390 PHENOMENA, ATOMS, AND MOLECULES 



Let us now analyze the conditions that must be fulfilled if the inter- 

 action between atoms is to result in the formation of a complete compound. 



A given group of neutral atoms may interact to complete their sheaths 

 in two ways : 



1. By transfer of electrons. 



a. Atoms having sheaths containing only a few electrons may give 



up these extra electrons to other atoms. 

 h. Atoms having nearly complete sheaths may take up electrons 



from other atoms. 



2. By sharing duplets. 



Atoms may share duplets with other atoms (Postulate 2) and thus 



complete their sheaths with fewer electrons than would otherwise 



be necessary. 



Let e be the number of electrons in the sheath of any neutral atom and 



let J' be the number of electrons in the sheath after the atom has interacted 



with others. For the atoms of any complete compound the values of s can 



be only o, 2, 8, 18 or 32. 



In any group of atoms, the only electrons available for the formation of 

 the complete sheaths are those which originally form the incomplete 

 sheaths. The number of such electrons, 2(^), is found by adding the values 

 of e for the individual atoms. In the resulting compound, if no duplets are 

 shared by the atoms, the total number of electrons in the complete sheaths 

 is 2 {s) . Every duplet held in common by two atoms, however, decreases 

 by two the number of electrons required to form the sheaths. If then we let 

 B be the total number of duplets shared within the given group of atoms, 

 the number of electrons in the completed sheaths of the atoms of the com- 

 pound is ^{s) — 2B. Since this must equal the number in the original 

 neutral atoms, we have the relation ^ 



2(0 = 2(.?)-25. (i) 



This is the condition for the formation of a complete compound. We shall 

 now proceed to put this equation into a simpler form and one which has 

 more significance to the chemist. 



The transfer of electrons that may occur during the interaction between 

 atoms corresponds to what has been called positive and negative valence 

 while the sharing of duplets corresponds to covalence. We shall see that 

 the positive and negative valence differ from one another fundamentally 

 only in algebraic sign, so that we shall find it convenient to include both 

 positive and negative valence under the term electrovalence, which we may 



^ Equation ( i ) is a more general statement of the relation e = %n — 2p which has 

 been used previously by the writer in discussing the "octet theory." 



