42 THEORY OF HEAT. [CHAP. I. 



near enough to the point m, to act directly on it during the first 

 instant. 



The quantity of heat communicated by the point n to the 

 point m depends on the duration of the instant, on the very small 

 distance between these points, on the actual temperature of each 

 point, and on the nature of the solid substance ; that is to say, if 

 one of these elements happened to vary, all the other remaining 

 the same, the quantity of heat transmitted would vary also. Now 

 experiments have disclosed, in this respect, a general result : it 

 consists in this, that all the other circumstances being the same, 

 the quantity of heat which one of the molecules receives from the 

 other is proportional to the difference of temperature of the two 

 molecules. Thus the quantity would be double, triple, quadruple, if 

 everything else remaining the same, the difference of the tempera 

 ture of the point n from that of the point m became double, triple, 

 or quadruple. To account for this result, we must consider that the 

 action of n on m is always just as much greater as there is a greater 

 difference between the temperatures of the two points : it is null, 

 if the temperatures are equal, but if the molecule n contains more 

 heat than the equal molecule m, that is to say, if the temperature 

 of in being v, that of n is v + A, a portion of the exceeding heat 

 will pass from n to m. Now, if the excess of heat were double, or, 

 which is the same thing, if the temperature of n were v + 2 A, the 

 exceeding heat would be composed of two equal parts correspond 

 ing to the two halves of the whole difference of temperature 2A ; 

 each of these parts would have its proper effect as if it alone 

 existed : thus the quantity of heat communicated by n to m would 

 be twice as great as when the difference of temperature is only A. 

 This simultaneous action of the different parts of the exceeding 

 heat is that which constitutes the principle of the communication 

 of heat. It follows from it that the sum of the partial actions, or 

 the total quantity of heat which m receives from n is proportional 

 to the difference of the two temperatures. 



59. Denoting by v and v the temperatures of two equal mole 

 cules m and n t by p t their extremely small distance, and by dt, the 

 infinitely small duration of the instant, the quantity of heat which 

 m receives from n during this instant will be expressed by 

 (v v)&amp;lt;f) (p) . dt. We denote by $ (p) a certain function of the 



