456 Prof. FORBES on the Variations which take place 



the difference of the temperatures of the molecules * combined 

 with the conducting power of B (that of A being considered con- 

 stant), and with the element of the time. Or, putting the tem- 

 perature of A a, that of B 13, and its conducting power K, 

 and the element of time :n dt, the proportion of caloric trans- 

 mitted will be 



( a p). K. dt. 



56. It appears to me indubitable, that whether the time be 

 short or long, the quantity of caloric transmitted, and the conse- 

 quent amount of expansion, must increase with K. The idea of 

 an accumulation of heat at the surface producing more effect 

 than a rapid communication with the interior, is obviously an 

 oversight. For if the heat be accumulated at the surface, the tem- 

 perature of that surface rapidly approaching to that of the source 

 of heat A, : will, in the same ratio, diminish the amount of heat re- 

 ceived ; and it can require no demonstration to prove, that the ex- 

 pansion depends solely upon the amount of temperature acquired 

 above its initial temperature by the prism of metal, which by its ex- 

 pansion is to raise the bar from d to a, (Fig. 9.) modified of course 

 by the amount of expansion proper to any substance employed f . 



* For such small differences of temperature the Newtonian law may be viewed 

 as absolutely accurate. 



f In fact, let AB represent the surface of the 

 body, receiving heat at the point a ; and let a b 

 be a line normal to the surface, consequently the 

 expansion of which is to produce the elevation at 

 the point a. The ordinates of the curve cd may 

 represent the acquired temperatures, and the to- 

 tal acquired temperature will be denoted by the area of the curve, to which likewise 

 the expansion will be proportional without regard to its particular form (the distri- 

 bution of heat), which will vary with the conducting power ; and although it is very 

 possible that the ordinate ac of the curve may be greatest in a bad conductor, it is 

 very easy to see that the total area never can. 



