1052 Mr. A. Fairbourne on Restricted Movements 



both those considered under case 1, and those considered 

 under case 2, only that one point, which is midway between 

 B and C will allow molecules entering equally in all possible 

 directions to escape through AD to the extent of fifty per 

 cent. All other points of entry on BO are placed so that the 

 walls return through BC more than (and in most cases very 

 considerably more than) half the total number of molecules 

 which enter. 



Let N molecules enter the vessel through AD in any 

 representative or sufficiently long period of time, when, as 

 has been shown, these all pass out through BG. Since BC = 

 2AD and two dimensions only are being considered, therefore 

 2N molecules enter the vessel through BC in this same 

 period of time, but of these, whatever points they enter 

 through, and whatever be their directions, more than half nre 

 returned through BC and less than half pass out through 

 AD. Thus, while N molecules pass from AD to BC, less 

 than half 2JN", or less than N, pass from BC to AD : that is 

 a downward flow has been created. This result (which is 

 dependent upon the mean free path being so great in 

 proportion to the size of the vessel that intermolecular 

 collisions inside and in the immediate neighbourhood of the 

 vessel are occurring with only a relatively small number of 

 molecules) is due, as has already been explained, to a 

 deliberate restriction or re- direction of movement applied 

 selectivelv to molecules having certain velocity directions 

 only (directions other than those included in angle BZC), 

 and the effects of such restrictions have been shown to be 

 theoretically independent of the second law of thermo- 

 dynamics. This flow will produce a pressure potential on 

 surfaces exposed to it, and external work can consequently 

 be obtained at the expense of the kinetic energy of the gas 

 enclosed in the system, precisely as in the case of the purely 

 hypothetical experiment described by Maxwell. 



The same effect may also be proved with equal simplicity 

 for vessels with walls inclined to each other at smaller angles. 

 For example, if BZC is an angle of 30°, from any point on 

 the base BC draw OX and OY, each at 45° to BC, cutting 

 AB at X and DC at Y. OX and OY then meet AB and 

 DC each at 60°, and are consequently reflected to strike the 

 opposite side at 90°, whence it will be seen that all molecules 

 entering at 0, and travelling in directions included in angles 

 XOB and YOC are returned through BC. This is true even 

 in the extreme case where O almost coincides with B or C, 

 since Y'BC and X'CB are themselves then each 45°. Angles 

 .OB are together always equal to a right angle, 



