190 Prof. Forbes's Researches on the Vibrations which take place 



must increase with the conducting power of the material. 

 Upon the very fundamental axioms of the theory of heat, 

 the amount of caloric which passes from a molecule A into a 

 molecule B, in an infinitely short interval of time, is pro- 

 portional to the difference of the temperatures of the mole- 

 cules* combined with the conducting power of B (that of A 

 being considered constant), and with the element of the time. 

 Or, putting the temperature of A = «, that of B = /3, and its 

 conducting power " = K, and the element of time = dt, the 

 proportion of caloric transmitted will be 

 («-/3). K. dt. 



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

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

 consequent 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 ob- 

 viously an oversight. For if the heat be accumulated at the 

 surface, the temperature of that surface, rapidly approaching 

 to that of the source of heat A, will, in the same ratio, di- 

 minish the amount of heat received; and it can require no 

 demonstration to prove, that the expansion depends solely 

 upon the amount of temperature acquired above its initial 

 temperature by the prism of metal, which by its expansion 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. 

 Consequently this amount, or da, will be proportional to 



-(«-/3).K.^, 



E being the measure of expansibility, c the capacity for heat 

 of the substance, taken by volume not by weight. 



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

 viewed as absolutely accurate. 



t In fact, let A B represent the 

 surface of the body, receiving heat 

 at the point a ; and let abbe & line 

 normal to the surface, consequent- 

 ly the expansion of which is to 

 produce the elevation at the point 

 a. The ordinates of the curve erf 

 may represent the acquired tem- 

 peratures, and the total 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 distribution of heat,) which will vary with the conducting power ; and 

 although it is very possible that the ordinate a c of the curve may be greatest 

 in a bad conductor, it is very ea*y to see that the total area never can. 



