44 THEOHY OF HEAT. [CHAP. I. 



62. If the medium is maintained at a constant temperature, 

 and if the heated body which is placed in that medium has 

 dimensions sufficiently small for the temperature, whilst falling 

 more and more, to remain sensibly the same at all points of the 

 body, it follows from the same propositions, that a quantity of heat 

 will escape at each instant through the surface of the body pro 

 portional to the excess of its actual temperature over that of the 

 medium. Whence it is easy to conclude, as will be seen in the 

 course of this work, that the line whose abscissae represent the 

 times elapsed, and whose ordinates represent the temperatures 

 corresponding to those times, is a logarithmic curve : now, ob 

 servations also furnish the same result, when the excess of the 

 temperature of the solid over that of the- medium is a sufficiently 

 small quantity. 



63. Suppose the medium to be maintained at the constant 

 temperature 0, and that the initial temperatures of different 

 points a, b, c, d &c. of the same mass are a, ft, y, B &c., that at the 

 end of the first instant they have become a , ft , y, S &c., that at 

 the end of the second instant they have become a&quot;, ft , 7&quot;, 8&quot; &c., 

 and so on. We may easily conclude from the propositions enun 

 ciated, that if the initial temperatures of the same points had 

 been get, g/3, gy, g$ &c. (g being any number whatever), they 

 would have become, at the end of the first instant, by virtue of 

 the action of the different points, got. , gff, gy , g$ &c., and at the 

 end of the second instant, gen&quot;, g/3 -, gy&quot;, gS&quot; &c., and so on. For 

 instance, let us compare the case when the initial temperatures 

 of the points, a, I, c, d &c. were a, ft, 7, B &c. with that in which 

 they are 2a, 2/5, 27, 2S &c., the medium preserving in both cases 

 the temperature 0. In the second hypothesis, the difference of 

 the temperatures of any two points whatever is double what it 

 was in the first, and the excess of the temperature of each point, 

 over that of each molecule of the medium, is also double ; con 

 sequently the quantity of heat which any molecule whatever 

 sends to any other, or that which it receives, is, in the second 

 hypothesis, double of that which it was in the first. The change 

 of temperature which each point suffers being proportional to the 

 quantity of heat acquired, it follows that, in the second case, this 

 change is double what it was in the first case. Now we have 



