18 
FIFTH REPORT -1835. 
these experiments, which have since been repeated by others, 
it appears, that for differences of temperature which do not ex¬ 
ceed 50° centigrade, this geometrical progression represents the 
process of cooling with tolerable accuracy; not, however, with 
complete exactness, for it is found that at higher temperatures 
the cooling really takes place faster than the rate this law would 
assign. 
The processes of the communication of heat to a surrounding 
medium, and to bodies in contact, have obviously much in com¬ 
mon ; and it was assumed that the rate of conduction , as well as 
the rate of cooling , are proportional to the excess of tempera¬ 
ture. Philosophers were naturally led to endeavour to explain 
or illustrate this process by some physical notions. Lambert 
in 1755* published an u Essay on the Force of Heat,” in which 
he compares the communication of heat to the flow of a fluid 
out of one vessel into another by excess of pressure, and mathe¬ 
matically deduces the laws of the process on this ground. But 
the general facts of radiation, which soon after came into no¬ 
tice, modified this view, since it appeared that cold might he 
radiated as well as heat. 
The doctrine of radiation was put in a simple and satisfactory 
form by Pierre Prevost of Geneva, about 1790 ; in which form 
it is often called the Theory of Exchanges ; its leading princi¬ 
ple being, that all bodies are perpetually exchanging their heat 
with one another by radiation. The mathematical reasoning 
upon the subject, of which we shall shortly have to speak, by 
Fourier, Laplace, and others, proceeded upon the assumption 
of the truth of Newton’s law, that the rate of communication 
of heat, both in conduction and radiation, varies as the excess 
of heat. This is so far an approximation to the truth, that va¬ 
rious experiments, made with a view to verify the theory, gave 
satisfactory results. Thus Biotf, by heating a long metallic 
bar at one end, found that the heights of thermometers, placed 
at equal intervals along it, followed a decreasing geometrical 
progression, as by mathematical reasoning from the theory it 
appears they ought to do. And in 1808, when Fourier had de¬ 
duced from his formulae certain peculiar relations of temperature 
when heat is propagated in an arrnil or ring, he made experi¬ 
ments which agreed with the calculation, and thus confirmed the 
theory, at least approximately. The whole mathematical doc¬ 
trine of heat, as hitherto treated, has been founded on the truth 
of the Newtonian law thus verified. 
Yet we now know that this law is not exactly true. At an 
* Act. Helvet., tom. ii. p. 172. 
f Traite de Physique, tom. iv. p. 671. 
