July 22, 1921] 



SCIENCE 



61 



trons than would otherwise be 

 necessary. 



Let e be the number of electrons in the 

 sheath of any neutral atom and let s 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 0, 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 elec- 

 trons, 2(e), 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 5(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 elec- 

 trons in the completed sheaths of the atoms 

 of the compound is 2(s) — 2i?. Since this 

 must equal the number in the original neutral 

 atoms, we have the relation ^ 



2(e) =2(s) — 2B. 



(1) 



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 corre- 

 sponds to what has been called positive and 

 negative valence while the sharing of duplets 

 corresponds to eovalence. We shall see that 

 the positive and negative valence difPer 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 

 designate by the symbol v,,. We shall then 

 adopt the convention that the electrovalence 



3 Equation (1) is a more general statement of 

 t"he relation e =r 8n — 2j> whieh has heen used 

 previously by the writer in discussing the ' ' octet 

 theory. ' ' 



of an atom is positive when the atom gives up 

 electrons and negative when it takes up elec- 

 trons. The electrovalence of an atom in any 

 compound may thus be defined as the number 

 of electrons which the neutral atom must give 

 up in forming that compound. If the neutral 

 atom must tahe up electrons, the electrovalence 

 is expressed as a negative number. The elec- 

 trovalence of any atom is thus given by the 

 expression 



Ve = e — s. (2) 



Electropositive atoms in complete com- 

 pounds lose all the electrons in their sheaths 

 so that s is zero and therefore v^ is positive 

 and equal to e. For electronegative atoms s 

 is always greater than e so that v,, is negative. 



Let u's define the eovalence (vc) of an atom 

 as the number of duplets which that atom 

 shares with neighboring atoms. Every duplet 

 shared by two atoms corresponds to a (co- 

 valence) hand between atoms, and we have 

 already represented the number of such bonds 

 in a given group of atoms by the symbol B. 

 If we now form 5('Vc) ^J adding the values of 

 Vc for all the atoms in the given group, we 

 count each bond twice. Hence we may place 



:2B. 



(3) 



By substituting (3) and (2) in (1) and re- 

 arranging terms we find 



^Ve + 'S.Vc = 0. (4) 



This simple result may be stated as fol- 

 lows: 



The sum of the electrovalences and co- 

 valences for all the atoms in any complete 

 compound is zero. 



Electrovalence and eovalence are thus in 

 a sense supplementary to one another. If 

 we represent v^ + '"c by v. Equation 4 takes 

 the form 



2ti = (5) 



for any complete compound, and this sug- 

 gests that the quantity v may have some 

 simple physical significance. 



In accordance with the nomenclature in- 

 troduced by Lewis we may define the Icernel 

 of an atom as that part of an atom which re- 



