eme parts with greater or
less velocity or intensity, according to the nature of the substance of
which the bar is composed; thus they suggested the original idea of
_conductibility_. The same epoch, if I were not precluded from entering
into too minute details, would present to us interesting experiments. We
should find that it is not true that, at all degrees of the thermometer,
the loss of heat of a body is proportional to the excess of its
temperature above that of the medium in which it is plunged; but I have
been desirous of showing you geometry penetrating, timidly at first,
into questions of the propagation of heat, and depositing there the
first germs of its fertile methods.

It is to Lambert of Mulhouse, that we owe this first step. This
ingenious geometer had proposed a very simple problem which any person
may comprehend. A slender metallic bar is exposed at one of its
extremities to the constant action of a certain focus of heat. The parts
nearest the focus are heated first. Gradually the heat communicates
itself to the more distant parts, and, after a short time, each point
acquires the maximum temperature which it can ever attain. Although the
experiment were to last a hundred years, the thermometric state of the
bar would not undergo any modification.

As might be reasonably expected, this maximum of heat is so much less
considerable as we recede from the focus. Is there any relation between
the final temperatures and the distances of the different particles of
the bar from the extremity directly heated? Such a relation exists. It
is very simple. Lambert investigated it by calculation, and experience
confirmed the results of theory.

In addition to the somewhat elementary question of the _longitudinal_
propagation of heat, there offered itself the more general but much more
difficult problem of the propagation of heat in a body of three
dimensions terminated by any surface whatever. This problem demanded the
aid of the higher analysis. It was Fourier who first assigned the
equations. It is to Fourier, also, that we owe certain theorems, by
means of which we may ascend from the differential equations to the
integrals, and push the solutions in the majority of cases to the final
numerical applications.

The first memoir of Fourier on the theory of heat dates from the year
1807. The Academy, to which it was communicated, being desirous of
inducing the author to extend and improve his researches, made the