Electron Theory of Matter. 189 
and (2), the atoms being independent. For this particular 
amalgam the magnetization curve is practically a straight 
line up to H = 3200 C.G.S. so that the condition o£ inde- 
pendence is satisfied; hence we may put A = H. 
Let p = x .10~ 8 cm., where 10 -8 cm. is the conventional 
radius of the atom. We at once find from the second 
equation of (26), or (27) that 
1-8 . 10 -* . *a >p 2 > 1-05 . 10-^ . x\ 
for when u = 2, tan^- =1, while /3 2 is very small, and when 
rrr <jr 
n— co , limit n tan — = 9 , while /3 2 is nearly unity. 
The ratio p x /p 2 is of the order—— where a is the radius of 
the electron, given by a= g-^— . Since 2w/b/w is the distance 
between consecutive electrons, ~ j s smai l ? an( j ^^ 
negligible. -7r P 
A *19 per cent, iron amalgam contains '025 gr. iron per c. c. ; 
taking the mass of the hvdrogenatom to be 1*1 . 10 _24 gr. we 
find N = 4 . 10 20 . Hence since *==N/i 
•0007. a? 3 >&> -0004. a 3 . 
Nagaoka's curve gives Zj = # 0013. 
We see that an atom containing only a single ring of radius 
10~ 8 cm., for which #=l, gives a value of from one half to- 
one quarter of the experimental value of h. An atom con- 
taining from two to four independent rings, or one slightly 
larger ring, could account for the actual atomic magnetism 
of iron ; since, however, the rings could not be independent, 
the above investigation will not apply. Before proceeding 
to the study of systems of rings, it will be convenient to 
consider the performance of the formulae of Voigt and 
Thomson already referred to. 
§ 22. Voigt considers a medium containing a large number 
of independent electrons describing elliptic orbits and subject 
to damping, the irregular stationary state being maintained 
by subjecting each electron to periodic shocks which renew 
its energy. Let yjr be the mean kinetic energy of an electron, 
and <j> 1 its mean potential energy, ^ its mean kinetic energy 
just after a shock. Voigt's formula (51) (I. c. p. 128) is in 
our notation equivalent to the following : — 
eY ft-fr (28> 
12c- m y v 
for a single electron. 
