34 
MESSRS. G. E. C. SEARLE AND T. G. BEDFORD 
Intrud action. 
§ 1. Tm "0 ideal physical processes have been devised as the foundations of two methods 
of deducing mathematical expressions for the energy dissipated in magnetic material 
through magnetic hysteresis ; these processes are due to Professor E. Warburg and 
to the late Dr. J. Horkinsox. 
In Warburg’s theory^ the specimen, in the form of a slender wire, is j^laced in 
a magnetic field due to a })air of permanent magnets so arranged as to produce 
magnetic force parallel to the length of the specimen. The mechanical work spent 
in moving these magnets through such a cycle of changes of position, that the iron 
is subjected to a cycle of magnetic changes, is clearly equal to the energy dissipated 
on account of magnetic hysteresis in the specimen. In terms of the magnetic 
quantities the energy dissipated per cub. centim. per cycle is — JIc/H or jlldl ergs, 
where H is the magnetic force and I the intensity of magnetisation. Professor 
J. A. Ewing! has applied the principle involved in Warburg’s theory to the 
design of a simple instrument by which the hysteresis of aii}^ specimen of sheet 
iron (for the range of induction B = 4000 to B = — 4000 C.G.S. units approxi¬ 
mately) is deteimined by comparison ^\dth two standard specimens supplied with 
the instrument, and previously tested for hysteresis by the ballistic method. The 
principle has also been employed by W. tS. Franklin,^ by H. S. Webb,§ and by 
(h L. W. Gill|| to obtain absolute determinations of hysteresis. 
The theory of the late Dr. John HopkixsonA proceeds in a difierent manner. 
The specimen now takes the form of a fine wire bent into a large circular ring, the 
ends of the wire being welded together ; the length of the wire is I centim., and 
its cross-section A sq. centim. Let this ring be uniformly overwound with insulated 
wire at the rate of N turns per centim. so that the total number of turns is N/, 
and let the wire be without resistance. Then if C be the current at any time, the 
mao'iietic force actino- on the iron is H = 47rNC. If B be the magnetic induction 
in the iron, the number of linkages of lines of induction with the electric circuit 
at anv instant is A/NB, and hence, when B changes, there is bv Faraday’s law a 
voltage A/N(/B;'c/i between tlie ends of the coil. We have supposed here that tlie 
wire is closely wound ujion the iron. The power spent in driving the current against 
this voltage is A^NCdB/(/^ ergs per second. 
Lhsing the relation H = IttNC, and noticing that kl is the volume (r) of the iron, 
tlie expression becomes r/47r . HJB We 
* ‘tVied. Ann.,’ vol. 13 (1881), p. 141. 
t ‘ Magnetic Induction in Iron and other Metals,’ 3rd ed., revised, § 199. 
I tv. S. Franklin, ‘ Physical Revieiv,’ vol. 2, ji. 466. 
§ II. S. tVEi'-ii, ‘ Physical Review,’ a'oI. 8, p. 310. 
[j G. E. tv. Gill, ‘Science Abstracts,’ vol. 1 (1898), p. 413. 
‘Phil. Trans.,’ vol. 176 (188.6), p. 466. 
