254 Mr. W. Sutherland on Molecular 



variation of its distance from its neighbours. Evidence 

 bearing upon a real or apparent change of es with R will be 

 discussed in the next section, the subject of the present 

 section being: resumed in 8. 



7. The virial of molecular attraction repressed empirically. 



In " The Laws of Molecular Force " (Phil. Mag. [5] xxxv. 

 1893, p. 211) it was shown from the extensive experiments 

 of Amagat that the equation of van der Waals applies to the 

 whole gaseous region of the element gases H 2 , 2 , N 2 , and to 

 CH 4 , down to and a little beyond the critical volume. Let 

 us write that equation in its properly extended dynamical 

 form for comparison with the equation of the virial of 

 Clausius. It is 



l^-lBT+lmjig-fS. ... (6) 



The term on the left is the virial of the external pressure, 

 the first term on the right is the translator^ kinetic energy 

 of the molecules, the second is the virial of the repulsive 

 forces which act during molecular collisions, and the third 

 is the virial of molecular attraction. The form of this third 

 term when compared with (2) with p = l\v, shows that for 

 the element gases and CH 4 the electric moment es does not 

 vary with the distance between neighbour molecules either 

 in reality or in effect. But in the same paper it was shown 

 from Amagat's expeiiments on C0 2 and from those of 

 Ramsay and Young on (C 2 H 5 ) 2 that for typical compounds 

 the equation takes empirically not the form of that of van 

 der Waals, but this 



5jw-?BT+?BT-^.-J-^. . . (7) 



2 r 2 2 v + k 2 v + k ' 



This applies from v=<x> to the critical volume which is 

 nearly 7kj6, and it holds approximately down to v = k. 

 Here we have two remarkable differences from the equation 

 of the van der Waals type. Originally I supposed these to 

 be due to a pairing of the compound molecules, but in later 

 papers attributed them to molecular entanglements during 

 collision. We have now again to consider them more closely. 

 In the first place the virial of the repulsive forces during 

 collision takes the form 2kj(v-\-k) times, instead of b\(y — b) 

 times 3RT/2. Now in the kinetic theory of gases v — b enters 

 because under given conditions the mean free path of a mole- 

 cule diminishes with increasing size of the molecule, the 



