252 PHENOMENA DEPENDENT ON MOLECULAR PATHS 95 



where N l and N 2 are put for the number of molecules of the 

 first and second sort in the unit volume. 



But the mixture is not homogeneous ; the nearer to one 

 end of the tube, the more in excess are the molecules of one 

 kind, just as those of the other kind are at the opposite end. 

 The pressure and density of one gas diminish along the 

 tube in one direction, while those of the other gas increase 

 in the same direction in equal measure. If the experiment 

 has already lasted some time, the diminution of pressure all 

 along the tube will have become uniform, so that we can 

 represent the pressure and the number of particles of the 

 one gas at the distance x from the junction of the diffusion- 

 tubes by formulae of the form 



p l = $) + $x , N l = 31 + nx, 

 while the same magnitudes for the other gas are 

 P*='P ty $x , N 2 = N 91 nx. 



Here the magnitude p which determines the increase and 

 decrease of the partial pressures is the same for our problem 

 as what is called in hydraulics the slope of pressure, or the 

 diminution of pressure in unit length along a line of flow. 

 The analogous magnitude n determines the decrease or 

 increase of density along the same length ; it will result, in 

 agreement with the views mentioned in 93, that the 

 strength of the diffusion-flow is proportional to it. 



If such a uniform distribution of pressure and density 

 has not yet been established along the whole tube, the 

 foregoing simple formulae can still be employed without 

 error, if we use them for only a very short portion of the 

 tube, and therefore, for instance, if by x we understand a 

 length which is shorter than a molecular free path, as in the 

 following calculation. 



We have to determine how many particles of each kind 

 cross any section of the tube in a given time in consequence 

 of the inequality of the pressure and density that has been 

 described, or, more correctly, how many more cross in 

 one direction than in the other. If the distribution were 

 uniform, the number of particles which in unit time meet 



