510 Mr.. W. Sutherland on the Viscosity 



that in the case of molecules which do collide amongst, them- 

 selves a portion of the viscosity will be due to molecular 

 attraction on account of mutual deflection of paths experienced 

 by those pairs of molecules which pass close to one another 

 without actual collision. 



It i- thus apparent that a full mathematical theory of the 

 viscosity of a medium composed of colliding molecules which 

 attract one another would be a complicated affair, but to 

 anyone familiar with the available knowledge of the size 

 of molecules and the strength of molecular attraction, the fol- 

 lowing considerations lend themselves to simplify the problem 

 of the viscosity of actual gases : — First, that where the average 

 relative velocity is so low and the molecular force is so strong 

 that it happens in a large number of cases that a pair of 

 molecules describe closed paths relative to their centre of 

 mass, then there must be a still larger number of cases of 

 pairs of molecules which deflect each other's path through 

 a large angle. In other words, deflection of paths, on account 

 of molecular attraction and irrespective of collisions, may 

 become an appreciable factor in viscosity in the case of 

 vapours below their critical temperatures. Second, that 

 where a closed path is of rare occurrence, that is, in the case 

 of gases above the critical temperature and at no great 

 pressure, the effect of deflection due to molecular attraction 

 is negligible in comparison with that due to collision as a 

 factor in the production of viscosity, except in so far as 

 molecular attraction causes collisions to occur which would 

 not happen in its absence. This effect of molecular force is 

 illustrated by the figure, where AB represents the relative 



path of the two spheres C and D when no molecular force is 

 supposed to act between them, C being considered to be 

 at rest : according to the figure no collision can occur in the 

 absence of molecular attraction ; but if molecular attraction 

 acts a collision can occur as in the position C F, and the 

 relative path is changed into the two curved branches AF 

 and FH, AB being the asymptote to the branch AF, if in 

 respect to molecular force A is practically at an infinite 

 distance from C. It is evident that this effect of molecular 



