These expressions of heat gained or lost are, moreover, themselves evidently incorrect, for heat can no longer be considered as a sort of fluid passing from one body to another.
The real reason which makes entropy somewhat mysterious is that this magnitude does not fall directly under the ken of any of our senses; but it possesses the true characteristic of a concrete physical 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.