of Molecules at very low pressures. 1049 



the axis of the tube will pass through and out without any 

 interference whatever to their motion, since the length is 

 much less than the mean free path of the gas. Those, 

 however, which enter at angles sharply inclined to the axis 

 of the tube cross from side to side many times during their 

 passage through the tube, and receive in this way many 

 impacts from the walls. In fact, not only do they receive 

 more impacts in unit time than do those which pass directly 

 through the tube, but they also receive more impacts than 

 do those outside the tube, since an extra restriction has been 

 imposed * upon these molecules selectively. 



With a suitable shape of vessel in place of the tube, it may 

 be proved as follows that this extra restriction on the move- 

 ments of the molecules can be applied selectively in such a 

 manner that molecules which enter the vessel moving in 

 haphazard directions will be diverted to leave it moving in 

 one preponderating direction. 



For the sake of simplicity, although the case is general, it 

 will be assumed for the moment that the molecules are 

 moving in two dimensions only, and it will also be assumed 

 that the mean free path of the gas is so great in proportion 

 to the size of the vessel that intermolecular collisions during 

 the short journeys in the vessel are occurring with only a 

 negligibly small fraction of the total number of molecules 

 which pass through in any representative period of time. 



Let ABCD be a two dimensional vessel, the shape of which 

 corresponds to the cross sectional elevation of a truncated 

 right angled cone. Let it be open at the top, AD, and 

 bottom, BC, and, moreover, let BC be twice the length of 

 AD. 



* Any gas in a hollow cube, the length of whose face is many .times 

 less than the mean free path of the gas, receives more impacts per 

 molecule, in unit time, than does the same gas, at the same temperature 

 and pressure, outside the cube, since, inside, no molecule can travel the 

 calculated free path without receiving extra impacts from the walls. 



