1921-22.] On Models of Ferromagnetic Induction. 
103 
makes x - 
a — r 
^ jr 
since in the limit = x‘^ {a — . On substituting these 
values the field producing rupture is found to have the value 
9 
H = 
4/-2 
_3x/3(/- 1)2. 
and rupture occurs when the angle OAP (fig. 1) is tan“^ - r-. or 35° 16'. 
v 2 
Fig. 3. — Rupture of a row of magnets for various values oi i, when a =90°. 
When a is made less than 90° (but not less than a^) the limiting stable 
deflection for a given value of i is slightly increased in consequence of the 
term in cot a, in equation (2). The quantity has a minimum when a is 
approximately 90° + and rises rapidly as a approaches the value 
Taking again as an example the case i — Vl, we have the following 
relation of and F^ to a : 
Rupture of a Row of Magnets when t = 
1 
For a — 
20 
o 1 
30 ’ 
o 
35 
45 1 
o 
70 
o 
90 
115° 
135 
145° 
6r= \ 
4-7° 
4-4° ! 
4-3° 
4*0° 
3-8° 
3-6° 
3-5° 
3'5° 
3-4° 
Fr=: 
149 
92 
78 
i 
61 
44 
40*4 
43 
54 
65 
