SECT. III.] PRINCIPLE OF COMMUNICATION. 43 



distance p which, in solid bodies and in liquids, becomes nothing 

 when p has a sensible magnitude. The function is the same for 

 every point of the same given substance ; it varies with the nature 

 of the substance. 



60. The quantity of heat which bodies lose through their sur 

 face is subject to the same principle. If we denote by a- the area, 

 finite or infinitely small, of the surface, all of whose points have 

 the temperature v, and if a represents the temperature of the 

 atmospheric air, the coefficient h being the measure of the ex 

 ternal conducibility, we shall have ah (v a) dt as the expression 

 for the quantity of heat which this surface cr transmits to the air 

 during the instant dt. 



When the two molecules, one of which transmits to the other 

 a certain quantity of heat, belong to the same solid, the exact 

 expression for the heat communicated is that which we have 

 given in the preceding article ; and since the molecules are 

 extremely near, the difference of the temperatures is extremely 

 small. It is not the same when heat passes from a solid body into 

 a gaseous medium. But the experiments teach us that if the 

 difference is a quantity sufficiently small, the heat transmitted is 

 sensibly proportional to that difference, and that the number h 

 may, in these first researches 1 t be considered as having a constant 

 value, proper to each state of the surface, but independent of the 

 temperature. 



61. These propositions relative to the quantity of heat com 

 municated have been derived from different observations. We 

 see first, as an evident consequence of the expressions in question, 

 that if we increased by a common quantity all the initial tempe 

 ratures of the solid mass, and that of the medium in which it is 

 placed, the successive changes of temperature would be exactly 

 the same as if this increase had not been made. Now this result 

 is sensibly in accordance with experiment ; it has been admitted 

 by the physicists who first have observed the effects of heat. 



1 More exact la^vs of cooling investigated experimentally by Dulong and Petit 

 vrill be found in the Journal de VEcole Poll/technique, Tome xi. pp. 234294, 

 Paris, 1820, or in Jamin, Cours de Physique, Le$on 47. [A. F.] 



