322 



Thus, since we have taken SS' to denote its actual resistance, we have 



$ow, Weber's system of absolute measurement for electromotive 

 forces and for resistances being followed, I have shown* that the 

 mechanical value of the heat generated per unit of time in any 

 fixed conductor of uniform metallic substance is equal to the square 

 of the electromotive force between its extremities, divided by its 

 resistance. This in the present case is equal to 



and if J denote Joule's mechanical equivalent of the thermal unit, 



we therefore have 



0* 

 J/cr 



for the rate per second at which heat is generated in SS'. This will at 

 first go entirely to raise its temperaturef. Now wl is its mass in 

 grains, and therefore wls is its whole thermal capacity ; and if we 

 divide the preceding expression by this, we find 



e z 



for the rate per second at which it commences to rise in temperature 



at the instant when the battery is applied. If we call - the electro- 



l 



motive force per foot, we may enunciate the result thus : 



The rate at which a linear conductor of uniform metallic sub- 

 stance commences rising in temperature at the instant when, an elec- 

 tric current commences passing through it, is equal to the square of 

 the electromotive force per unit of length divided by the continued 

 product of Joule's equivalent into the specific heat of the substance, 

 into the specific resistance of the substance. 



Let us suppose, for example, that the conductor in question is 



* In a paper " On the Mechanical Theory of Electrolysis," Philosophical 

 Magazine, Dec. 1851. 



t As soon as it has risen sensibly in temperature it will begin to give out 

 heat by conduction, or by conduction and radiation, to the surrounding matter ; 

 and the rate at which it will go on rising in temperature will be the rate ex- 

 pressed by the formula in the text (with the true specific resistance, &c., for each 

 temperature), diminished by the rate of loss to the surrounding matter. 



