Prof. Thomson on the Measurement of Electric Resistance. 157 



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

 we therefore have 



e 2 w 



Ma 

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

 first go entirely to raise its temperature*. Now ivl is its mass in 

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

 divide the preceding expression by this, we find 



e 2 



Jl 2 s<r 

 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- 



t 



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



The rate at which a linear conductor of uniform ?netallic 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" 1 s equivalent into the specif c heat of the substance, 

 into the specif c resistance of the substance. 



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

 copper of best electric conductivity. Its specific resistance will be 

 about 7 X 10 6 , and its specific heat about *1. The value we must use 

 for Joule's equivalent will be 32*2 times the number 1390, which 

 Joule found for the mechanical value in foot-grains of the thermal unit 

 Centigrade, since the absolute unit of force, being that force which 

 acting on a grain of matter during a second of time generates 1 foot 



per second of velocity, is - — - of the weight of a grain in middle 



latitudes of Great Britain. Thus we find 



J = 44758. 

 Hence the expression for the rate in degrees Cent, per second, at 

 which the temperature begins rising in a copper conductor, is 



©* 



313 XlG 8 . 



S> have found the electromotive force of a single cell of Daniell's to 



h< . . . 1 



, About 2*3 x 10 8 British absolute unitst ; and if we suppose —of 



n 



his to go to each foot of the cond actor in question, we shall have 



2-3 2 xl0 12 5-29 XlO 12 



(t)- : 



n 2 n* 



* As soon as it ha3 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, 



f Proceedings of the Royal Society, February 1860. 



