174-176] Equations of Mass Motion 155 



Molecules of Finite Size. 



176. In order to separate the difficulties as much as possible, and so 

 simplify the treatment of the subject, it has been found convenient to defer 

 the difficulties introduced by the finite size of the molecules. The finite size 

 can, as has already been explained, be supposed to have been allowed for in 

 the field of intermolecular force, but if we wish to get results which admit of 

 easy interpretation it is best to suppose the molecules to be of finite size, in 

 addition to possessing fields of intermolecular force. 



If v x , y , z is the " effective molecular density " at #, y, z, then the expecta- 

 tion of the number of molecules of which the centres lie within any element 

 of volume is 



\\\v Xi y tZ dxdydz, 



where the integration extends throughout the element of volume in question. 

 It is, however, also equal, by the definition of v, to 



v \\\dxdydz, 



so that v x> y> z, averaged through a volume large enough to contain a great 

 number of molecules, becomes equal to v. 



Similarly the number of molecules crossing an element of surface dS 

 contains as a factor 



(fvxyzdS ...(367), 



i **> yt ** \ / ' 



and if this element of surface is great compared with the size of a molecule, 

 while at the same time v is approximately constant while we pass in any 

 direction over a distance comparable with the size of dS, then the factor may, 

 we know, also be written 



vffdS (368), 



so that v is the average value of v x , y , z over the element of surface dS. 



A complication occurs in the neighbourhood of the boundary, because 

 here, as appeared in the last chapter, the value of v may vary perceptibly 

 over a distance comparable with the molecular diameter. If, then, dS is an 

 element of surface at a distance <r from the boundary and parallel to 

 the boundary, expression (366) must be replaced, not by expression (368), 

 but by 



7 (369), 



where v\, is the same as the v b of 137. 



