Cuar. VI, § 6.] HEAT.—FOURIER. 949 
in a given way, but so that points equi-distant from 
the centre have a common temperature.’ It might 
be expected that the symmetry of the conditions would 
admit of a simple solution; and such indeed was 
sought by Professor Playfair long before, in a paper 
in the Edinburgh Transactions, with reference to Geo- 
logical Speculations. It was, however, by no means 
sufficiently: general. It is shown by Fourier, that 
that the progression of temperature is very gradually 
and slowly disturbed. 
Application to the Thermal condition of the Earth. (675. 
—This last case has been discussed by Fourier with Applica- 
great address, relatively to the present condition of wade as 
the Earth, considered as a mass which has been once siples to 
at a high temperature, of which we have evidence the ther- 
in the general increase of heat as we descend in mines, ™*! condi 
tion of the 
even in the simplest supposable case—that where the 
temperature of the sphere was originally uniform— 
the resulting expression for the temperature of any 
stratum at any time, though capable of algebraic ex- 
pression, cannot be assigned in finite terms, and no 
attempt has been made to evaluate it generally. The 
special cases which have been considered, are when 
the sphere is extremely small, or has been cooling 
for a very long time. 
or when we penetrate its crust by Artesian wells. g,.1n, 
The surface of our planet receives a large amount of 
heat annually by absorbing the sun’s rays, but parts 
with it by radiation into free space, to an extent which 
preserves a sensible uniformity of temperature from 
age to age. The considerations connected with the 
subject are these :—(1.) The proper heat of the earth, 
and how much heat reaches the surface from the 
(perhaps) still incandescent interior; (2.) How much 
(674.) The extreme complication of even such apparently heat do we receive from the sun, what share of it 
tray bag simple cases when solved in all their generality con- enters the surface, and how far, and according to 
asta the Sists in this, that the flow of heat across each partis what periods does the influence of the seasons extend 
Problem ofin fact dependent at each instant on the state of heat 
the Sphere. 
in each other part, and this distribution of the whole 
is equally unknown with the local distribution on 
which the movement of heat in each part depends. 
To this must be added the peculiarity of conditions 
at the surface, where the temperature undergoes an 
abrupt change. The law according to which the su- 
perficial particles radiate heat, is also different from 
that according to which they receive it from the in- 
terior. When a body uniformly heated to a consider- 
able temperature cools in air, the subtraction of heat 
from the surface commences with great rapidity, the 
excess of temperature of the superficial particles being 
very much greater than it ever can be afterwards. 
The drain of heat from the interior of the sphere is 
at first nearly imperceptible. The exterior cooling 
will by and by become slower; and the degree in 
which it takes place, will depend upon the rapidity 
with which the conducting mass of the sphere is able 
to supply fresh heat to the surface; then the rate of 
superficial cooling will become relatively somewhat 
accelerated, and a fresh drain will take place from 
the interior towards the surface. It is only in the 
ease of exceedingly small bodies, or those of an in- 
finite degree of conductivity, that the body will cool 
according to a simple law. In all other cases, there 
will be characteristic periodical inflections in the 
below the surface? (3.) What is the amount of refri- 
geration of the earth’s surface ?—how does the atmo- 
sphere affect it ? and, if the cooling be due entirely 
to radiation, what are we to set down for the temper- 
ature of space, so as to account for the heat lost? 
First, As to the proper heat of the globe. Not to 
go further back than the last century, 
(676.) 
the incandes- The proper 
heat of the 
cence of the earth’s nucleus was assumed as very pro- giobe ; 
bable by Buffon and other popular writers, and their 
opinions were, on the whole, confirmed by the pro- 
gress of observation. The existence of voleanoes was, 
of course, an obvious argument; another was, that 
if the earth were once hot it must be still cooling ; con- 
sequently, climates are continually becoming colder, 
especially in the Arctic regions, which it was supposed 
depended most on the supply of heat from within. In 
evidence of this change were quoted, not only the 
remains of elephants found interred with flesh and 
skin in the midst of Siberian ice, but also the un- 
equivocal proofs, so well known to geologists, that 
at a period indefinitely more remote, tropical plants 
of gigantic growth, and animals of a class which now 
frequent only southern seas, appear to have lived 
and flourished in high northern latitudes. But even 
in the time of Buffon, attention was directed to a fact 
yet more important for the theory of heat, namely, 
the increase of temperature observed in deep mines. 
course of cooling. These, no doubt, are represented 
Notwithstanding many sources of doubt and confu- manifested 
in Fourier’s series, if it could be numerically caleu- 
sion, such as the heat from candles, and from men at by the in- 
crease of 
lated ; and it is to be desired that some attempt were 
made to represent it approximately. When the cool- 
ing has endured for a very long time, these gushes 
of heat cease altogether; the surface has attained 
nearly to the temperature of the surrounding space, 
and the drain of heat from the interior is so slow, 
work in mines, from chemical changes in some cases, peat in 
and from the increased density of the air, the fact of mines. 
the increase is now well established, and also its 
rate of progression with more certainty than in the 
time of Fourier. On an average (including the best 
data of all, those yielded by Artesian springs), the, 
1 The problem of the Armil or ring, heated at one or several points, is one which offers considerable facilities for its solution, 
but the results are of little utility, the form being so peculiar ; and even as a test of theory, the variations of temperature from 
point to point are insufficient under the limited conditions in which the numerical solution is practicable, 
