22 
FIFTH REPORT— 1835 . 
we may hereafter consider. But we may venture to say, that 
when Laplace, at the period of which we speak, asserted his own 
reasoning to be the only real basis of Fourier’s equations, he 
took a partial view of the question. Fourier was not bound to 
take Laplace’s solution of the difficulty, if, in his mode of rea¬ 
soning, the difficulty did not occur, which was really the case. 
Fourier maintained that the quantity of heat transferred from 
one slice to the next in unit of time was a finite quantity, in¬ 
dependently of molecular reasoning. For, as he showed, the 
quantity of heat transferred from one side of a slice to the other, 
is not only as the difference of temperatures of the two sides 
directly, but as their distance inversely: and when, in conse¬ 
quence of the evanescent thickness of the slice, one of those 
quantities vanishes, the other does so too, and the flow of heat 
remains expressed by a finite quantity; or, to take the matter 
in another form, if a bar of iron, one end of which is kept con¬ 
stantly hot and the other cold, be supposed to have acquired a 
permanent state of temperature in all its parts, there is a flow 
of heat from the hot to the cold end ; and the quantity which 
passes through any section of the bar is equal to the quantity 
which in the same time is radiated from the whole of the colder 
surface beyond that section, and is therefore finite. Fourier’s 
reasoning no more requires the introduction of molecular action, 
than do the reasonings by which the common formulae of Hy¬ 
drostatics (formulae much resembling those of Fourier) are esta¬ 
blished in Mechanical Treatises. 
But there are other circumstances bearing upon this question 
which well deserve to be considered. Fourier’s reasonings ap¬ 
ply to radiated as w T ell as to conducted heat; and radiation is 
governed by peculiar laws, which may throw additional light on 
that kind of molecular action. There are, in particular, two laws, 
discovered by experiment, to which the theory must conform 
itself. One of these is founded on general and obvious experi¬ 
ence,—that all bodies placed in an inclosed space assume, in 
the course of some time, the temperature of the inclosure; the 
other was established by special experiments by Leslie*. It is 
this :—that heat is emitted from every point of the surface of a 
hot body in all directions, and that the intensity of the heating 
ray in any direction is as the sine of the angle which it makes 
with the surface. 
Fourier’s theoretical explanation of these two laws must be 
looked upon as happy and successful; for he has shown that 
the same suppositions are requisite to explain the former general 
and simple fact, as to give the latter less obvious rule. The law 
* Experimental Inquiry into the Nature and Propagation of Heat, 1804. 
