises to a 

 greater height than the oxygen, so that at considerable 

 heights the nitrogen predomina'es. Thus the uniform 

 diffusion of the constituents of the atmosphere through 

 each other is prevented by gravity. It may, perhaps, be 

 just as well to note in connection with this point that 

 those gases which are observed at the surface of nebulas 

 are not necessarily at the surface because of their greater 

 lightness, but this is also determined by quantity; for 

 as we have observed, each gas (according to the known 

 conditions of equilibrium) arranges itself about a centre 

 as if no other gas were present ; and therefore each gas 

 must penetrate to the centre of the nebula, and therefore 

 could not reach as far as ihe surface unless its quantity 

 were sufficient (though, no doubt, by a greater lightness 

 a less quantity of gas will suffice for that purpose). There 

 might possibly be a tendency to assume (unless the conse- 

 quences of the above principle were rigidly kept in view) 

 that the light gas ob-erved (such as hydrogen) was 

 floating on the surface of the nebula. We know that 

 according to the conditions of gaseous equilibrium this is 

 wrong, and that each gas (if freed from other disturbing 

 causes) will have its basis at the centre of the nebula, 

 where, therefore, the comDOsition or mixture of gaseous 

 matter is uniform, but nowhere ele (excepting in the 

 very improbable case where the quantities and densities 

 of all the gaseous cocstituents are the same). If gravity 

 were to cease (and the gaseous constituents of the nebula 

 were supposed confined or prevented from expanding), 

 the constituents of the nebula would uniformly diffuse 

 themselves throughout the entire mass, and this act 

 of diffusion would be attended by a transference of heat, 

 even if all the gaseous constituents were at the same 

 temperature. 



6. Thus we may observe that by merely modifying the 

 action of gravity or by altering the position of a portion 

 of gas relatively to gravity, work may be derived through 

 diffusion. Thus if we suppose a portion of gas to be 

 moved to different positions in a nebula, the constitution 

 of the portion of gas or the mixture of its constituents is 

 changed according to its position, and in these changes 

 work is derived, or available. Only when the portion of 

 gas is situated at the centre of th^ nebula are its con- 

 stituents uniformly diffused through each other ; less and 

 less so towards the outside. 



7. It would thus appear to foUow that, as far as present 

 knowledge goes, a uniform diffusion of matter as well as 

 a uniform diffusion of energy would be at least required, 

 in order that all capacity for work and physical change 

 should cease in the universe. At the same time does it 

 not rather behove us to look to k time when, through 

 increase of knowledge, a means for recurrence may 

 possibly be discovered, whereby physical change is con- 

 tinued, rather than to look to the purposeless end of a 

 chaos of uniform temperature and uniform distribution of 

 matter? Humboldt says relatively to this point (Preface 

 to " Cosmos") : " I would therefore venture to hope that 

 an attempt to delineate nature in all its vivid animation 

 and exalted grandeur, and to trace the stable amid the 

 vacillating ever- recurring alternation of physical meta- 

 morphoses, will not be wholly disregarded at a future 

 age." S. ToLVER Preston 



MUSIC A SCIENCE OF NUMBERS^ 



HTHE subject which I submit for your consideration this 



-*■ afternoon is the influence of numbers in music, as in 



the various combinations of consonances iind dissonances 



' Read before the Musical Association of London, November 5, 1877, by 

 W. ChappcU, F.S.A. 



