330 H. A. Rowland—Studies on Magnetic Distribution. 
When the helix is symmetrically placed on the bar, we have 
s’=s’, A’=A”; whence, adding the positive and negative parts 
together, we have 
jag DOR AeA ky a 6 
Oar Fei) 
which gives the number of lines of induction passing out from 
the rod along the length AL when the helix is symmetrically 
placed on the rod. 
To get the number of lines of induction passing along the 
rod at a given point, we 
ve '" Lf. és 
Q= [Orden ® Ca ler ti-et— e400", (6) 
H fe ant 
~F(Ae = RR=8) 
When the bar extends a distance L’ out of both ends of the 
helix, so that 
; a ee 
F _fpomnant , 
WRR ep 
where | Oe 
+1 
—1 
. ie. ) (e? —1)(""'—1) Z 
we have Cc =F (FRU L I) ON RB 
It may be well, before proceeding, to define what is meant 
by magnetic resistance, and the units in which it is measure 
If « is the magnetic permeability of the rod, we can get an idea 
of the meaning of magnetic resistance in the following manner 
Suppose we have a rod infinitely long placed in a magnetic 
field of intensity § parallel to the lines of force. Let Q’ be the 
number of lines of inductive force passing through the rod = 
the surface-integral of the magnetic induction across its section; 
and A’=—eé*""" 
also let a be the area of the rod. Then by definition “= aS 
If L is the length of the rod, the difference of potential at the 
ends will be L§; hence 
a LO a LO ae L 
W=_RomMR=G=s> 
and R in the formulsz becomes 
CR ge ee 
R=; = 
_ It is almost impossible to estimate R’ theoretically, seems 
that it will vary with the circumstances. We can get some 
idea of its nature, however, by considering that the principal 
"part of it is due to the cylindric envelope of medium imme 
