ch can be obtained out
of any substance working between two temperatures depends entirely and
solely upon the difference between the temperatures at the beginning
and end of the operation; that is to say, if T be the higher
temperature at the beginning, and _t_ the lower temperature at the end
of the action, then the maximum possible work to be got out of the
substance will be a function of (T-_t_). The greatest range of
temperature possible or conceivable is from the absolute temperature
of the substance at the commencement of the operation down to absolute
zero of temperature, and the fraction of this which can be utilized is
the ratio which the range of temperature through which the substance
is working bears to the absolute temperature at the commencement of
the action. If W = the greatest amount of effect to be expected, T and
_t_ the absolute temperatures, and H the total quantity of heat
(expressed in foot pounds or in water evaporated, as the case may be)
potential in the substance at the higher temperature, T, at the
beginning of the operation, then Carnot's law is expressed by the
equation:

/ T - t \
W = H( ------- )
\ T /

I will illustrate this important doctrine in the manner which Carnot
himself suggested.

[Illustration: THE GENERATION OF STEAM. Fig 2.]

Fig. 2 represents a hillside rising from the sea. Some distance up
there is a lake, L, fed by streams coming down from a still higher
level. Lower down on the slope is a millpond, P, the tail race from
which falls into the sea. At the millpond is established a factory,
the turbine driving which is supplied with water by a pipe descending
from the lake, L. Datum is the mean sea level; the level of the lake
is T, and of the millpond _t_. Q is the weight of water falling
through the turbine per minute. The mean sea level is the lowest level
to which the water can possibly fall; hence its greatest potential
energy, that of its position in the lake, = QT = H. The water is
working between the absolute levels, T and _t_; hence, according to
Carnot, the maximum effect, W, to be expected is--

/ T - t \
W = H( ------- )
\ T /
/ T - t \
but H = QT [therefore] W = Q T( ------- )
\ T /

W = Q (T - t),

that is to say, the greatest amount of work which can be expected is
found by multiplying the weight of water into the clear fall, w