the area of heating surface, gives the area of the
shaded portion of the figure, which is the total work which should
have been done, that is to say, the work of evaporating 544 lb. of
water per hour. The actual work done, however, was only 485 lb. To
give the speculations we have indulged in a practical turn, it will be
necessary to examine in detail the terms of Carnot's formula. Carnot
labored under great disadvantages. He adhered to the emission theory
of heat; he was unacquainted with its dynamic equivalent; he did not
know the reason of the difference between the specific heat of air at
constant pressure and at constant volume, the idea of an absolute zero
of temperature had not been broached; but the genius of the man, while
it made him lament the want of knowledge which he felt must be
attainable, also enabled him to penetrate the gloom by which he was
surrounded, and enunciate propositions respecting the theory of heat
engines, which the knowledge we now possess enables us to admit as
true. His propositions are:

1. The motive power of heat is independent of the agents employed to
develop it, and its quantity is determined solely by the temperature
of the bodies between which the final transfer of caloric takes place.

2. The temperature of the agent must in the first instance be raised
to the highest degree possible in order to obtain a great fall of
caloric, and as a consequence a large production of motive power.

3. For the same reason the cooling of the agent must be carried to as
low a degree as possible.

4. Matters must be so arranged that the passage of the elastic agent
from the higher to the lower temperature must be due to an increase of
volume, that is to say, the cooling of the agent must be caused by its
rarefaction.

This last proposition indicates the defective information which Carnot
possessed. He knew that expansion of the elastic agent was accompanied
by a fall of temperature, but he did not know that that fall was due
to the conversion of heat into work. We should state this clause more
correctly by saying that "the cooling of the agent must be caused by
the external work it performs." In accordance with these propositions,
it is immaterial what the heated gases or vapors in the furnace of a
boiler may be, provided that they cool by doing external work and, in
passing over the boiler surfaces, impart their heat energy to the
water. The temperature of the furnace, it follows, must be