332 
Equalizing the contents of the square brackets to zero gives a 
relation between «a and 9. In most practical cases 5°/B* may be 
neglected and we find 
e.g. for a= 39°14’ | 54°44’ 
the value: B= 90° 17920 
as corresponding sets. For the most favourable semi-angle a = 54°44’ 
it is thus possible ‘to combine uniformity and intensity of the field. 
For a = 63°26’ the same value is obtained for 8 and we have the 
ordinary non-protruding truncated cones. These results, somewhat 
at variance with current ideas, were shown to be correct by 
measurements with a very small test-coil, for which 1 am indebted 
to Dr, W. J. pe Haas. 
For excentric axial points, at a distance z from the centre A, the 
value of the first term 1s 
a) = Any (2 = ae = Tess) - « 
Vata tb" Wa) +b? 
STe | 808 63°26’ 
76°52’ | 72°49’ | 63°26’ 
That of the second term for one single cone 
B--a sin a cos a + V B?-2Bz sina cos ara? sin? a 
5 (z) = 2ar3 sin’ a cos a log SSS 
EN . . 7 
b-x sin a cos a+ V b?-2bex sin a cosa +2’ sint a 
a nn 
V B?—2Bxsinacosa+ a' sina Vb?—2bersinacosa + 2’ sin’? a 
xtga—2B xztg a—2b 
- (5) 
This formula was developed by Czermak and HAUSMANINGER in a 
somewhat different form. 
By (4) and (5) the total field for any axial point may be calculated, 
whether the vertices coincide or not. However a cone is a magnetic 
“optimum-surface” relatively to its vertex only. 
For excentric points on an equatorial y-axis the first term becomes 
Qn 
ip | a(ry cos O—a*—4/’) [sb 
RE 23 f a | ‚() 
(a* Hy? sin? AV a +y?— 2ry cos 8+ r?|\r=0 
which is reducible to elliptic integrals. For the second term a still 
more complicated integral is found, of which the first part also 
leads to elliptic integrals of the third kind; whereas the logarithmic 
term can only be expressed by series of elliptic integrals, a result 
kindly worked out by Prof. W. Karrrrn. In fact for two concentric 
cones we find 
