392 PHENOMENA, ATOMS, AND MOLECULES 



( covalence zero) then the total charge of the atom is e — s. If, however, 

 any two atoms hold a duplet in common the total charge of the two atoms 

 is decreased by two vmits. // the tzvo atoms are substantially alike in size 

 and structure, we may assume that this decrease in charge is to be divided 

 equally between the two atoms. Thus if an atom in a compound has .v 

 electrons in its sheath and it has a covalence Vc then the effective charge 

 of its sheath is s — z'c- The total charge of the atom may thus be taken as 



e — (s — Vc) ^ Ve -\-'Vc = v. 



Thus V, the sum of the electrovalence and the covalence, for any atom in a 

 compound, is equal to the residual atomic charge. 



When two atoms which hold a duplet in common differ considerably in 

 size, it is no longer obvious that the two electrons of the duplet should be 

 divided equally between the two atoms in determining the residual charge. 

 We may, however, arbitrarily so define the boundaries of the individual 

 atoms in molecules that a duplet binding two atoms together is to be 

 regarded as belonging equally to the two atoms. In this case we may con- 

 sider V to be the residual atomic charge even when the atoms differ 

 greatly in size. 



It is evident from Coulomb's law that the separation of positive from 

 negative charges requires in general the expenditure of work. The most 

 stable forms of matter should be those in which the positive and negative 

 charges are as near together as possible. However, we can not rely entirely 

 upon Coulomb's law for this would indicate that the distance between un- 

 like particles should decrease without limit. The exact distribution of 

 charged particles in their most stable arrangement thus requires a knowl- 

 edge of the repulsive forces whose existence we have already assumed. 

 A further discussion of this point will be reserved for a future paper. At 

 present we may attempt to express this relation by the following postulate. 



Postulate J. — The residual charge on each atom and on each group of 

 atoms tends to a minimum. 



By "residual charge" is meant the total charge of an atom or group of 

 atoms regardless of sign. By "group of atoms" is meant any aggregate of 

 atoms which are characterized by proximity to one another. It is felt by the 

 writer that this postulate is a crude expression of a very important and 

 fundamental law. When we understand the repulsive forces between 

 charged particles better we shall be able to state the law in a more nearly 

 quantitative form. The law is of very wide application. The uniformity of 

 distribution of positive and negative ions in a salt solution is a familiar 

 example of the working of this law. In any small finite element of volume 

 the charges of the positive and negative ions tend to be very nearly equal 

 or the residual charge tends to a minimum. 



