Electron Theory of Matter. 191 
Lastly, J. J. Thomson gives a formula (1) (I. c. p. 689), 
equivalent to 
'--ssH^aW- 
dt, 
where the motion of the electron in its orbit is supposed to be 
resisted by a force equal to mic times the velocity. In con- 
sequence p is supposed to diminish. To obtain definite results 
integrate by parts, and let p be the initial value of p ; we get 
P= ^{pl^-f + Ke-^Wdt} <-£- W -p*), (31) 
since p 2 <p<? in the integral. 
This result shows that the paramagnetism due to dissi- 
pation of energy from the moving electron is at most of the 
order of magnitude of /> l5 as given by (26) or (27). 
From this discussion we conclude that the formulae (28) 
and (30), although from their form capable of accounting for 
the paramagnetism of iron, can be regarded as little more 
than empirical ; because the very terms, which make them 
capable of doing so, the factor Pl ^ l in (28). and the term h 
in (30), are too ill-defined to serve as the basis for numerical 
calculations. On the other hand, the formulae (29) and (31), 
which are free from theoretical objections, will only account 
for diamagnetism. The formulse (26) and (27) again can 
account for the paramagnetism of iron, but cannot explain 
diamagnetism, because the term^, which gives diamagnetism, 
is far too small to counteract the term p 2 , which gives para- 
magnetism ; thus these formulse, although successful to the 
extent of accounting for the paramagnetism of iron, and 
therefore superior to the others hitherto proposed, are 
incomplete. The remedy has been already indicated in the 
remarks made respecting (29) : the paramagnetic moment p 3 
can be balanced, in whole or part, by the diamagnetic moment 
due to a charged sphere of either sign and of atomic dimen- 
sions, set in motion by the induction set up in starting the 
magnetic field. 
§ 23. We are thus led to consider the following system: — 
(3) A single ring of negative electrons inside a rigid, but free, 
positive sphere of uniform density (type of J, J. Thomson). 
It is not difficult to prove that the tilting of the ring due to 
the radial magnetic force produces no couple tending to rotate 
the sphere ; this couple is due entirely to the inductive effect 
