466 
DR. J. HOPKINSON ON THE MAGNETISATION OF IRON. 
retain is a very little less than three times the force required to reduce the magnetisa¬ 
tion to zero. 
In a similar way any spheroid could he readily dealt with, and the best material 
judged for a permanent magnet of given proportions. It should, however, be noted 
that any conclusions thus deduced might be practically vitiated by the effect of 
mechanical vibration in shaking out the magnetism from the magnet. 
Dissipation of energy by residual magnetism. 
Imagine a conducting circuit of resistance R, let x be the current in it at time t, 
E the electromotive force other than that due to the electro-magnetic field, and a the 
total magnetic induction through the circuit, then 
Bx=E-~. 
clt 
The work done in time dt by the electromotive force is xKdt=(Rx~ -{-x- f )dt; of this 
R x°dt goes to heat the wire, the remainder, or xda, goes into the electro-magnetic 
field. Imagine a surface of which the conducting circuit is a boundary, and on it take 
an elementary area; through this area draw a tube of induction returning into itself; 
the line integral of force along the closed tube is ivx. If therefore we assume that 
the work done in any elementary volume of the field is equal to that volume multi¬ 
plied by the scalar of the product of the change of induction, and the magnetising 
force divided by 47 t, the assumption will be consistent with the work we know is done 
by the electromotive force E. Now apply this to any curve connecting induction and 
magnetic force. Let PQ be two points in the curve, draw PM and QN parallel to the 
axis of magnetic force OX ; the work done on the field per cubic centimeter passing 
from P to Q is equal to area LMN g ome 0 f this is converted into heat in the case 
47r 
of iron, for we cannot pass back from Q to P by diminishing the magnetising force. 
