PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
315 
Ci * 
— (A' cos pt + D' siny>£) 
+ 2 A'sin 9 cos <f> B' sin 9 sin <p + C’ cos 9] cos pt 
dd^ 
+ — [— 2 D' sin 9 cos </> + E' sin 9 sin <f> -f- F' cos 9~\ sin pt 
+ higher harmonics. 
The magnetic potential at or, y, z of the current in the infinite wire is 
2 ltan 1 
cos pt, 
and hence at 9, <p on the a, b sphere is 
21 
_ , c — a sin 6 sin <f>~l 
tan 1 ;-r —-i - 7 cos pt, 
o + a sm 6 cos q> J 
or 
2 l cos pt 
_! c ah sin 6 sin cp ac sin 6 cos cp 
fcan b I, 2 + c? 
1 
••j, 
omitting hannonics of second and higher degrees. 
Hence the first harmonic of the magnetic potential of the system external to the 
a, b shell is upon its surface, 
fi 0 = ('A sin 0 cos (p + 'B sin 9 sin <f> + 'C cos 9) cosyrt 
4- ('D sin 9 cos <p + 'E sin 9 sin <p + 'F cos 9) sin pt, 
where, if 6 3 -f c~ = p 3 , 
y 2I« 2 aa'~ , , 
p : </ 3 
'T> _ 2Irt& I 0M ' 3 -D' 
— — c, -r ™ B 
p ~ a * 
'D = 
'E = 
'C = 
'F = 
2 aa' 2 
d s 
D' 
+ 
aa 
+ - rf T C 
+ F. 
2 s 2 
