442 



NATURE 



\Aprilc), 1874 



" On a Universal Tendency in Nature to the Dissipation 

 of Mechanical Energy. 



The essence of Joule's discovery is the subjection of 

 physical phenomena to dynamical law. If, then, the mo- 

 tion of every particle of matter in the universe were pre- 

 cisely reversed at any instant, the course of nature would 

 be simply reversed for ever after. The bursting bubble 

 of foam at the foot of a waterfall would reunite and de- 

 scend into the water : the thermal motions would recon- 

 centrate their energy and throw the mass up the fall in 

 drops reforming into a close column of ascending water. 

 Heat which had been generated by the friction of solids 

 and dissipated by conduction, and radiation with absorp- 

 tion, would come again to the place of contact and throw 

 the moving body back against the force to which it had 

 previously yielded. Boulders would recover from the 

 mud the materials required to rebuild them into their 

 previous jagged forms, and would bscome reunited to the 

 mountain peak from which they had formerly broken 

 away. And if also the materialistic hypothesis of life 

 were true, living creatures would grow backwards, with 

 conscious knowledge of the future, but no memory of the 

 past, and would become again unborn. But the real phe- 

 nomena of life infinitely transcend human science, and 

 speculation regarding consequences of their imagined re- 

 versal is utterly unprofitable. Far otherwise, however, is 

 it in respect to the reversal of the motions of matter unin- 

 fluenced by life, a very elementary consideration of which 

 leads to the full explanation of the theory of dissipation 

 of energy. 



To take one of the simplest cases of the dissipation of 

 energy, the conduction of heat through a solid — consider 

 a bar of metal warmer at one end than the other and left 

 to itself To avoid all needless complication, of taking 

 loss or gain of heat into account, imagine the bar to be 

 varnished with a substance impermeable to heat. For the 

 sake of definiteness, imagine the bar to be first given 

 with one half of it at one uniform temperature, and the 

 other half of it at another uniform temperature. In- 

 stantly a diffusing of heat commences, and the distribu- 

 tion of temperature becomes continuously less and less 

 unequal, tending to perfect uniformity, but never in any 

 finite time attaining perfectly to this ultimate condition. 

 This process of diffusion could be perfectly prevented by 

 an army of Maxwell's " intelligent demons "* stationed at 

 the surface, or interface as we may call it with Prof James 

 Thomson, separating the hot from the cold part of the bar. 

 To see precisely how this is to be done, consider rather a gas 

 than a solid, because we have much knowledge regarding 

 the molecular motions of a gas, and little or no knowledge 

 of the molecular motions of a solid. Take a jar with the 

 lower half occupied by cold air or gas, and the upper half 

 occupied with air or gas of the same kind, but at a higher 

 temperature, and let the mouth of the jar be closed by an 

 air-tight lid. If the containing vessel were perfectly im- 

 permeable to heat, the diffusion of heat would follow the 

 same law in the gas as in the solid, though in the gas the 

 diffusion of heat takes place chiefly by the diflusion of 

 molecules, each taking its energy with it. and only to a 

 small proportion of its whole amount by the interchange 

 of enerj^y between molecule and molecule ; whereas in 

 the solid there is little or no diffusion of substance, and 

 the ditiusion of heat takes place entirely, or almost en- 

 tirely, through the communication of energy from one 

 molecule to another. Fourier's exquisite mathematical 

 anal>sis expresses perfectly the statistics of the process 

 of diffusion in each case, whether it be " conduction of 

 heat," as Fourier and his followers have called it, or the 

 diffusion of substance in fluid masses (gaseous or liquid) 

 which Fick showed to be subject to Fourier's formuht. 

 Now, suppose the weapon of the ideal army to be a club, 



* The definition of a " demon." accordinK to the use of this word ly 

 Maxwell, IS an intcihgent beuig endowed with free will, and fine enough tac- 

 tile and perceptive org.inisation to give him the faculty of observing cuid 



nftuencing individual molecules of matter. 



or, as it were, a molecular cricket-bat ; and suppose for 

 convenience the mass of each demon with his weapon to 

 be several times greater than that of a molecule. Every 

 time he strikes a molecule he is to send it away with the 

 same energy as it had immediately before. Each demon 

 is to keep as nearly as possible to a certain station, 

 making only such excursions from it as the execution of 

 his orders requires, fie is to experience no forces except 

 such as result from collisions with molecules, and mutual 

 forces between parts of his own mass, including his 

 weapon : thus his voluntary movements cannot influence 

 the position of his centre of gravity, otherwise than by 

 producing collision with molecules. 



The whole interface between hot and cold is to be 

 divided into small areas, each allotted to a single demon. 

 The duty of each demon is to guard his allotment, turning 

 molecules back or allowing them to pass through from 

 either side, according to certain definite orders. First, 

 let the orders be to allow no molecules to pass from either 

 side. The effect will be the same as if the interface were 

 stopped by a barrier impermeable to matter and to heat. 

 The pressure of the gas being, by hypothesis, equal in the 

 hot and cold parts, the resultant momentum taken by 

 each demon from any considerable number of molecules 

 will be zero ; and therefore he may so time his strokes 

 that he shall never move to any considerable distance 

 from his station. Now, instead of stopping and turning 

 all the molecules from crossing his allotted area, let each 

 demon permit a hundred molecules chosen arbitrarily to 

 cross it from the hot side ; and the same number of mole- 

 cules, chosen so as to have the same entire amount of 

 energy and the same resultant momentum, to cross the 

 other way from the cold side. Let this be done over and 

 over again wiihin certain small equal consecutive intervals 

 of time, with care that if the specified balance of energy 

 and momentum is not exactly lulhlled in respect to each 

 successive hundred molecules crossing each way, the 

 eiror will be carried forward, and as nearly as may be 

 corrected, in respect to the next hundred. Thus, a cer- 

 tain perfectly regular diffusion of the gas both ways across 

 the interface goes on, while the original different tempera- 

 •ures on the two sides of the interface are maintained 

 without change. 



Suppose, now, that in the original condition the tempe- 

 rature and pressure of the gas are each equal throughout 

 the vessel, and let it be required to discqualise the tem- 

 perature but to leave the pressure the same in any two 

 portions A and B of the whole space. Station the army 

 on the interface as previously described. Let the orders 

 now be that each demon is to stop all molecules from 

 crossing his area in either direction except 100 coming 

 from A, arbitrarily chosen to be let pass into B, and a 

 greater number, having among them less energy but 

 equal momentum, to cross from B to A. Let this be 

 repeated over and over again. The temperature in A 

 will be continually diminished and the number of mole- 

 cules in it continually increased, until there are not in B 

 enough of molecules with small enough velocities to fulfil 

 the condition with reference to permission to pass from 

 B to A. If after that no molecule be allowed to pass the 

 interface in either direction, the final condition will be 

 very great condensation and very low temperature in A ; 

 rarefaction and very high temperature in B ; and equal 

 temperature in A and B. The process of disequal- 

 isation of temperature and density might be stopped at 

 any time by changing the orders to those previously 

 specified (2), and so permitting a certain degree of diffu- 

 sion each way across the interface while maintaining a 

 certain uniform dirterence of temperatures with equality of 

 pressure on the two sides. 



If no seleciive influence, such as that of the 

 ideal "' demon," guides individual molecules, the ave- 

 rage result of their free motions and collisions 

 must be to equalise the distribution of energy among 



