molecules of their surfaces, but also from the particles
in the interior. Let us suppose, moreover, that the heat of these latter
particles cannot arrive at the surface by traversing a certain thickness
of matter without undergoing some degree of absorption. Fourier has
reduced these two hypotheses to calculation, and he has hence deduced
mathematically the experimental law of the sines. After having resisted
so radical a test, the two hypotheses were found to be completely
verified, they have become laws of nature; they point out latent
properties of caloric which could only be discerned by the eye of the
intellect.

In the second question treated by Fourier, heat presents itself under a
new form. There is more difficulty in following its movements; but the
conclusions deducible from the theory are also more general and more
important.

Heat excited, concentrated into a certain point of a solid body,
communicates itself by way of conduction, first to the particles nearest
the heated point, then gradually to all the regions of the body. Whence
the problem of which the following is the enunciation.

By what routes, and with what velocities, is the propagation of heat
effected in bodies of different forms and different natures subjected to
certain initial conditions?

Fundamentally, the Academy of Sciences had already proposed this problem
as the subject of a prize as early as the year 1736. Then the terms heat
and caloric were not in use; it demanded _the study of nature, and the
propagation_ OF FIRE! The word _fire_, thrown thus into the
programme without any other explanation, gave rise to a mistake of the
most singular kind. The majority of philosophers imagined that the
question was to explain in what way _burning_ communicates itself, and
increases in a mass of combustible matter. Fifteen competitors presented
themselves; _three_ were crowned.

This competition was productive of very meagre results. However, a
singular combination of circumstances and of proper names will render
the recollection of it lasting.

Has not the public a right to be surprised upon reading this Academic
declaration: "the question affords no handle to geometry!" In matter of
inventions, to attempt to dive into the future, is to prepare for one's
self striking mistakes. One of the competitors, the great Euler, took
these words in their literal sense; the reveries with which his memoir
abounds, are not compensated in this instance by a