PRESIDENTIAL ADDRESS. 393 
principle was established its exponents failed to perceive exactly where the dis- 
crepancy between the two theories lay. In reality both were correct, if fairly 
interpreted in accordance with experiment, but they depended on different 
methods of measuring a quantity of heat, which, so far from being inconsistent, 
were mutually complementary. 
The same misconception, in a more subtle and insidious form, is still prevalent 
in such common phrases as the following : ‘ We now know that heat is a form of 
energy and not a material fluid.” The experimental fact underlying this state- 
ment is that our ordinary methods of measuring quantities of heat in reality 
measure quantities of thermal energy. When two substances at different tempera- 
tures are mixed, the quantity remaining constant, provided that due allowance 
is made for external work done and for external loss of heat, is the total quantity 
of energy. Heat is a form of energy merely because the thing we measure and 
call heat is really a quantity of energy. Apart from considerations of practical 
convenience, we might equally well have agreed to measure a quantity of heat, 
in accordance with Carnot’s principle, by the external work done in a cycle per 
degree fall. Heat would then not be a form of energy, but would possess all the 
properties postulated for caloric. The caloric measure of heat follows directly 
from Carnot’s principle, just as the energy measure follows from the law of 
conservation of energy. But the term heat has become so closely associated with 
the energy measure that it is necessary to employ a different term, caloric, to 
denote the simple measure of a quantity of heat as opposed to a quantity of heat 
energy. The measurement of heat as caloric is precisely analogous to the measure 
of electricity as a quantity of electric fluid. In the case of electricity, the 
quantity measure is more familiar than the energy measure, because it is generally 
simpler to measure electricity by its chemical and magnetic effects as a quantity 
of fluid than as a quantity of energy. The units for which we pay by electric 
meter, however, are units of energy, because the energy supplied is the chief 
factor in determining the cost of production, although the actual quantity of 
fluid supplied has a good deal to do with the cost of distribution. Both methods 
of measurement are just as important in the theory of heat, and it seems a great 
pity that the natural measure of heat quantity is obscured in the elementary 
stages of exposition by regarding heat simply asso much energy. The inadequacy 
of such treatment makes itself severely felt in the later stages. 
Since Carnot’s principle was adopted without material modification into the 
mechanical theory of heat, it was inevitable that Carnot’s caloric, and his 
solution for the work done in a finite cycle, should sooner or later be redis- 
covered. Caloric reappeared first as the ‘thermo-dynamic function’ of Rankine, 
and as the ‘equivalence-value of a transformation’ in the equations of Clausius; 
but it was regarded rather as the quotient of heat energy by temperature than as 
possessing any special physical significance. At a later date, when its import- 
ance was more fully recognised, Clausius gave it the name of entropy, and esta- 
blished the important property that its total quantity remained constant in 
reversible heat exchanges, but always increased in an irreversible process. Any 
process involving a decrease in the total quantity of entropy was impossible. 
Equivalent propositions with regard to the possibility or impossibility of trans- 
formations had previously been stated by Lord Kelvin in terms of the dissipa- 
tion of available energy. But, since Carnot’s solution had been overlooked, no 
one at the time seems to have realised that entropy was simply Carnot’s caloric 
under another name, that heat could be measured otherwise than as energy, and 
that the increase of entropy in any irreversible process was the most appropriate 
measure of the quantity of heat generated. Energy so far as we know must 
always be associated with something of a material nature acting as carrier, and 
there is no reason to believe that heat energy is an exception to this rule. The 
tendency of the kinetic theory has always been to regard entropy as a purely 
abstract mathematical function, relating to the distribution of the energy, but 
having no physical existence. Thus it is not a quantity of anything in the kinetic 
theory of gases, but merely the logarithm of the probability of an arrangement. 
In a similar way, some twenty years ago the view was commonly held that 
electric phenomena were due merely to strains in the ether, and that the electric 
fluids had no existence except as a convenient means of mathematical expression. 
Recent discoveries have enabled us to form a more concrete conception of a charge 
of electricity, which has proved invaluable as a guide to research. Perhaps 
