652 SCIENCE PROGRESS 



hotter one must decrease. This is a progressive change requir- 

 ing some time (a matter of minutes). At each momentary phase 

 of the progressive change there is a new distribution of the 

 molecules and of their directions and velocities of movement. 

 Every such phase is, of course, a dynamical consequence of the 

 preceding phase. When thermal equilibrium has been attained 

 the mixture of molecules has a new mean molecular velocity 

 with individual deviations from the mean represented by a new 

 frequency distribution. 



Now it can be shown that if, at the moment at which thermal 

 equilibrium is attained, the direction of motion of each molecule 

 were to be reversed, the series of changes through which the 

 mixture had passed would also be reversed. It would gradually 

 become separated into two masses of gas, each of them char- 

 acterised by its original temperature. Instead of having a gas 

 at uniform temperature in every region we should have a gas 

 separated into two parts, in thermal contact with each other, 

 but having different temperatures. The progressive change 

 from two masses of gas at unequal temperatures to one mass of 

 gas at uniform temperature would be reversed. The series of 

 momentary phases leading from inequality to equality of tem- 

 perature would be exactly followed, but in inverse order. 



It is important to note here that the second law of thermo- 

 dynamics would apparently be " violated." Heat would flow, 

 of itself, from a body at low, to a body at high temperature. 

 But if this were to happen perpetual motion would be possible, 

 whereas we know (at least it is our experience) that it is im- 

 possible. Therefore we must conclude that heat cannot flow, 

 of itself, from a body at lower to another body at higher temper- 

 ature, and we seem to be justified in concluding that this 

 imaginary simultaneous reversal of motion of all the molecules 

 of a gas cannot take place. 



Yet it may conceivably take place. At any instant many of 

 the molecules in a decilitre of gas must be approaching each 

 other in the same straight line, and with the same velocity. As 

 the result of such collisions the direction of motion of these 

 molecules must be reversed, the magnitude of their motions 

 remaining unchanged. The number of such molecules as collide 

 " end on " is continually changing, sometimes there are relatively 

 many, sometimes few. The probability of any fraction of all the 

 molecules so colliding can be calculated, and also the probability 



