62 



SCIENCE 



[N. S. Vol. LIV. No. 1386 



mains after the sheath is removed. Since the 

 neon atom has no sheath the whole atom con- 

 stitutes a kernel with zero charge. The kernel 

 of the sodium atom is the sodium ion with 

 single positive charge, while the kernel of the 

 fluorine atom (or fluorine ion) consists of the 

 nucleus and two electrons, the whole having 

 Y positive charges. 



Since the sheath of any neutral atom con- 

 sists of e electrons, the positive charge on the 

 kernel is also e. In any complete atom there 

 are s electrons in the sheath. When the atom 

 does not share duplets with other atoms (co- 

 valence 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 units. If 

 the two atoms are substantially alike in size 

 and structure, we may assume that this de- 

 crease in charge is to be divided equally be- 

 tween the two atoms. Thus if an atom in a 

 compound has s electrons in its sheath and it 

 has a covalence v^ then the effective charge 

 of its sheath is s — Vc- The total charge of 

 the atom may thus be taken as 



e — (s — Uc) = '^e + fc = ■"• 



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 com- 

 mon 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 mole- 

 cules that a duplet binding two atoms to- 

 gether 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. How- 

 ever, we can not rely entirely upon Coulomb's 



law for this would indicate that the distance 

 between unlike particles should decrease with- 

 out limit. The exact distribution of charged 

 particles in their most stable arrangement! 

 thus requires a knowledge of the repulsive 

 forces whose existence we have already as- 

 sumed. 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 S. — 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 regard- 

 less of sign. By " group of atoms " is meant 

 any aggregate of atoms which are character- 

 ized by proximity to one another. It is felt 

 by the writer that this postulate is a crude 

 expression of a very important and funda- 

 mental law. When we understand the re- 

 pulsive 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 dis- 

 tribution of positive and negative ions in a 

 salt solution is a familiar example of the 

 working of this law. In any small finite ele- 

 ment of volume the charges of the positive 

 and negative ions tend to be very nearly equal 

 or the residual charge tends to a minimum. 



Postulate 3 expresses merely a strong ten- 

 dency so that in general the charges of indi- 

 vidual atoms are not necessarily zero. When 

 the atomic charges depart from zero, however, 

 they do so only as the result of a definite force 

 or action which opposes the tendency of Postu- 

 late 3. We shall see that Postulates 1 and 3 

 are often in conflict and in such cases the 

 tendency of Postulate 1 may prevail against 

 that of Postulate 3. 



We may now classify chemical compounds 

 according to the types of valence exhibited by 

 their atoms and will consider the application 

 of Postulate 3 to each class of compound. 

 There are 3 general subdivisions to consider: 



(1) Complete Compounds, (2) Incomplete 

 Compounds, and (3) Exceptional Cases. 



1. Complete Compounds. — All electrons are 



