95 DIFFUSION OF GASES 255 



since the pressure is always directly proportional to the 

 number of particles which give rise to it, and therefore the 

 excess of pressure p# is proportional to the surplus number of 

 particles nx, or p to n. 



Our theory is now so far developed that the strength 

 of the diffusion-current has been expressed in terms of the 

 numbers n and p, which give the measure of the inequality 

 of the distribution. We thereby find an analogy, already 

 hinted at, with the flow of heat that is caused by in- 

 equality in the distribution of temperature, which is so far 

 confirmed as touches the proportionality in both cases of 

 the flow to the surplus that is present. We therefore define 

 as the coefficient of diffusion the factor of proportionality 



We have still in this formula to determine more closely 

 the two distances denoted by A. We have already said that 

 they are smaller than the mean free paths of the molecules. 

 The determination of the numerical ratio in which they are 

 less than the free paths is of secondary importance. We 

 easily see without calculation that A must for every gas be 

 about half as large as the mean free path of its molecules ; 

 for the path on which a particle crosses the plane considered 

 will lie, on an average, half on the one side of the plane 

 and half on the other. But since the more rapidly moving 

 particles attain a greater free path than the slower ones, the 

 more rapid particles will exert a greater influence on the 

 value of the product AH ; by an accurate calculation, there- 

 fore, we may expect to find a rather larger value for the ratio 

 of A to the mean free path. As a matter of fact, we find 

 by a calculation founded on Maxwell's law of distribution 

 of speeds, and given in 52* of the Mathematical Appendices, 

 that the ratio of A to the free path is equal to 77-. The 

 formula for the coefficient of diffusion therefore becomes 



D = ^(JV^A + N&QJIN, 



if we denote by ^ and 2 the free paths of the two kinds 

 of molecules in the mixture, and in this form it exhibits a 

 striking likeness to the value of a coefficient of viscosity. 



