REPORT ON ELECTRICITY, MAGNETISM, AND HEAT. 29 
pevatures in the interior of the globe are much greater than those 
of the exterior space. The temperature increases in descend¬ 
ing, but the rate of increase becomes slower and slower as we 
approach the centre. 
Before I say anything of the comparison of these and the pre¬ 
ceding results with observed facts, I will terminate the history 
of the subject as a branch of mathematics, or rather as an ex¬ 
emplification of analytical artifices. It is in this point of view 
mainly that we must consider Count Libri’s investigations, read 
to the Academy of Sciences of Paris in 1825*. He is the only 
person, so far as I know, who has made the basis of his reasoning 
Dulong and Petit’s exact law, instead of Newton’s inaccurate one. 
He applies his analysis to the case of an armil, in which, as 
we have already said, Fourier had obtained some curious conse¬ 
quences. We may doubt, however, whether he is justified in 
reasoning from Fourier’s experimental results, so as to modify 
his own formulae, (as he does in his memoir, p. 28.) 
It is impossible not to look with admiration at the consum ¬ 
mate analytical skill with which the mathematicians whose 
names I have had to mention have explored this subject. At 
the same time we may be permitted to observe, that the direc¬ 
tion which the speculations of our mathematicians concerning 
heat have thus taken, has not been in all respects favourable to 
the progress of the subject as a branch of experimental and in¬ 
ductive science. The great beauty and curiosity of many of 
the mathematical investigations which offered themselves to 
our analytical discoverers, have led them to wander in that 
deep and charmed labyrinth much longer and further than the 
demands of physical science required; and this proceeding has 
been attended with the additional consequence, that all the cul¬ 
tivators of science, except a very few, well equipped for the 
mathematical race, have been left behind by the course of dis¬ 
covery, and have almost lost sight of their leaders. There can 
be no doubt that this might have been otherwise;— that the sub¬ 
ject might have been treated by means of mathematics of a sim¬ 
pler kind ; such, for instance, as Newton would have employed, 
had his steps turned into this train of inquiry. This would in 
all probability have been attended by some sacrifice of rigour 
and of generality, and the highest analysis would always have 
been requisite, in order to obtain the best solution, as we see in 
the problem of vibrating cords, with which the problems of the 
distribution of heat have many points of resemblance. But still 
such solutions would have been just in all the material points; 
and, by showing to common students the nature of the operations 
* Mem. de Math . et de Phys. Florence, 1829. 
