, so to speak, the price at which this
transformation is bought, measure its invariable value by a common
measure (for instance, the melting of the ice), and, without any
ambiguity, define the energy lost during the transformation as
proportional to the mass of ice which can be associated with it. This
measure is, moreover, independent of the particular phenomenon taken
as the common measure.

Sec. 3. THE PRINCIPLE OF CARNOT AND CLAUSIUS

The principle of Carnot, of a nature analogous to the principle of the
conservation of energy, has also a similar origin. It was first
enunciated, like the last named, although prior to it in time, in
consequence of considerations which deal only with heat and mechanical
work. Like it, too, it has evolved, grown, and invaded the entire
domain of physics. It may be interesting to examine rapidly the
various phases of this evolution. The origin of the principle of
Carnot is clearly determined, and it is very rare to be able to go
back thus certainly to the source of a discovery. Sadi Carnot had,
truth to say, no precursor. In his time heat engines were not yet very
common, and no one had reflected much on their theory. He was
doubtless the first to propound to himself certain questions, and
certainly the first to solve them.

It is known how, in 1824, in his _Reflexions sur la puissance motrice
du feu_, he endeavoured to prove that "the motive power of heat is
independent of the agents brought into play for its realization," and
that "its quantity is fixed solely by the temperature of the bodies
between which, in the last resort, the transport of caloric is
effected"--at least in all engines in which "the method of developing
the motive power attains the perfection of which it is capable"; and
this is, almost textually, one of the enunciations of the principle at
the present day. Carnot perceived very clearly the great fact that, to
produce work by heat, it is necessary to have at one's disposal a fall
of temperature. On this point he expresses himself with perfect
clearness: "The motive power of a fall of water depends on its height
and on the quantity of liquid; the motive power of heat depends also
on the quantity of caloric employed, and on what might be called--in
fact, what we shall call--the height of fall, that is to say, the
difference in temperature of the bodies between which the exchange of
caloric takes place."

Starting with this idea, he endeavours to demonstrate, b