324-328] Diffusion 273 



327. We now examine the effect of the persistence of velocities. When 

 the molecule arrives in a given direction we found that the expectation of 



the distance it had described in that direction was not X, but - - a where 



I u 



'406. Hence the expectation of its belonging to one gas or the other is 



not that appropriate to a distance A, back, but to a distance - -^ . The 



1 u 



effect of " persistence " is therefore to multiply the value of 3) given by 

 equation (636), by a factor - - ^ . Also, as we have already seen, the effect 



on equation (637), is to multiply the value of there found by - - ^a- 



2 



The two equations, both corrected for persistence, accordingly become 



so that the corrected form of equation (638) must be 



fr- 1 -** * 



-T^d'p- 



Putting 6 = '406, the value found in 291, this becomes 



2) = 1-34- .............................. (640). 



P 



It is of interest to examine the difference between the effect of persistence 

 of velocities on diffusion on the one hand, and on viscosity and conduction 

 of heat on the other. Diffusion, it will be seen, is -a transport of a quality, 

 while viscosity and heat-conduction are transports of quantities. The differ- 

 ence rests ultimately upon the circumstance that qualities remain unaltered 

 by collisions, whereas quantities do not. 



Comparison with Experiment. 



328. The last equation gives a quantity which it is impossible to measure 

 experimentally, the interdiffusivity of a gas into itself. 



If, however, we take any three gases, and measure the coefficients of 

 diffusion :Dj 2 , 2) 23 , 1) 31 of the three pairs of gases separately, we can calculate 

 2) n , 3)22 and X^. For our knowledge of 3) 12 , T>23 and 2) 31 will, by the use of 

 equation (635), lead to three equations between <r lt <r 2 and o- 3 . If we solve 

 these equations, we can use the values of <r lt tr a and o- 3 to calculate 3) u , 

 $22 and 2>3s. 



j. 18 



