272 Mr. William Sutherland on the 



We see that the ratio is small for the uncombined ele- 

 ments and CH 4 and C 2 H 4 , a result of the important fact that 

 while the refraction-equivalent of a non-metallic element is 

 almost the same in the uncombined state as in the combined, 

 the dynic equivalent is much smaller in the uncombined state 

 of an element. The meaning of this fact will be discussed 

 later on ; connected with it is the fact that the ratio for most 

 of the typical compounds in the last table is notably less than 

 unity. A molecule has to reach a certain degree of com- 

 plexity before the summative law holds as regards its dynic 

 equivalent ; the same maybe said about its heat of formation. 

 Further comment on the connexion between dynic equivalent 

 and heat of formation must be deferred for a little. 



We can now give a formal enunciation of the law of the 

 virial constant : — If the molecule of an organic compound is 

 of a degree of complexity higher than that of the ordinary 

 typical compounds, then the virial constant for one gramme 

 of the compound is given in terms of the megamegadyne, 

 gramme, and centimetre as units by the relation 



Wl = 6S + -66S 2 



where M is the usual molecular weight of the compound, and 

 S is the sum of the dynic equivalents of the atoms in its 

 molecule (measured in terms of that for CH 2 as unity). 



According to the law of force 3 Am 2 /?* 4 , Am 2 is propor- 

 tional to M 2 / and therefore follows the same law. 



13. Return to the Discontinuity during Liquefaction of 

 Compounds and proof that it is due to the pairiiig of Molecules. 

 — The interpretation of the form of the internal virial expres- 

 sion above the volume k is of the highest importance in the 

 theory of molecular force, and can now be attempted in the 

 light of the law for M 2 /. If the molecules of a substance do 

 pair to produce an actual chemical polymer of it, then its 

 molecular mass changes from M to 2M, while S the dynic 

 equivalent changes to 2S, and consequently 



I or (6 S + '66 S 2 )/M 2 



changes to a value given by 



V ' = (6 S/2 + '66 S 2 )/M 2 . 



When S is small we see that the pairing of molecules to pro- 

 duce a polymer causes the virial constant (for one gramme) 

 to diminish to nearly the half of its value for free molecules ; 

 when 8 is larger this statement becomes less exact. In the 



