1921-22.] On Models of E'erromagnetic Induction. 101 
In the same figure the curve is drawn for a = 30° (also with 'i=l-l); 
there e represents the point of rupture, namely, the point at which F is a 
maximum, ef is the violent swing outwards during the application of the 
field, and gh is the violent return swing during the removal of the field. 
The angle of rupture is 4°’3. 
6. When a is reduced to a certain value (depending on i), the maxi- 
mum and minimum of F coalesce, and the curve of F in relation to 0 
(i’^F dF 
exhibits a point of inflexion at which = 0 as well as = 0. This is 
^ dO^ do 
approximately true of the curve for « = 15° in the same figure. For any 
value of a less than there is no unstable phase in the deflection of the 
magnets; as an example the curve is given for a = 10° (still with 'i = lT). 
Here the whole process of deflection is reversible, though it includes a stage 
do 
during which is relatively large. 
7. By differentiating equation (1) an expression is found connecting 
the angle of rupture with a and i, from which the value of H that will 
dF 
produce instability is determined. The condition is that ^=0, which 
(to 
involves the relation 
(2-1-3 sin^ 0) cos ^ - 3 siii^ 6 cot a = ^ -f i 
i 
( 2 ) 
When a and i are assigned, this gives, for values of a greater than a^, two 
values of 0. The lesser of these is Or, the deflection at which instability 
occurs during the application of the deflecting field ; the greater is the 
value of 0 at which instability occurs during the return of the magnets 
after deflection by a strong field. On substituting these values of 0 in 
equation (1), the corresponding values of H are determined. 
Again, to find a^, the limiting value of a below which there is no insta- 
d^ 
= 0 as well as ” 7 ^ = 0. This requires 
dO 
bility, we have the condition that 
d^F 
dO^ 
that 
cot = 
|- - sin^ 0 
sin 6 cos 9 
(3) 
At that angle equation (2) must also be satisfied. Hence when a = a-^ we 
obtain from equations (2) and (3) together 
5 sec (9j -f- cos 9^ = z(i -i- . . . . • (4) 
as an expression for the deflection at which the point of inflexion occurs 
for any assigned value of i. From this, along with equation (3), we may 
