276 Mathematical Theories of the Earth. — Woodioard. 
of the extraordinary analysis which^Fourier developed and illustrated 
by numerous applications in this treatise, it is evident that he opened 
a field whose resources are still far from being exhausted. A little 
later Poisson took up the same class of questions and published anoth- 
er great work on the mathematical theory of heat; Poisson narrowly 
missed being the foremost mathematician of his day. In originality, 
in wealth of mathematical resources, and in breadth of grasp of phys- 
ical principles, he was the peer of the ablest of his contemporaries. 
In lucidity of exposition it would be enough to say that he was a 
Frenchman, but he seems to have excelled in this peculiarly national 
trait. His contributions to the theory of heat have been somewhat 
overshadowed in recent times by the earlier and perhaps more bril- 
liant researches of Fourier, but no student can afford to take up that 
enticing though difficult theory without the aid of Poisson as well as 
Fourier. 
It is natural, therefore, that we should inquire what opinions these 
great masters in the mathematics of heat diffusion held concerning the 
earth's store of heat. I say "opinions," for, unhappily, the whole sub- 
ject is still so largely a matter of opinion that in discussing it one may 
not inajiproi^riately adopt the famous caution of Marcus Aurelius, — 
"Remember that all is opinion." It does not appear that Fourier 
reached any definite conclusion on this question, though he seems to 
have favored this view that the earth in cooling from an earlier state 
of incandescence reached finally, through convection, a condition in 
which there was a uniform distribution of heat throughout its mass. 
This is the consistentoir status of Leibnitz, and it begins with the for- 
mation of the earth's crust if not with the consolidation of the entire 
mass. It thus affords an initial distribution of heat and an epoch 
from which analysis may start, and the problem for the mathematician 
is to assign the subsequent distribution of heat and the resulting 
mechanical effects. But no great amount of reflection is necessary to 
convince one that the analysis can not proceed without making a few 
more assumi)tions. The assumptions which involve the least difficult}', 
and which for this reason partly have met with most favor, are that 
the conductivity and thermal capacity of the entire mass remain con- 
stant, and that the heat conducted to the surface of the earth passes 
off by the combined process of radiation, convection, and conduction, 
without producing any sensible effect on surrounding space. These 
or similar assumptions must be made before the application of theory 
can begin. In addition, two data are essential to numerical calcula- 
tions, namely, the diflfusivity, or the ratio of the conductivity of the 
mass to its thermal capacity, and the initial uniform temperature. 
The first of these can be observed approximately at least ; the second 
can only be estimated at present. With respect to these important 
points which must be considered after the adoption of the consistentoir 
status, the writings of Fourier afford little light. He was content, per- 
haps, to invent and develop the exquisite analysis requisite to the 
treatment of such problems. 
