Bismuth and Cale-spar in Absolute Measure. 361 
The proper expansion of the magnetic potential for this 
case is therefore a series of zonal spherical harmonies, including 
only the uneven powers. Hence, if V is the potential, 
(1) V=A,Q,r+A,,Q,,,7° + Ay Qy7* + ete. 
dV dV dV 
Pf (eG thE) : 
which is simply the surface integral of V over any surface 
whose edge is in the wire. ae ee 
In the present case, take the axis of x in the direction of the 
axis of the poles and the surface, S, parallel to the plane YZ, 
and let p be the distance in this plane from the center of the 
coil we are calculating. Then 
dv GN x) 
: Paonf pdp=xf 7 ar’) 
for a single circle, 
From (1) TV = 1+ 1) Au r'Q 
and == @” canes ; f== 
& Gi ) = 
: #Q:dyu 
P= — 220? FE+DAnf oral 
r Qi: 
i+2 
P=2x97 ma. Au 
: 
