Magnetization of Lron in Bulk. 633 
of terms of gradually diminishing amplitude and increasing 
coefficient of decrement *, viz. : 
H ad rd Be Jo(nr) pe z 
" na(1+s?n?) ~ J,(ma) © : 
where H, is the magnetic intensity at a radius 7, H, the 
initial value at the boundary. The radius of the core is a; 
n the successive roots of the equation 
Jo(na)=snJ1 (na), 
J and J, being the usual Bessel functions. The coefficient 
Lip 
s = >=——,, In which L is the inductance and R the 
2m pak 
resistance of the coil winding; so that 
pee. 
oe bales? 
where A is the cross-sectional area of the core, J its mean 
length, p its specific resistance, w its permeability, and T the 
turns on the winding. 
— pn 
At - 
D the damping coefficient = 
In the case of the cast steel ring s=°6055, assuming as a 
; . : . . to) 
first approximation that the core is circular. 
For a=4°87 cms. — /=193 cms. 
p=12,000. P= 777. 
p19 10°. 
Thus 
Ea 52466 Dé 
By Ve B6r5r2 * 
The n’s are the roots of ae == 14S. 
ile 
This can be most readily solved by inspection and trial 
from tables of J) and J,. The roots so found are given in 
the following Table, which also gives the working of the 
different terms. It will be seen that the sum of the first twenty 
terms of the amplitude is only -9 instead of nearly unity. 
The reason for this is that in the expression for s the 
conductivity enters as an unknown figure. The best values 
* Loe. eit. p. 397. 
