M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 123 



tending to various depths according to their duration and amplitude. 

 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 ex- 

 tended throughout the whole mass, because the time of its transporta- 

 tion has been very short, that body thus transported to our climate 

 will present the phaenomenon of an increase of temperature with the 

 distance from the surface. 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 ])ower, to 

 take throughout its mass the temperatures of the different regions through 

 which it has passed. 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 jiresent ; 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. It is necessary to observe 

 that the alternations of temperature of space are positive causes which 

 have an increasing influence upon the heat of the globe at least near its 

 surface ; while the original heat of the earth {chaleur d'origine de la 

 terre), however sIoav it may be in dissipating, is but a transitoiy circum- 

 stance, the existence of which it would not be possible at the present 

 epoch to demonstrate, and to which we should not be forced to have 

 recourse as a hypothesis except in the case of the permanent and neces- 

 sary causes being insuflicient to explain the different phsenomena." 



The following are the titles of the different chapters of the work, to- 

 gether with a short abstract of the contents of each. 



Chapter I. Preliminary Notions. — After having given the definition 

 of temperature and many other definitions, it is explained how we have 

 been led to the principle of a continual radiation and absorption of heat 

 by the molecules of all bodies. The interchange of heat between 

 material particles of an insensible magnitude, but yet comprising im- 

 mense numbers of molecules, cannot disturb the equality of their tem- 

 peratures when it actually exists. From this condition we conclude, that 

 for each particle the ratio of the emitting to the absorbing power is inde- 

 pendent of the substance and of density, and that it can only depend on 

 temperature. In the case of the inequality of temperatures, we give the 

 general expression of their variations during every instant, equal and 

 contrary for two material particles, radiating one toward the other. We 



