722 
PROFESSOR F. Cl. BAILY ON THE HYSTERESIS OF 
Let n = number of revolutions per second of the armature. 
3B 
Then EMF in the circuit = — . 2irnmz . 4 z. 
17 
= 24 B nmz z 10 ~ 8 volts. 
Then the energy spent in eddy currents per second (from OP' to OP) in the 
elementary circuit abed . dx . dz 
Ey _ 24 3 B 3 . i? . m~ . a*. 1 0~ 16 m. d . dz. civ _ 144 EL i? . m*. £. d. dz. dx 
R 4 pz (cl + in dm?d? — x 2 ) 10 16 p (cl + rn dm 2 d 2 — x 2 ) 
Therefore the loss in the whole section Q Q' 
144 B hihidc l 
10 16 p * cl -f- m 
36B 2 n~m? cl 3 dx 
10 lfi p ‘ d + in\/in? cl 2 —. x? * 
Over the whole plate the loss is obtained by taking sections from G to P; i.e., 
integrating from x = 0 to x = OM = OP sin GO 0 = ind sin ir/3. 
The integral 
rid d sill 7T/3 
dx 
j o 
d + m\/v? cl? — 
,, —„ may be solved by writing x = md sin 3, 
x 
/*7t/ 3 QQg ^ 
when it becomes -—;——-- cl 3, but since m is a large number and d is small, 
JO 1 
1 + m? cos 3 
it may be simplified to the form - 
This 
1 
in 
dx 
in 
\/ m? d? — x 3 ’ 
sm 
-l 
x 
in cl 
m d sin 7 r/3 
7T 
Therefore the eddy current losses in each plate 
„ 36B% 2 m s d? ir 
— 9 - watts. 
10 16 p oin 
The volume of each plate = 2i7ni' cl 3 , therefore the eddy current loss per cubic 
centimetre 
121PV d? 
watts. 
For calculation it is more convenient to replace d the half thickness of the plate 
SB ~n~fi 
by t the thickness. Then the loss per cub. centim. = -— . The expression given 
by Professor J. J. Thomson for the loss due to eddy currents in iron plates in an 
