then solidified at a lower temperature and under a less degree of pressure, and thus in progressive succession to the surface."
If the increase observed in the temperature of the earth near its surface is due to its original heat, it follows that at the present epoch at Paris 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 within 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 between each inequality at a given depth and the inequality corresponding 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 inequalities 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 circumstance 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 thermometer 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 different state, and not two thermometers only, as is generally said. This formula also furnishes the means of comparing the temperatures indicated by different thermometers in relation to their radiating powers and to their property of absorbing the rays of the sun.
