Siméon Denis Poisson

“ Suppose, for the sake of example, a block of stone transported from the equator to our latitudes; its cooling will have commenced at the surface, and then become propagated into the interior; and if the cooling has extended throughout the whole mass, because the time of its transportation has been very short, that body thus transported to our climate will present the phænomenon of an increase of temperature with the distance from the surface. ”

“ When a body is composed of two parts of different materials, two equations of the motion of heat exist at their surface of separation, which are demonstrated in the same manner as the equation relative to the surface ”

“ If we suppose that radiant heat emanating from the stars falls in the same quantity on all points of the globe, this temperature, higher than 13°, will be that of space at the place where the earth is at this time. Without being able to assign the degree of heat of space, we may however admit, that its temperature differs little from zero, instead of being, as had been asserted, below the temperature of the coldest regions in the globe, and even of the freezing-point of mercury. ”

“ At present the degree of temperature of the globe is increasing below the surface; the contrary has in former times been, and will hereafter be, the case: besides, at epochs separated by many series of ages this temperature must have been, and will in future be, much higher or lower than what it is at present; a circumstance, which renders it impossible that the earth should always be habitable by man, and has perhaps contributed to the successive revolutions the traces of which have been discovered in its exterior crust. ”

“ To elucidate these general considerations, we apply them to examples by means of which we show that the different integrals, in the series of the same equation of partial differences, are transformed into one another, and may be expressed under a finite form by definite integrals, which also contain one or several arbitrary functions. In the single case, in which the integral in series contains only arbitrary constants, every term of the series by itself satisfies the given equation, so that the general integral is found expressed by the sum of an infinite number of particular integrals. ”

“ When a homogeneous sphere, the cooling of which we are considering, is changed into a body terminated by an indefinite plane, and is indefinitely prolonged on one side only of that plane, the analytical expression 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 ”

“ In applying to the earth the general solution of the problem of a sphere at first heated in any manner whatever, Laplace was led to participate in the opinion of Fourier, which attributes to the primitive heat of the earth the increase in temperature which is observed in descending from the surface, and the amount of which is not the same in all localities. This hypothesis of a temperature proceeding from the original heat of the globe (la chaleur d'origine) , and which must rise to millions of degrees in its central layers, has been generally adopted ”

“ The increase of the mean temperature of the earth, in proportion as we descend below the surface, has long been established as a fact in all deep places, at different latitudes, and at different elevations of the soil above the level of the sea. ”

“ When we have obtained the expressions of the unknown quantities in functions of the time, in either of these kinds of questions, if we make the time in them equal to zero, we deduce from that, series of different forms which represent, for all the points of the system which we consider, arbitrary functions, continuous or discontinuous, of their coordinates. ”

“ The earth is in the case of this block of stone;—it is a body coming from a region the temperature of which was higher than that of the place in which it now is; or we may regard it as a thermometer moveable in space, but which has not had time, on account of its magnitude and according to its degree of conducting power, to take throughout its mass the temperatures of the different regions through which it has passed. ”

“ The interior temperature to which the earth is subjected arises from three different sources, namely, from sidereal heat, from atmospherical heat, acting either by radiation or by contact, and from solar heat. ”

“ It follows from this theorem that a thermometer placed in any point whatever of the space which the sphere terminates, will finally indicate the same temperature, which will be equal to that of the sphere ”

“ The solar heat, which reaches each point of the globe, varies at different hours of the day; it is null when the sun is beneath the horizon; during the year it varies also with its declination; and the expression changes its form as the latitude of the point under consideration is greater or less than the complement of the obliquity of the ecliptic. ”

“ Experiment has shown that in a cooling body, covered by a thin layer or stratum of a substance different from that of which it is itself composed, the velocity of refrigeration only arrives at its maximum when the thickness of this additive stratum, though always very small, has notwithstanding attained a certain limit. ”

“ When the bar is indefinitely lengthened, or supposed to be heated only in one part of its length, the laws of the propagation of heat on each side of the heated place are determined; this propagation is instantaneous to any distance ”

“ That in a sphere of very large dimensions, and at distances from the surface very small in proportion to its radius, the part of the temperature independent of the time does not vary sensibly with these distances ”