Residual Valence of Various Molecules 475 



radioactive and decompose. It is not impossible, on the 

 electronic theory of valence, to ascribe the acquiring of addi- 

 tional or residual valence by the atoms of molecules to internal 

 rearrangements of the electrons within the atoms, similar 

 to that rearrangement which, in radioactive substances, leads 

 to an explosion of the atom. 



The method I have used to determine the quantity of 

 residual valence is a physical one, based on the cohesion of 

 molecules. While the method is not very accurate at present, 

 owing to several doubtful points in the calculations, it probably 

 places the molecules in the order in which they occur when 

 arranged according to the amount of average residual valence 

 they possess; and it will become more precise as the critical 

 data are more accurately known and the cohesion or internal 

 pressure more accurately determined. The method is as 

 follows : The internal or cohesive pressure of a fluid is rep- 

 resented by the value a/V 2 of van der Waals' equation. 

 In this expression V 2 represents how the cohesional attraction 

 varies with the distance; and "a" is the "mass" factor of the 

 attraction. Now "a" includes the factor N 2 , N being the 

 number of molecules in the volume V, and if "a" is divided 

 by N 2 then the quotient represents the "mass" factor of the 

 cohesional attraction of two molecules and it may be written 

 M 2 K to correspond with the mass factor of the gravitational 

 attraction, m 2 k, in which "m" is the gravitational mass and 

 "k" the gravitational constant. The relationship was found 1 

 that M 2 K is proportional to the two-thirds power of the 

 product of the molecular weight by the number of valences 

 in the molecule, or M 2 K = C(Wt. X Val.) 2/ '. How accu- 

 rately this relationship holds is shown in Table I in which the 

 value of "a" which is of course proportional to M 2 K, and 

 is the mean value computed from various formulas, is com- 

 pared with the value of "a" computed from the molecular 

 weight and the number of valences. The method of com- 

 puting "a" was given in another paper. 2 



1 Mathews: Jour. Phys. Chem., 17, 181 (1913). 



2 Mathews: Ibid., 17, 603 (1913)- 



