RESEARCHES IN MAGNETISM. 
553 
the induction of currents vanish. The positive value which the integral — 
always has is of itself conclusive evidence, and the magnitude of this quantity can be 
determined in absolute measure with an accuracy which would be unattainable in 
direct measurements of the heating effect which it represents. Warburg, who has 
made determinations of the value of — in certain cases, has (along with 
L. Honig, Wied. Ann., xx., 1883, p. 814) compared them with the results of direct 
calorimetric measurements, the difficulty of which is well illustrated by the poor 
agreement he finds between the two classes of observations.* 
From the values given above for the integral —J2><Ap we may easily calculate the 
rise of temperature which a piece of iron or steel suffers when subjected to the cyclic 
changes of magnetism to which these values refer. Let us assume that the operation 
is conducted so slowly that —represents the whole work done, and that the heat 
produced is prevented from leaving the metal. Then, taking Joule’s equivalent as 
41,600,000 ergs, per gramme-degree (centigrade), the specific gravity of the metal as 
77, and its specific heat as 0 - 11, we have— 
Itise of temperature for every erg. expended per cubic centimetre 
1 
_ 41,600,000X77 _ X0T1 
= 2'84 X 10~ 8 
in degrees centigrade. 
We have seen that the double reversal of a strong condition of magnetism in soft 
iron involves the expenditure of about 10,000 ergs, per cubic centim., and the con¬ 
sequent rise of temperature is therefore 0'000284° C. Nearly 4000 double reversals 
of a magnetic state approaching saturation would therefore be necessary to raise the 
temperature of a piece of soft iron by 1° C., if we could eliminate the action of 
induced currents in the metal. 
The largest of the values given above (for the case of hard steel) is 117,000 
ergs., which corresponds to a rise of temperature of 0 - 0033° C. per cycle. The 
rise in other instances of reversal of magnetism, and that caused by removal and 
reapplication of the magnetising force, may easily be found from the figures already 
given. 
These developments of heat are so small as to make it apparent that the very con¬ 
siderable thermal effects which reversal of magnetism causes in the revolving cores of 
some dynamo-electric machines must be due almost wholly to the internal induction 
of currents, so far as they are not due directly to the current circulating in the coils 
* Another direct method of observing experimentally the dissipation of energy involved in cyclic 
changes of magnetism is to measure the “ damping” of a swinging magnet by the induction of magnetism 
in an iron plate placed near it; but this also depends lai’gely on the induction of currents. Cf ■ Warburg, 
loc. cit., also E. Himstedt, Wied. Ann., xiv. (1881). Himstedt has concluded from an experimental 
examination that the greatest part of this damping is due to what I term statical hysteresis, for the 
effects were found to be in great measure independent of the frequency of vibration of the needle. 
