1879J Electric Lighting by Incandescence . 169 
a generation of heat due to the resistance opposed to the 
passage of the electric current. 
The method of solution that must be employed consists in 
first calculating the amount of heat that will be lost per 
second by conduction, convection, and radiation in each very 
small section of the bar, as well as the amount generated 
per second by the eledtric current in the same section. 
Then, when the temperature of the bar has settled down 
into a constant state, that is when the temperature of any 
one point does not vary from second to second (although the 
temperature of different points of the bar may be very 
different at the same time), the total loss and the total 
generation of heat per second in any one sedtion must be 
equal. This equality leads to a differential equation, the 
solution of which is an exponential formula, connecting the 
strength of the current required with the temperature of the 
middle point of the wire, its dimensions, specific resistance, 
heat condudtivity, and surface emissivity. 
In order to apply this formula to the two very important 
cases of illuminating by an incandescent platinum wire, or 
by an incandescent carbon rod, it is necessary to know the 
surface emissivity, or heat radiating power, of the substance 
of our incandescent wire. 
Now probably no experiments have yet been made to 
determine the absolute loss of heat per unit of surface from a 
body of a given temperature when the difference of tem- 
perature between the heated surface and the walls of the 
room exceeds 100 or 200 degrees centigrade. And, in fadt, 
when this difference is even less than 100 degrees the 
accurate information at our disposal is scanty. Fortunately, 
however, the law of radiation of heat is such that unless 
there is a total discontinuity in the phenomenon as the 
temperature rises we are enabled to make a very good rough 
estimate of what this absolute amount of radiation must be, 
even at very high temperatures, such as that of white-hot 
charcoal. 
Formerly, it was thought that Newton’s law of cooling, 
viz. : — that the rate of loss was simply proportional to the 
excess of temperature, was corredt ; next the experiments of 
MM. Dulong and Petit seemed to show that in a vacuum 
the rate of loss was proportional to m 1*00770 (1*0077* — I ) 
where m is a constant depending on the radiating surface, 
9 the temperature of the enclosure, and t the excess of tem- 
perature of the hot body; while those of Mr. Hopkins led to 
the result that the loss by the convedtive adtion alone of the 
gas in which the heated body was placed was proportional 
