Conductivity of Metals with Temperature. 201 



rent meaning. The product cp is the capacity for heat of unit 



volume of the rod (p being the mass of unit volume) ; hence 



k 



— is the conductivity in terms of a unit of heat which can 



raise unit volume of the rod one degree. This Professor Max- 

 well calls the thermometric conductivity*, as distinguished 

 from the calorimetric conductivity k. 



4. In equation (3), is a function of ; and if the element 

 were not supplied with heat, it would cool at the rate 0, and 

 both and would be functions of the time. But when heat 

 is supplied to the element at a compensating rate by its neigh- 

 bours, is constant, and therefore also is constant as regards 

 time; yet still the rod will emit heat at the same rate Has before, 

 and will be the same function of as if it were actually 

 cooling : hence was called by Forbes the statical rate of 

 cooling. 



The relation between and for a cooling body, or the 

 curve which expresses as a function of 0, has been investi- 

 gated experimentally by Dulong and Petit, and found to be of 

 an exponential form. Newton's law made it a straight line. 

 Forbes called it the secondary curve of cooling, and found a 

 point of inflection on it for a long body cooling in air. For 

 a rod in a permanent state, is a function of x ; and the curve 

 0, x is the statical curve of temperature down the rod, and is the 

 one we want to investigate. The curve 0, x is what Forbes called 

 the statical curve of cooling. Finally, the curve expressing 

 as a function of time is the ordinary curve of cooling of a 

 body. The general nature of these last three curves is the 

 same, and depends on that of the first curve 0, 0. The first 

 rough approximation to them is that they are all logarithmic, 

 this being a consequence of the hypothesis that the first curve 

 is a straight line. I suppose that the fact that is only appa- 

 rently a function of the time renders abortive the analogy be- 

 tween equation (3) and the equation to the variable flow of 

 heat in a slab. 



k 

 On the Variation of — with Temperature as at present known. 



5. Professor Tait has given theoretical reasons for assuming 

 the conductivity (i. e. the thermometric conductivity) of every 

 substance to be inversely proportional to the absolute tempe- 

 raturef; but I do not know whether he lays much stress upon 



* See Maxwell's l Theory of Heat/ p. 235. 

 See ' Recent Advances/ p. 271. 



