Mr. Hopkins on the Conductive Poivers of various Substances. 31 1 



which the conductivity or conducting poicer of a substance with 

 reference to heat, is accurately measured. For this purpose, conceive 

 the conducting substance to be bounded by two parallel plane sur- 

 faces of indefinite extent, the distance between them being h. 

 Suppose one of these bounding surfaces (which, for convenience, 

 may be called the loiver one) to be kept at a uniform and constant 

 temperature t, ; let the temperature of the upper surface be also 

 constant and uniform, and equal to t^ ; and let r denote the tempe- 

 rature of the free space into which the heat radiates from the %tpper 

 surface. Then, if we denote the conducting power of the substance 

 by k, and the radiating power of its upper surface by^, we obtain 

 by mathematical investigation, 



p t^ — t^. 



It is here supposed that k is independent of the temperature of the 

 substance, and that p is equally independent of that of the surface 

 from which the radiation takes place. It may also be remarked, 

 that the quantity of heat which radiates from a unit of area in a unit 

 of time, is measured by the product of p, and the difference of the 

 temperatures, f., and t, of the radiating surface and surrounding 



medium. It is the ratio ( -j which the conducting bears to the 



radiating power, which has more frequently been determined in 

 researches of this kind ; but this would not have sufficed for the 

 author's object, which has been the determination of the values of ^ 

 for different substances. The radiating power (j)) probably varies 

 for different substances as much as the conductive power (A), but all 

 consideration of the former power will be avoided if we suppose the 

 radiating surface of the substance to be covered with a thin layer of 

 some given substance which shall take the temperature of the upper 

 surface of the substance itself, and from which the radiation shall 

 always take place, whatever be the nature of the substance experi- 

 mented on. Thus if c denote the radiating power of the superim- 

 posed thin layer (which was mercury in these experiments), we shall 

 have 



c t^-t, ' 



a formula which (c being always the same) enables us to compare 

 the conducting powers for different substances, or to determine their 

 absolute numerical values when that of c is once determined. In 

 the actual cxijerimcuts some error was necessarily superinduced by 

 the necessity of working with portions of the different substances of 

 comparatively small instead of indefinitely large horizontal extent, 

 such as strict mathematical accuracy would require. This error, 

 however, was undoubtedly small, and, moreover, can have had ex- 

 tremely little effect on the relative values of /c, since it must have 

 been nearly the same for all the substances on which the experiments 

 were made. 



