602 



Fourier's Theory of Heat. 



which passes off through the polar regions ; so that the earth thus 

 gives back to the terrestrial spaces all the heat which it received 

 from the sun. 



The final state of the mass, whose heat has pervaded all its 

 constituent parts, is exactly comparable to that of a vessel which 

 receives, from openings above, a constant supply of liquid, which it 

 suffers to escape, in precisely the same quantity, by one or more 

 orifices below. We may conclude, from what we have said, that, 

 if the earth were exposed, for a long series of ages, to the single 

 action of the solar rays, we should observe, below the envelope 

 where the periodical variations operate, a constant temperature, 

 which would be the same as to all the points of the same vertical 

 line ; that this uniform temperature would perceptibly continue to 

 the lowest accessible depths ; and would be every where equal to 

 the temperature of the superficies ; and, that, consequently, it would 

 depend, for each point, principally on the latitude of the place at 

 which the observations might be made. 



" If the action of the solar rays had not been continued for a time 

 sufficient to allow the heating to reach its extreme term, the tempera- 

 ture of deep places would not be uniform, as far as the centre of the 

 earth, but would decrease in proportion to the descent. But, under 

 any supposition, the influence of the solar rays could not produce a 

 heating which augments with the depth ; that is to say, which causes 

 the deep strata to be hotter than those which are superficial." 



All the preceding truths, the existence of which reasoning can 

 only indicate, have been demonstrated by M. Fourier, with mathe- 

 matical rigour. He has even given formulae, by the assistance of 

 which we may arrive, as regards each point, at results as precise as 

 those which the most careful direct observation could furnish. Let 

 us make this clearer, by an example. 



We have just shewn, and we might, indeed, have assumed it as a 

 fact, evident of itself, that the depth at which the temperature be- 

 comes constant and uniform, as respects each place, depends, among 

 other things, on the duration of the period which occasions the same 

 effects on the surface ; that, for instance, it is necessary to penetrate 

 lower, to withdraw from the influence of the seasons, than to cease 

 to feel that of the day and night; but, it would be impossible to 



