418 H. A. Rowland—Magnetic Permeability, and the 
of helix and n’ the total number on a ring magnet, 7 the 
strength of current, and p the distance from the axis of the ring 
to any point in the interior of the ring-solenoid, the magnetic 
field at that point will be* 2n’¢ = and at a point within an 
infinitely long solenoid 477m. If the solenoid contain any 
magnetic material of magnetic permeability yu. the field will be 
for the ring 2n’t ¥ and for the infinite solenoid 47min. 
Therefore the number of lines of force in the whole section 
of a ring-magnet of circular section will be, if a is the mean 
radius o i 
=47n'i(a—V a? —R?), 
+R S/R? 72 
Q'= 4n't ju VR? =a? 
R 
a-z 
or since n’=2zan and M, the magnetizing force of helix, =i, 
we have, by developing 
; TR? 1 Ré 
Q =4aMy(aR?)(1 +iategat ke.) 
For the infinite electromagnet we have in the same way 
QO’ =40M (zB ?). 
When the section of the ring is thin, these two equations be- 
come the same and either gives 
P= tnM(xR2)’ 
from which the value of « can be found when we have simul- 
taneous values of Q’ and M in absolute measure. ; 
The apparatus to measure Q’ was based upon the fact discov- 
ered by Varad: that the current induced in a closed circutt 18 
pene to the number of lines of force cut by the 
or measuring the induced currents a modified form 
son’s galvanometer was used: the mirror was quite larg 
the needle loaded to make it vibrate slowly: the needle Mee 
astatic to prevent external magnetic forces from affecting i ms 4 
sufficient directive force was given by a magnet above: 
deflections were read by a telescope and scale. 
so that from one to forty-eight turns could be placed. ee 
cuit at pleasure. The value of each coil in producing ‘shall 
tions was experimentally determined by a method which 1s 
soon publish. 
* Maxwell’s Treatise on Electricity and Magnetism, vol. ii, p. 254- 
* 
