8 
Davies.—Some Electric and Elastic Analogies. 
and lines of magnetic force in cores, if we have produced in the core a 
magnetic force represented by iT, and an electro-motive force per unit 
length at distance r from the axis of the core represented by e, giving 
rise to a current of density y (using the square of the same unit of 
length for the unit area) at the distance r, then H is parallel to the 
axis and a function of r , y is a function of r and is perpendicular to r 
and to if; and since a tube of thickness dr and unit of length must carry 
a current ydr , and produce a magnetic force in the core of 47tydr ivithin 
the current tube, and zero without , irtydr is the amount by which H 
decreases in passing from within outwards over a distance from r to r + dr. 
The relation thus established between the induced core current and core 
force is: 
y— — (— - 7— H' for short. \ 
' 4 - 77 " n.r \ Art / 
This is a special case of Maxwell’s 4Tty— Curl H. 
Mag.) If p denote specific resistance 
e=py~— 
pH' 
4:71 ’ 
(See 2d vol. Elec, and 
The core is supposed to be symmetrically situated with respect to the 
center of the surrounding coil. 
The magnetic induction (total) through a core of radius r is equal to 
y j 27cr. dr 
and as the electro motive force is e and its line integral 27tr.e this must 
equal the time rate of decrease of the definite integral just given, i. e., 
2nre~ — yj^H. 2itrdr 
If in this the value of 
y~H‘ 
4tc 
above be substituted we will have one form of the differential equation 
of the magnetic force viz: 
rH ’=~So * irdr • 
the dot denoting a fluxion and the prime mark differentiation to r. Dif¬ 
ferentiating this equation to r we get 
- d-< rH ) 
r dr 
4ny 
U 
a partial differential equation which is a well known special case of the 
more general one given further on as equation (3).* 
*See Fourier’s Analytical Theory of Heat; Rieman’s Partial Diff. Eqs.; 
Rayleigh on Sound; Maxwell Elec, and Mag.; Induction of Currents in 
Cores, Oliver Heaviside, London “Electrician,” Vol. X., etc-, etb!)' 
