1921-22.] 
On Models of Ferromagnetic Induction. 
115 
Weber element, possessing magnetic moment and capable of turning in 
response to an applied field ; and an outer group or shell which is to be 
regarded as held more or less completely fixed relative to neighbouring 
atoms when the atom is part of a solid body — as for instance when it takes 
its place in the space-lattice of a crystal. The outer group of electrons 
acts on the inner group or Weber element like a number of fixed directing 
magnets. The mutual magnetic forces between the Weber element and 
the outer group determine the range through which the Weber element 
can turn stably, and when this range is exceeded it 
turns irreversibly (in a manner involving hysteresis) 
from one position of stability to another. In each 
position of stability there are strong magnetic forces 
acting between the Weber element and separate 
portions of the outer group ; these make the range 
of stable deflection very narrow, but they are more 
or less completely balanced, with the result that the 
stability is feeble. 
22. To make this clear we may consider, in the 
first place, the equilibrium of a magnet W (fig. 11) 
pivoted at its centre 0, and set between two fixed 
magnets A and B which are oppositely directed 
towards O. Thus the fixed poles P' and P" are of 
the same name. Let m and m" be their pole strengths 
and let m be the pole strength of the pivoted magnet. 
Assume that the clearance between W and the fixed 
magnets is small, and that it is the same at both 
ends. Write r for OP, the half length of W, and a 
for OP' or OP". Let a field H act with a constant inclination a to the 
line of centres, deflecting W stably through a very small angle Q. Write 
X for PQ and c for PP'. Then for the pole P the deflecting moment 
is Hm . OM = Hm r sin (a — d), and the restoring moment due to P' is 
mm'ON mm ax m , r- ttt ■ , . . 
— “ 2 — 3 — . laking both poles ot W into account, but neglecting the 
Fig. 11. 
effects of other than the nearest fixed poles, the equation of equilibrium is 
2Hm r sin (a 
2Hr 
0^ _ m{m — m')ax 
or 
a{ni - m) sin (a - 0) 
As H is increased the limit of stable deflection is reached when 
d / X 
dx \c^ sin (a — 0)y 
0. 
