SECT. II.] EXTERIOR CONDUCIBILITIES COMPARED. 281 



temperature common to all points ; it is evident that the quantity 

 of heat which flows during the instant dt into the medium 

 supposed to be maintained at temperature is hSvdt, denoting 

 by 8 the external surface of the body. On the other hand, 

 if C is the heat required to raise unit of weight from the tem 

 perature to the temperature 1, we shall have CDV for the 

 expression of the quantity of heat which the volume V of the 

 body whose density is D would take from temperature to 



temperature 1. Hence TT/TTT- ^ s tne quantity by which the 



temperature v is diminished when the body loses a quantity of 

 heat equal to hSvdt. We ought therefore to have the equation 



hSvdt gp 



~ or v = e 



If the form of the body is a sphere whose radius is X, we shall 



-M 



have the equation v = e DX . 



297. Assuming that we observe during the cooling of the 

 body in question two temperatures v l and v z corresponding to 

 the times t t and t z , we have 



hS _ log 0j log v 2 

 CDV~ t t -t v &quot; 



7 Cf 



We can then easily ascertain by experiment the exponent ,. 



If the same observation be made on different bodies, and if 

 we know in advance the ratio of their specific heats G and C , 

 we can find that of their exterior conducibilities h and h . 

 Reciprocally, if we have reason to regard as equal the values 

 h and h r of the exterior conducibilities of two different bodies, 

 we can ascertain the ratio of their specific heats. We see by 

 this that, by observing the times of cooling for different liquids 

 and other substances enclosed successively in the same vessel 

 whose thickness is small, we can determine exactly the specific 

 heats of those substances. 



We may further remark that the coefficient K which measures 

 the interior conducibility does not enter into the equation 



