magnitude, since it is, in principle at least, measurable. Various
authors of thermodynamical researches, amongst whom M. Mouret should
be particularly mentioned, have endeavoured to place this
characteristic in evidence.

Consider an isothermal transformation. Instead of leaving the heat
abandoned by the body subjected to the transformation--water
condensing in a state of saturated vapour, for instance--to pass
directly into an ice calorimeter, we can transmit this heat to the
calorimeter by the intermediary of a reversible Carnot engine. The
engine having absorbed this quantity of heat, will only give back to
the ice a lesser quantity of heat; and the weight of the melted ice,
inferior to that which might have been directly given back, will serve
as a measure of the isothermal transformation thus effected. It can be
easily shown that this measure is independent of the apparatus used.
It consequently becomes a numerical element characteristic of the body
considered, and is called its entropy. Entropy, thus defined, is a
variable which, like pressure or volume, might serve concurrently with
another variable, such as pressure or volume, to define the state of a
body.

It must be perfectly understood that this variable can change in an
independent manner, and that it is, for instance, distinct from the
change of temperature. It is also distinct from the change which
consists in losses or gains of heat. In chemical reactions, for
example, the entropy increases without the substances borrowing any
heat. When a perfect gas dilates in a vacuum its entropy increases,
and yet the temperature does not change, and the gas has neither been
able to give nor receive heat. We thus come to conceive that a
physical phenomenon cannot be considered known to us if the variation