640 Mr. W. Sutherland on the 



molecular radius on account of the mutual impenetrability of 

 molecules. According to the kinetic theory k/2 stands for 

 4 times the volume of the molecules which occupy v. Then 

 in compounds we must regard the v + k, which comes in 

 instead of volume minus 4 times the actual volume of the 

 molecules, to represent a lengthening of the mean free path, 

 that is to say a diminution of the number of collisions. In 

 the case of compounds then a collision is an event which, 

 instead of shortening the interval between two successive 

 ones from what it would be if the molecules could penetrate 

 one another, actually prolongs it, so as not only to neutralize 

 the term ( — 4 times volume of molecules) but to add on k. 

 In ethylene we meet with a transition case where the negative 

 term is only neutralized, and the collisional virial is H'Lk/v. 

 In compounds in general then, a collision is an entanglement 

 of the parts of the molecules which lasts long enough to 

 produce an appreciable effect on the dynamics of the mole- 

 cules, namely a diminution of the collisional virial below 

 what it would be if the molecules collided like hard 

 spheres. 



But in the present connexion the contrast between the 

 virials of the attractive forces in element and compound gases 

 is most important. From v = co to v=k (nearly) in element 

 gases it is — l/v, and in compounds —l/(v + k). For volumes 

 less than k the form for compounds is —l/2v. For com- 

 pounds then we write the virial of the attractions 



1 l +1, k 



v + k v v v + A:' 



and so see in it the general attractional virial — l/v numeri- 

 cally reduced because a repulsional virial, which is a fraction 

 k/(v + k) of it, enters into the equation. When v~k the 

 fraction takes the value ^, which it retains for smaller values 

 of v, the virial then being —l/v + l/2v=—l/2v. Evidently 

 then the entanglement during a collision of two compound 

 molecules, which diminishes the virial of the collisional 

 repulsive forces, introduces the virial (l/v){k/(v + k)} of 

 repulsive forces of electrical origin. 



We must briefly inquire into the probable cause of the 

 contrast between the behaviour of element and compound 

 gas-molecules during collision. In an element gas like H 2 

 we have # attached to H, and also b attached to H, whereas 

 in a compound gas like HC1 # is associated only with H, 

 and b with CI. We can imagine then that in H 2 or £H Hb it 

 is possible for # and b to change places so as to form bH H^ 

 without displacing the atoms, whereas in the case of #HC1? 



