Theory of the Dissipation of Energy. 293 



liquid), which Fick showed to be subject to Fourier's formulas. 

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

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

 venience, 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 ex- 

 cursions from it as the execution of his orders requires. He 

 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, other- 

 wise 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 con- 

 siderable number of molecules will be zero ; and therefore he 

 may so time his strokes that he shall never move to any con- 

 siderable 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 

 within certain small equal consecutive intervals of time, with 

 care that if the specified balance of energy and momentum is 

 not exactly fulfilled in respect to each successive hundred 

 molecules crossing each way, the error will be carried forward, 

 and as nearly as may be corrected, in respect to the next 

 hundred. Thus, a certain perfectly regular diffusion of the 

 gas both ways across the interface goes on, while the original 

 different temperatures on the two sides of the interface are 

 maintained without change. 



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

 ture and pressure of the gas are each equal throughout the 

 vessel, and let it be required to disequalize the temperature, 

 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 



