136 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 



then solidified at a lower temperature and under a less degree of pres- 

 sure, and tlius in progressive succession to the surface." 



If the increase observed in the temperature of the earth near its sur- 

 face is due to its original heat, it follows that at the present epoch at 

 Pai'is this heat raises the temperature of the surface itself only by the 

 fortieth part of a degree. Not knowing the radiating power of the 

 substance of the globe, we cannot estimate the quantity of this initial 

 heat which traverses in a given time from Avithin to without an extent, 

 also given, of the surface ; but such would be its slowness in dissipating 

 into space, that more than one thousand million of centuries must elapse 

 to reduce the small increase of the fortieth of a degree to one half. 



With regard to periodical inequalities, the relation which exists be- 

 tween each inequality at a given depth and the inequality corre- 

 sponding to the exterior temperature is determined. Relations of this 

 nature, for the knowledge of which we are indebted to M. Fourier, 

 take place between the interior inequalities and those of the surface of 

 the ground; these relations leave unknown the ratios of these latter in- 

 equalities to those of the outside which are the immediate data of the 

 question. 



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. 

 These three sources of heat are successively examined. With regard to 

 the first it is observed, that it is not at all probable that radiant heat 

 emanating from the stars has the same intensity in all directions when it 

 arrives at the earth. The experiments are indicated which it would be 

 necessary to make in order to ascertain whether it really varies in the 

 different regions of the sky. M. Melloni intends immediately to apply 

 himself to these experiments, employing in them an extremely sensible 

 instrument, of which he has made use in his researches on heat ; a cir- 

 cumstance which cannot fail to lead to the solution of this important 

 question of celestial physics. 



Before considering the influence of atmospherical heat, I have formed a 

 complete expression for the temperature, marked every instant by a ther- 

 mometer suspended in the air, at any height above the surface of the 

 earth exposed in the shade or in the direct rays of the sun. Although the 

 greatest part of the quantities which this formula contains are unknown 

 to us, many general consequences may however be deduced from it, 

 which accord with experiment; it hence follows, that to determine the 

 proper temperature of the air, it is necessary to employ the simultaneous 

 observation of three thermometers, the surfaces of which are in a differ- 

 ent state, and not two thermometers only, as is generally said. This for- 

 mula also furnishes the means of comparing the temperatures indicated by 

 different thermometers in relation to their radiating jiowers and to their 

 property of absorbing tlie rays of the sun. 



