30 



Prof. J. J. Thomson. 



Let 7^0 be the fraction of the number of pairs of molecules which 

 come into collision in the unit of time and contain one molecule from 

 the group A and another from the group B, and for which is 

 between and + d<£>. Then if the states in which the A and B 

 molecules are in after the collision be called A' and B' respectively, 

 the number of pairs of molecules which in the unit of time leave the 

 state {AB} and enter the state {A'B'} is — 



CD J 1 d^{e~ h{T+Tl) ^dxdydzd^drjd^dcvd^ 



2 



Now the distribution will be steady if this equals the number of 

 molecules which leave the state {A'B'} in the unit of time, but this 

 number is — 



TT 



CD P cZ0{e- ;i(T ' +T, V^'^W^ 

 J -J 



We can see that if the gas does not exhibit vector properties 7 

 must equal 7'. For since the motion is reversible, if any two molecules 

 whose coordinates are £17, w ; rj^ u lt come into collision, then 

 the molecules whose coordinates are — |f, —q, — g", 10 • —g^ — 

 — Tu w i5 w ^ a l so collide. Let these latter molecules be said to be in 

 the states (—A'), ( — B') respectively. Thus the percentage of collision 

 for the states (AB), that is for collisions between two molecules in the 

 states A and B, respectively is the same as for the state ( — A', — B'). 

 But since as many molecules are moving in any direction as in the 

 opposite, the number of molecules in the state —A' will equal the 

 number in the state A', and similarly the number of molecules in the 

 state — B' is the same as the number in the state B', and since the 

 gas exhibits no vector properties, the mean path between the collisions 

 between the molecules in the states A' and B' must equal the mean 

 path between the collisions between the molecules in the states —A' 

 and — B' ; and thus the percentage of collisions must be the same. 

 So that the percentage for the state (A'B') equals the percentage for 

 the state ( — A', — B'), but this, as we saw, equals the percentage for 

 the state AB ; and, therefore, the percentage for the state AB 

 equals the percentage for the state (A'B') ; or 7=7'. Since the 

 collision may be fixed with regard to either molecule, and since is 

 positive for one molecule, negative for the other, we see that 7 cannot 

 change sign with 0, so that if 7 is a function of it must be one of 

 the form — 



7 = 70 + 71 cos + 72 cos ^0 + • • • • 



