H. A. Rowland—Studies on Magnetic Distribution. 327 
ference of magnetic potential of those points divided by the 
resistance to the lines, 
The complete solution of the problem before us being impos- 
sible, let us limit it by two hypotheses. First, let us assume 
that the permeability of the bar is a constant quantity; and 
secondly, that the resistance of the lines of induction 1s com- 
posed of two parts, the first being that of the bar, and the 
second that of escaping from the bar into the medium, and that 
the latter is the same at every part of the bar. The first of 
these assumptions is the one usually made in the mathematical 
theory of magnetic induction; but, as has been shown by the 
experiments of Miiller, and more recently by those of Dr. 
Stoletow and myself, this is not true, and we shall see this when 
we come to compare the formula with experiment. The second 
assumption is more exact than the first for all portions of the 
bar except the ends. 
first take the case of a rod of iron with a short 
helix placed on any portion of it, through which a current of 
electricity is sent. The lines of magnetic induction stream 
down the bar on either side; at every point of the bar two 
paths are open to them, either to pass further down the rod, or 
to pass out into the air. We can then apply the ordinary 
equations for a derived circuit in electricity to this case. 
Let yu be the magnetic permeability of the iron, 
: R be the resistance of unit of length of the rod, 
R’ be the resistance of medium along unit of length of 
rod, 
Pp be the resistance at a given point to passing down the 
T 3 
? 
s be the resistance at the end of the rod, 
Q’* be the number of lines of induction passing along 
the rod at a given poin P 
’.*+ be the number of lines of induction passing from 
SS rod into the medium along a small length of the 
A 
L be the distance from the end of the rod to a given 
point, 
f= : 
R 
A=“ RR’ +s 
“RRs 
are the surface-integrals of magnetic induction (see Maxwell’s “‘ Elec- 
tricity,” art, 402); the first across the section of the bar, and the second along a 
length AL of the surface of 
