686 
Transactions of the Royal Society of South Africa. 
= i-pls Watts ... . . 4. 
where recurrent density, 
resistivity. 
1= length of conductor. 
s= cross section thereof. 
loo 20O doo -loo 
Tht rate of temperature increase is 
dd rate of heat gain ^ 
dt~ total heat 
Let C be the specific heat, G the specific gravity, then the heat per unit 
volume is CG-, so that the total heat is CGsL But the total heat lost per 
second is 
Pr== ASc( V - V) = APZ(a/ - 
where P is the perimeter of the conductor, and, since the heat gain is the 
difference between the heat generated and the heat lost, we obtain 
dd_ d(d^-8,) _ i^psl^ AVl(8/ - a,^) 
dt~ dt ~ CGrsl . . . b. 
We have assumed Stefan's law to be correct for our conductors ; but as 
this is not the case for machines and rheostats, and as the law varies with 
each apparatus, according to size, system of construction, and locality, it is 
