1921-22.] 
On Models of Ferromagnetic Induction. 
105 
This therefore (as was pointed out in my paper of 1890) is the criterion 
which determines the breaking up of the row when a = 180°. There is 
then nothing to prevent any one pair of neighbouring 
poles in the row from deviating — without limit — towards 
one side, provided the next neighbouring pairs deviate 
towards the other side. Hence in this mode of rupture 
. ^ ^ . 2 is the factor which corresponds to in the other 
— 1 )“ 
mode, for the particular case when a = 180°. Taking 
the same example as before, in which i = IT, its value 
is 100. This determines the point D in fig. 4, and shows 
that the field required to break up a row of magnets 
when a is 180° is about two and a half times * that 
which is required to break it up when a is 90°. 
10. When the applied field is inclined at an angle not 
far removed from 180° the magnets will assume, before 
rupture, an equilibrium position of the kind sketched 
in fig. 5, where one is deflected through an angle 0 and 
the next through a smaller angle 9'. The line PP' 
joining the poles tends, as the condition of instability 
is approached, to become nearly parallel to the applied 
field. It will be convenient to write (p for the inclina- 
tion of PP' to the line of centres. Draw PL and PX' 
perpendicular to that line. Then 
LL' _ '2a - r(cos 6 + cos O') _ r{2i - cos 0 - cos O') 
cos </) cos 0 cos 0 ’ 
Fig. 5. 
PP' = 
tan 0 = 
PL - P'L 
LL 
ON = r sin (0 + 0), 
OM = r sin (a + 0), 
sin 0 — sin O' 
'i - cos 0 - cos O'’ 
ON' = r sin (0 - O'] 
( 7 ) 
O'M' = r sin (a - O'). 
The condition of equilibrium is that on each of the two magnets the 
deflecting moment shall be equal to the restoring moment ; hence for 
the alternate magnets of an indefinitely extended row, 
Hm . OM = 
mX)N 
and . OM' = 
which makes 
(ppq‘2 
sin (0 + ^) _ sin (0 - O') 
sin(a-f^) sin (a - ’ 
m20N' 
(FP')2 
(«) 
* When i is made indefinitely small the ratio is 1 to or 2'598. As i increases the 
ratio is somewhat diminished, becoming 2’54 for f=l’05, 2*48 for and so on. 
