136 M. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 
then solidified at a lower temperature and under a less degree of pres- 
sure, and thus 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 
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 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, [have formeda 
complete expression for the temperature, marked every instant by ather- 
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 powers and to their 
property of absorbing the rays of the sun. 
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