333 
Qn 
fh (=d sin? acos « fs) > __b + Y—26 cos A) sin? acosO | 
c3 = (1-sin*acos*) Vb3-2b ysin® acosO-+y?sin’ a 
0 
a ear Re 2B cos B) sin? a cos @ 
(1 — sin? acos* 0) YB? — 2 By sin? a cos 6 + y? sin? a 
b — y sin® a cos @ +- Vb? — 2 by sin? a cos O + y* sin® a 
b — y sin® a cos O — Vb? — 2 by sin? a cos O + 7? sin? a 
ee a | 
(7) 
xX 
If the point considered neither lies on the «z-axis nor on the 
y-axis the equation for JD, (z, y) becomes more complicated still. 
By applying (4) to pole-shoes having parallel frontal planes only 
the field for any axial point is easily found; after integration and 
division by the polar distance the mean value is found to be 
en 8 NE SB 
Dti dje oa eee 
As a matter of fact the uniformity in such cases is generally 
rather satisfactory. It may even be improved within a larger range 
by hollowing out the front surfaces. If aspherical zone be considered 
of radius A, perforated in its centre; if the visual angle of the 
periphery be 2y, that of the aperture 2y' as seen from the sphere’s 
centre, then at a distance xz from the latter the field is 
P 225 |w*—2R*+(2R? - a?)Rex cos 0+ Rx" sin? 6)9=7 
= Ba" EVER Deko O EEn 
The sign depends upon whether the point considered lies on the 
concave or convex side (#< Ror > R). By (9) the field in any 
axial point of a centered pair of spherical zones may be calculated, 
the interferric space having the shape of a biconvex, biconcave or 
concave-convex lense ; without aperture we have y' = 0. The formula 
for 0?/dx* becomes rather complicated; this derivative vanishes for 
concentric concave hemispheres, for which we find after considerable 
(9) 
simplification 
4 
Bis Sys Aah ee ee eae 
independent of z, i. e. a perfectly uniform field, a result following 
moreover from known properties. The same holds more generally for 
a spheroidal cavity in the midst of a ferromagnetic medium, rigidly 
magnetised parallel to the axis of symmetry; we then have 
