FIFTH REPORT— 1S35. 
28 
the form of the definite integrals which these constant quantities 
represent* ; we cannot but consider the assertion of the physical 
falsity of Laplace’s view as somewhat arbitrary. Another ob¬ 
ject of M. Poisson’s memoirs on the distribution of heat was to 
remove some of the mathematical difficulties from which, as he 
says, Fourier’s analysis does not appear to him exempt. These 
occur in the expression of discontinuous functions, the roots of 
exponential equations, and similar matters : but such objects do 
not here form a principal point in the survey we have here to 
take, and I shall not dwell upon themf. 
In the investigations of Fourier and Poisson the functions 
which we have already spoken of under the name of Laplace’s 
coefficients were not employed. But Laplace himself published 
in 1820 a memoir on the Cooling of the Earth in which they 
were made use of^. Laplace’s more general solution includes 
that of Fourier, who had supposed the temperature to be a func¬ 
tion of the distance from the centre only. His conclusions as 
to the laws of cooling of a sphere agree with those of Fourier’s 
memoir on the secular cooling of the earth, of which an extract 
appeared in the Bulletin cles Sciences for 1820 (p. 58.). I will 
here briefly mention the general consequences which Fourier 
draws from his solution. 
1st. If the globe of the earth had no primitive heat (chaleur 
cVorigine), the temperature when we descend below the crust 
will be constant in each vertical line, and equal to the mean 
temperature. 
2nd. If the heating which is produced by the solar rays have 
not reached its limit, the temperature will decrease in descend¬ 
ing. 
3rd. If the temperature increase in descending, there must be 
some primitive central heat. 
4th. If the primitive heat and the solar heat were both dissi¬ 
pated, the temperature of the globe would be that of the planetary 
spaces. 
5th. There is a relation between the excess of the heat of the 
surface over the heat of the exterior space, and the increase of 
heat in descending below the surface. Thus an increase of 1 
degree in 30 inches descent, supposes that the primitive heat is 
sufficient to raise the temperature of the surface | of a degree 
above the exterior space, the globe being supposed to have the 
conducting power of iron. 
6th. The primitive heat being supposed to operate, the tem- 
* Poisson, Act. Capill., p. 15. 
f See Mr. Peacock’s Report, pp. 257, 343. 
% Conn, des Terns for 1823, p. 243. 
