On Variation of Thermal Conductivity of Metals. 199 



experimental data ; and the long-thin-rod form of experiment 

 is evidently suitable for observing the variation of electric con- 

 ductivity with temperature. 



The following paper is unfortunately rather long ; but the 

 length is due to the necessity of fully discussing experimental 

 results, and I have skipped nearly all the mathematical steps, 

 as they are elementary and of no interest. 



2. Consider a thin uniform infinitely long rod, of perimeter 

 p and cross section q, made of a material whose specific con- 

 ductivity is k, density p, and specific heat c. Let this rod be 

 surrounded by an enclosure at the absolute temperature v , 

 and let one point of the rod (which we will call the origin) be 

 kept by some means at a constant temperature © above that 

 of the enclosure ; then heat will flow from this point along the 

 rod and will be dissipated at its surface, and the temperature 

 of every point of the rod will rise at a rate proportional to the 

 excess of the quantity of heat which it gains per second by 

 conduction, over that which is dissipated by radiation and con- 

 vection. After a long time, however, this excess of heat 

 vanishes, and the temperature of any point of the rod ceases to 

 rise, having attained a constant temperature above that of 

 the enclosure — its absolute temperature, t, being therefore 

 6 + v . (I will adhere to the letter v for temperatures reckoned 

 in Centigrade degrees from absolute zero, and to 6 for tempera- 

 tures reckoned from the temperature of the enclosure as zero. 

 We shall have to use occasionally the Centigrade zero — the 

 temperature of melting ice ; and temperatures reckoned from 

 it may be denoted by t.) 



The heat which flows in unit time past any cross section of 

 the rod at a distance x from the origin will be 



t old 



and the gain of heat per second by an element of volume qdx 

 in this position will be the differential of this quantity, or 



h ^dx 

 If every unit area of the surface of the rod at this point is 

 losing by radiation and convection the quantity H per second, 

 the rate of loss of heat by the surface of the element is 



TLpdx, 

 the product pdx being the area of its surface. As long as the 

 temperature of the element is rising, the rate of rise of tempe- 

 rature will be the difference of the last two expressions divided 

 by the thermal capacity of the element — that is, divided by 



Q2 



