132 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 
covered with a stratum, also homogeneous, formed of a substance differ- 
ent from that of the nucleus. During the whole time of cooling, the tem- 
perature of this stratum, however small its thickness may be, is differ- 
ent from that of the sphere in the centre, and the ratio of the tempera- 
tures of these two parts, at the same instant, depends on the quantity 
relative to the passage from one substance into the other, of which we 
have already spoken. From this circumstance an objection arises 
against the method employed by all natural philosophers to determine, 
by the comparison of the velocities of cooling, the ratio of the specific 
heat of different bodies, after having brought their surfaces to the same 
state by means of a very thin stratum of the same substance for all 
these bodies. The quantity relative to the passage of the heat of each 
body in the additive stratum, is contained in the ratio of the velocities 
of cooling ; it is therefore necessary that it should be known in order 
to be able to deduce from this ratio, that of their specific heats. A 
recent experiment by M. Melloni proves that a liquid contained in a 
thin envelope, the interior surface of which is successively placed in dif- 
ferent states by polishing or scratching it, always cools with the same 
velocity, whilst the ratios of the velocity change very considerably, 
as was known long before, when it is the exterior part of the vessel 
that is more or less polished or scratched. The quantity relative to the 
passage of caloric across the surface of separation of the vessel and the 
liquid, is therefore independent of the state of that surface, a cireum- 
‘stance which assimilates the cooling power of liquids to that of the 
stratum of air in contact with bodies, which in the same manner does 
not depend on the state of their surface, according to the experiments 
of MM. Dulong and Petit. 
When a homogeneous sphere, the cooling of which we are consider- 
ing, is changed into a body terminated by an indefinite plane, and is 
indefinitely prolonged on one side only of that plane, the analytical ex- 
pression for the temperature of any point whatever changes its form, in 
such a manner that that temperature, instead of tending to diminish in 
geometrical progression, converges continually towards a very different 
law, which depends on the initial state of the body; but however great a 
body may be, it has always finite and determined dimensions; and it is al- 
ways the law of final decrease enunciated in ChapterVI. which it is neces- 
sary to apply ; even in the case, for example, of the cooling of the earth. 
If the distribution of heat in a sphere, or in a body of another form, 
has been determined, by supposing this body to be placed in a medium 
the temperature of which is zero, this first solution of the problem may 
afterwards be extended to the case in which the exterior temperature va- 
ries according to any law whatever. In my first Memoir on the theory of 
heat, I have followed, in regard to this part of the question, a direct me- 
thod applicable to all cases. According to this method, one part of the 
value of the temperature in a function of the time is expressed in the 
