600 SCIENCE PROGRESS 



sion, so that in the complete cycle, the whole S3'stem being 

 restored to its original state but for the separation of the 

 gases, no work on the whole is done. Does this result support 

 Rayleigh's doctrine ? It is true work is spent during the 

 separation, and gained during the subsequent expansion — that is, 

 the gases when separated have available energy. But this is 

 not because they are separated, but because they are com- 

 pressed, and they would have precisely the same available 

 energy if they were not separated at all, but expanded as a 

 mixture to their original state. 



5. In his second example Rayleigh shows how the separation 

 of two gases may in a certain case, and doubtless in other cases, 

 be effected by chemical means. 



6. In the third argument (p. 313, etc.), Rayleigh considers the 

 case in which two gases, a heavier and a lighter, say oxygen 

 and hydrogen, are partially separated by the action of gravity 

 in a vertical tube. Suppose them to have arrived at a state of 

 equilibrium, and the partial pressures at the base of the tube 

 are the same as those of the same two gases mixed in a 

 reservoir, so that if the tube communicates with the reservoir 

 at its base no oxygen or hydrogen escapes from or to the 

 reservoir. Rayleigh proves that if the mixture of gases in 

 each element of the tube be separately compressed to the total 

 pressure at the base, and is then brought down to the level of 

 the base, the work spent in the compression exceeds in the case 

 of two gases that gained from gravity in the descent. Were 

 only one gas present, it would be equal to the work gained. 



7. In order to make the cycle complete, except that at the 

 end the gases are partially separated, at the beginning uniformly 

 mixed, I will work out the problem independently. As will be 

 seen, I shall obtain Rayleigh's result above stated. I consider 

 two cases : 



Case /.—A single gas is at uniform pressure and temperature 

 in a horizontal tube ACB of length S. C is the middle point, 

 and initially the centre of gravity of the gases. I avail myself 

 of the permission given by Rayleigh (p. 318, line 3) to divide the 

 tube into elements of length, and to insert between each pair 

 of successive elements a piston, fixed or movable, to prevent 

 passage of molecules from one element to another, also per- 

 mission to remove such pistons. Then — 



Process (1). Fix the pistons and turn the tube about the end 



