394 TRANSACTIONS OF SECTION A. 
it is not too much to hope that it may be possible to attach a similar conception 
with advantage to caloric as the measure of a quantity of heat. 
It has generally been admitted in recent years that some independent measure 
of heat quantity as opposed to heat energy is required, but opinions have differed 
widely with regard to the adoption of entropy as the quantity factor of heat. 
Many of these objections have been felt rather than explicitly stated, and are 
therefore the more difficult to answer satisfactorily. Others arise from the diffi- 
culty of attaching any concrete conception of a quantity of something to such 
a vague and shadowy mathematical function as entropy. The answer to the 
question, ‘ What is caloric?’ must necessarily be of a somewhat speculative nature. 
But it is so necessary for the. experimentalist to reason by analogy from the seen 
to the unseen, that almost any answer, however crude, is better than none at 
all. The difficulties experienced in regarding entropy as a measure of heat quan- 
tity are more of an academic nature, but may be usefully considered as a pre- 
liminary in attempting to answer the more fundamental question. 
The first difficulty felt by the student in regarding caloric as the measure of 
heat quantity is that when two portions of the same substance, such as water, 
at different temperatures are mixed, the quantity of caloric in the mixture is 
greater than the sum of the quantities in the separate portions. The same diffi- 
culty was encountered by Carnot from the opposite point of view. The two 
portions at different temperatures represented a possible source of motive-power. 
The question which he asked himself may be put as follows: ‘If the total quan- 
tity of caloric remained the same when the two portions at different temperatures 
were simply mixed, what had become of the motive-power wasted?’ The answer 
is that caloric is generated, and that the quantity generated is such that its 
energy is the precise equivalent of the motive-power which might have been 
obtained if the transfer of heat had been effected by means of a perfect engine 
working without generation of caloric. The caloric generated in wasting a 
difference of temperature is the necessary and appropriate measure of the quan- 
tity of heat obtained by the degradation of available motive-power into the less 
available or transformable variety of heat energy. 
The processes by which caloric is generated in mixing substances at different 
temperatures, or in other cases where available motive-power is allowed to run 
to waste, are generally of so turbulent a character that the steps of the process 
cannot be followed, although the final result can be predicted under given con- 
ditions from the energy principle. Such processes could not be expected @ priori 
to throw much light on the nature of caloric. The familiar process of conduction 
of heat through a body, the parts of which are at different temperatures, while 
equally leading to the generation of a quantity of caloric equivalent to the motive- 
power wasted, affords better promise of elucidating the nature of caloric, owing 
to the comparative simplicity and regularity of the phenomena, which permit 
closer experimental study. The earliest measurements of the relative con- 
ducting powers of the metals for heat and electricity showed that the ratio of 
the thermal to the electric conductivity was nearly the same for all the pure 
metals, and suggested that, in this case, the carriers of heat and electricity were 
the same. Later and more accurate experiments showed that the ratio of the 
conductivities was not constant, but varied nearly as the absolute temperature. At 
first sight this might appear to suggest a radical difference between the two 
conductivities, but it results merely from the fact that heat is measured as energy 
in the definition of thermal conductivity, whereas electricity is measured as a 
quantity of fluid. If thermal conductivity were defined in terms of caloric or 
thermal fluid, the ratio of the two conductivities would be constant with respect 
to temperature almost, if not quite, within the limits of error of experiment. On 
the hypothesis that the carriers are the same for electricity and heat, and that 
the kinetic energy of each carrier is the same as that of a gas molecule at the 
same temperature, it becomes possible, on the analogy of the kinetic theory of 
gases, to calculate the actual value of the ratio of the conductivities. The value 
thus found agrees closely in magnitude with that given by experiment, and may 
be regarded as confirming the view that the carriers are the same, although the 
hypotheses and analogies invoked are somewhat speculative. 
When the electrons or corpuscles of negative electricity were discovered it was 
a natural step to identify them with the carriers of energy, and to imagine that 
a metal contained a large number of such corpuscles, moving in all directions, 
