Electron Theory of Matter. 197 
magnetic moment thus is 16,000, perhaps 65,000, times 
as great as the greatest diamagnetic moment. The curves 
give the extreme values 1*8 . Z> 3 and — 0*17. 6 3 , in the ratio 
10 : 1. 
By taking b a few times the conventional atomic radius, 
10~ 8 cm. (or by choosing several rings) the greatest para- 
magnetic moment can easily be brought within the range of 
the system, which so far is quite satisfactory. We cannot, 
however, explain diamagnetism so easily, although the margin 
available is very large, for the diagram shows that our single 
ring system cannot possibly be diamagnetic unless the radius 
of the ring is less than the critical radius, the greatest value 
of which is 0-72. b. 
Now ~ cannot be chosen at will, because the 'equation of 
steady motion (2) must be satisfied. In the present case of 
ixe" 
a neutral system we have v=n, P= y^p ; thus (2) becomes 
/> 3 e 2 n b it ^ ' 
The last term is positive ; in fact K is slightly greater 
than — log h, and in the series V J 2s+l {(2s + 1)/3} is 
positive, because j3< 1, and (s + i) cot ^ — ^ — ^— < — ; putting 
in this value for the cotangent, Ave get a series whose value 
is equal to ^ {/3 2 -(H-/3 2 ) log Vl^ 2 }. Hence 
(MffirZ > ^ {log(VI ^ ) _ /32}>0 
for all values of /3 which are actually possible with radiation 
small enough for permanence. 
Substituting the value j —0*72 in (39), we find 
log>* < 2tt^<2-0, n<S, 
on the assumption that /3 2 is negligibly small, which is 
certainly true for such small values of n. Hence we conclude 
that no single ring system can be diamagnetic unless the 
number of electrons is less than 8. 
This number obviously does not give sufficient margin to 
account for the large number of diamagnetic elements known, 
