Permeability of Iron and Steel. 89 
po Gear as) Cos0,) Teg Ge al. (CT) 
Cee Ge aig oh ey ae we a Le) 
k 60°—@a 
G3 — p ~sin@-* ° e ° e e ry a (3) 
Let 3%), », be the lowest pair of values given ; 
%., “ those corresponding to pz, the maximum value of p; 
33. the saturation-value of % as estimated from the 
experiments or assumed. : 
The first process aims at determining A by trial and error, 
under the condition that the maximum value of w represented 
by the formulze shall belong to the value 93, given by expe- 
riment. The theory of this is as follows. 
Since w is a maximum, we have from (1), 
du=0= —d& cos 8—(B,, —B) sin 6 db, 
or 
aa 
dd 
en Ss) 
whence from (2), 
d& 
pee na de 
ene ay (B.—B)' ° a « (4) 
Again, differentiating (3), 
ok 
d% sin 0+ % cos 0 d0= — i dO, 
or 
ds % + sec 0 
Wi te ta OE ua aca, vs (5) 
Combining (4) and (5), 
ak 
% + — sec 0 
a , (6) 
f tané(S_—-By OS Rtg 
which is the condition for the maximum value of pm. 
tan 6= 
The work proceeds as follows:— 
Assume a value of A, (A’). 
Find wé, from cos 6, = WW. 38, 
: is M2 
WO, from cos 6)= ANB. —B,) 
Phil. Mag. 8. 5. Vol. 19. No. 117. Feb. 1885. H 
