REPORT ON ELECTRICITY^ MAGNETISM; AND HEAT. 21 
of a memoir of Fourier’s on the Cooling of the Earth ; Fourier’s 
“Theorie de la Chaleur” appeared as a separate work with the 
date 1822, not containing, however,his investigations on the cool¬ 
ing of the earth. Notices of various results of the labours of 
Fourier and others appeared also from time to time in the An- 
nales de Chimie et de Physique. 
When Biot and Laplace turned their attention to this subject, 
they conceived that they saw a difficulty in the reduction of the 
question to a mathematical form, which difficulty Laplace thus 
states in the Memoirs of the Institute for 1809 (1810): “The 
quantities of heat received and communicated in an instant by 
any elementary slice of a conducting solid, must be infinitely 
small quantities, because the excess of temperature of each slice 
over the next is infinitely small; therefore the excess of the heat 
received over the heat lost will be an infinitely small quantity of 
the second order; and therefore the accumulation in a finite 
time will not be finite.” “This difficulty,” Laplace says at the 
period of which we speak, “has not yet been solved. Mathe¬ 
maticians often get true equations from false suppositions ; they 
have done so in this case in supposing heat communicated by 
contact. Fourier’s equations are right, but the true bases of them 
are to be found in the doctrine of the action of molecules ad di- 
stansP 
Laplace’s solution of this difficulty is, that we are to conceive 
each particle of a body receiving its heat, not from the particle 
immediately adjacent only, but from all the particles within its 
reach, the law of action diminishing rapidly as the distance in¬ 
creases. And he connects with this observation a series of re¬ 
marks on the various classes of phenomena which may thus be 
reduced to molecular action; among which he mentions capil¬ 
lary attraction, electric and magnetic phsenomena, the proper¬ 
ties of elastic bodies, and finally the laws of heat. All these, 
he says, ought to be treated as cases of systems of discrete mo¬ 
lecules, attracting and repelling each other at a distance. 
That by consideringfluid or solid bodies as composed of distinct 
particles, and by suitably assuming the forces which these parti¬ 
cles exert on each other, we may represent their mechanical con¬ 
dition, and trace its consequences, is undoubtedly true. But it 
would be to go too far, to assert, on this account alone, that the 
only true conception of the physical structure of bodies is that 
which represents them as so constituted. This w T ould be to mis¬ 
take the use of the differential calculus for the evidence of a phy¬ 
sical truth. Whether a comparison of special results of the mo¬ 
lecular hypothesis with facts, will give it any countenance as the 
real state of things, is another and a very curious question, which 
