Properties of a Molecule in a Substance. 



113 



deduced from equations (4) and (5). Table V. contains the 

 values of this ratio for a few liquids. They are not equal to 

 one another as we should expect. It will also be seen that 

 they are all greater than unity, which means that l 2 is less than 

 li in a liquid. In the case of a gas the opposite holds. It 

 appears, therefore, that when a molecule in a liquid passes 

 from a warmer to a colder part, it spends energy much more 

 rapidly than it acquires through changes in potential energy, 



Table V. 





C. n, 



y- 



Vy 



c" 



Chloroform 



Carbon \ 

 disulphide ...J 



•0,288 

 •0 3 343 

 •0 3 333 



•005876 



•00381 



■007172 



•2337 



•213 



•3319 



4-77 

 2-70 

 7-15 





It will be observed that l 2 is very small, less than the 

 average distance of separation of the molecules. But this 

 will cease to appear remarkable when it is pointed out that 

 the path l 2 is the straight line joining two definite points on 

 the path of the molecule, which is an undulating curve, and 

 the molecule is therefore often in describing its path separated 

 by a greater distance from its starting-point than the ulti- 

 mate distance defined as its mean free path l 2 . 



When there is no change in the potential energy of 

 attraction along the path of a molecule, as occurs in the 

 case of a gas, l x may be nearly equal to, or at least propor- 

 tional to, l 2 for all substances. This is the case with gases, 

 as is well known. In general, then, we ought to write 

 Z 2 = £ 1 . ^r(Tp), where -^(Tp) is a function of the temperature 

 T and density p of the substance, which is greater than 

 unity in the case of a liquid, and in the case of a gas is a 

 constant less than unity equal to about *7. 



A General Formula for the Coefficient of Diffusion. 



Suppose a mixture of two substances 3 and 4 is contained 

 between the planes ABC and DEF (fig. 2). Let the ingre- 

 dients be so distributed that the concentration of the substance 

 3 is proportional to the distance from the plane ABC, and 

 the concentration of the substance 4 proportional to the 

 distance from the plane DEF. The substance 3 will diffuse 



Phil Mag. S. 6. Vol. 24. No. 139. July 1912. I 



