﻿14 Mr. William Sutherland on the 



made of attracting smooth perfectly restitutional spheres, one 

 term is the virial of the collisional forces of all the spheres in 

 unit mass which takes the form ^afiv/2 (see Viscosity of 

 Gases and Molecular Force), where a is the radius of a 

 sphere, yu, the average momentum imparted to a sphere in a 

 collision, and v the average number of collisions per sphere 

 per second, the summation to extend to all spheres in unit 

 mass. This is closely similar to the expression which comes 

 in in diffusion for the resistance experienced by one medium 

 in passing through another, and which was written /ulv. In 

 the virial expression /jl is momentum due to velocity of agita- 

 tion, while in the diffusion resistance /jl is the momentum due 

 to relative motion of the two media, which is very slow com- 

 pared to the velocities of agitation. In the diffusion resistance 

 v denotes the number of collisions per second of a sphere of 

 one set with the spheres of the other in unit volume. It was 

 shown that ^a/nv/2 when evaluated takes the form 



|KT^(l + A/T)'; 



so that the theoretical characteristic equation becomes 



P »=RT{i+ B 4- 6 (i +1 oyT) l }-f; 



whereas Amagat's experiments on H 2 , 2 , N 2 , an d CH 4 above 

 the critical volume can be represented by the form 



pv 



L v — oj v 



so that the factor (1 + ^/T)* due to molecular force seems to 

 fall out. Now in the diffusion expression it is a factor 

 approximately equal to 1 + i0 2 /T that appears to drop out; and 

 the main difference between the two cases is that in diffusion 

 the velocity of diffusion involved in the momentum is small 

 compared to the average velocity of agitation involved in the 

 fi of the collisional virial. Thus it appears that the momentum 

 communicated from molecule to molecule in a collision is not 

 transmitted in the same manner as with smooth perfectly 

 restitutional attracting spheres, but that there is some 

 mechanism by which the transmission is made to depend on 

 the ratio of the potential energy at contact to the mean 

 kinetic energy in such a manner as to make the final effect 

 of the forces acting during the collision of molecules the same 

 as if the molecules w r ere both forceless and perfectly resti- 

 tutional smooth spheres. The mechanism is probably that 

 which preserves proportionality between the mean translator^ 

 kinetic energy and the mean vibratory energy of a molecule; 



