19,1 Perkins: The Octet Theory of Valence 5 
3, or 5) 8 * electrons, which then do duty in both shells. Thus two 
chlorine atoms, having incomplete shells of 7 each, can form two 
complete octets in which one pair of electrons is shared. This 
kind of union, which will be called in this paper a direct union, 
was represented graphically by Lewis as follows: 
: Cl : Cl : 
Langmuir has simplified the formulas, using a single line to 
represent a shared pair : Cl — Cl, HO — Cl — 0, 0=N — 0 — N=0, 
N=N=0, etc. He has shown that a large number of hitherto 
perplexing structures can be readily expressed in this way. 
VALENCE 
Chemists have always tried to make generalizations, concern- 
ing the valence (that is, the quantitative combining power) of 
atoms. An inspection of the Langmuir formulas above tells one 
nothing of the true valence relations of the atoms. He calls the 
number of lines attached to any atom (that is, the number of 
pairs which it shares in that compound) its covalence, and has 
developed some valuable generalizations regarding this variable 
property. What have been considered the true valence relations, 
however, he consigns to the equation : 3 
e = 8n — 2 p. 
It seems to the writer that there are two different kinds of 
direct union not hitherto distinguished. By recognition of this 
difference it is possible to construct formulas of considerable 
graphic value, at the same time dispensing with the equation. 
The proposed system is based on positive and negative valence, 
the maximum values of which are clearly expressed by 
Langmuir 10 as follows : 
Now the maximum positive valence is a definite conception — it repre- 
sents the total number of available elections in the shell * * * On the 
8 In the case of benzene and similar compounds, however, the writer 
believes that 3 electrons are shared. 
® This equation expresses the fact that in a molecule the total number 
of outer shell electrons (e) exist in completed octets, which requires 8 
electrons per octet (8n) less 2 for every pair shared ( — 2 p). The inter- 
pretation of the letters is somewhat modified for the case of hydrogen, 
where the completed shell has 2 electrons, and the heavy atoms, whose 
completed shells have 18 or 32 instead of 8 electrons. 
10 Langmuir, I., Journ. Am. Chem. Soc. 41 (1919) 926. 
