428 Mr. W. Sutherland on the 
with 6 as coefficient of linear expansion we take @ propor- 
tional to 68, equal to say Gbé@, and then 
y=KiGbT'e/47Oails, . . . . (15) 
This expression for the conductivity has been obtained by 
the consideration of an atom which contains only one doublet. 
Now there is reason for believing that the monatomic mole- 
cule of a divalent metal such as calcium or zine contains two 
doublets, and generally that the number of doublets in the 
molecule of a metal is equal to its valeney (Phil. Mag. [5] 
xxxix.). So far, then, we have considered only the case of a 
monad metal, for we put Q=1/(2a)*. For a metal of 
valency v we cannot treat the v doublets like entirely sepa- 
rate entities, as though they were in separate atoms, nor can 
we simply change the e of the previous calculations into ve. 
We must remember that all the doublets in a polyvalent 
metal atom have a resultant electric moment, and that if 
we still denote this by fes}, e and s separately have not 
their former meanings. Thus in the process of calculating 
y we used esX for the couple acting on a doublet. But 
the v doublets in an atom having a moment {es}X, we 
ought for the whole electrical system of the v-valent atom 
to use {es} instead of the simple es. But in “ Further 
Studies”? there are two lines of evidence that {es}? has 
only v times the value of és°*. Since we are now treating s as 
equal to the molecular diameter, it follows that if in {es} 
we still treat it so, then e in {es} has only v> times the 
value of e. But at each vibration of the electrical system 
of an atom, it is most likely that only one electron takes 
part in the transmission of current, and not v? electrons. . Q 
is still equal to the number of atoms per unit volume, and 
g remains the same. Consequently for v doublets in an 
atom e*s’ in (10) should be replaced by v%e’s°*, while the 
moment of inertia for the v doublets becomes v times that 
for a single one. Hence, when ¢’s* is eliminated as in (12) 
we shall get. 
y=Kel ew. . . 
The period of vibration 7 is not affected, because couple 
and moment of inertia are increased v times. So for a metal 
of valency v (15) becomes 
y =KGbT’e/470a3I3v2. 2 2). . (17) 
Now, in “Further Studies” it was shown in Table xxix. 
that M?/ for the main families is proportional to v(M/p) and 
in the subordinate families to a simple multiple of v(M/p). 
