334 
4 lo) 
5 lts cos—! m)) wa ea bd) 
Lm V1—m? 
here m denotes the ratio of the axis of revolution to a transverse 
axis of the spheroid; such a case might be approximately realized if 
the necessity arose. 
The attraction exerted upon a smali body inan axial point is pro- 
portional to 0.9/0 in case of saturation, or to  . 0.9/da if a magnetisation 
proportional to the field be induced in it. It may therefore be found 
by differentiation of the expressions (4), (5) or (9), though this gene- 
rally becomes rather intricate. 
Prismatic armatures. If we denote the length at right angles to 
the normal section (Fig.1) by 2c, then we have for c=, 1. e. 
practically for prisms of sufficient length, if the inclined planes have 
one mutual bisectrix through A 
B 
Hi = DH, 4D, = SRS BEE A SOG Ls oe Go tS 
For shorter prisms the first term becomes 
b ec” 
SH, = 85 tan—! — Da More ve TE 
1 a a a at +b? Hc? ( ) 
and the second term 
— ate as ae mm 
(14 —1) 
B c? sin? a 
5, = 83 sin a cos af log ar log — a 
B? 
de / et 
= B C° sin’? @ cae 
The subtractive term in brackets vanishes for c =  ; then evidently 
09,/da vanishes for a= 45°, which is the most favourable angle 
in this ease, giving the strongest field ; for shorter prisms however 
a > 45°. 
The uniformity along the z-axis is complete for prisms of sufficient 
. (1*,2) 
length, i.e. 07D,/d2? = 0; for this case we find 
OD, 0) — 33 sin 28 cos* B — 83 sin* B sin 28 ay 
on Oy? a” 6? 
This expression remains positive and passes through a maximum 
for B= tant //1/, = 30°, the non-uniformity consequently being 
greatest for this angle. 
The term , again behaves inversely, its second derivative vani- 
shing for this same angle; in fact cos 3a then vanishes in the formula 
