and Surfaces of Incandescence Lamps. 383 
and the two values of electromotive force at which the lamp 
becomes incandescent, and the resistance to which it finally 
tends to obtain. When, however, we are dealing with com- 
paratively small variations of electromotive force, it is possible 
to calculate both life and efficiency from a simpler exponential 
function of the form— J[qy 
Raw 
when # and y are numerics. Assuming such an approximate 
formula, it becomes possible to deal with an interesting 
question, which has been discussed also by Professors Ayrton 
and Perry*, but which is capable of being investigated in a 
slightly different manner from that adopted by them in their 
paper. We shall take the warrant we have in the above 
figures for the assumption that for electromotive forces not 
far from those at which the lamp is intended to be used in the 
case of an Hdison lamp, say 100 volts, 
Average life varies inversely as the twenty-fifth power of 
the electromotive force ; 
Efficiency, or candles per horse-power, varies as the fourth 
power of the electromotive force ; 
Candle’s light varies as the sixth power of the current, and 
therefore as the sixth power of the electromotive force, 
seeing that the resistance alters very little after the lamp 
has reached fair incandescence ; 
And that therefore life varies inversely as the sixth-and-a- 
quarter power of the efficiency, and also inversely as the 
fourth-and-a-quarter power of the candle-power. 
Let p be the price of a lamp in pounds sterling, or fractions 
of a pound. 
Let / be the average life in hours, ¢ the actual candle-power, 
and & the candles per horse-power, when run at a certain 
electromotive force v. 
Then E is the cost of one candle-light per hour as far as the 
lamp itself is concerned. Let P be the cost of 1 horse-power 
hour of electric energy expended in the filament. P will not 
be the same for all amounts, 1000 P costs less than ten times 
100 P, but for the small variations we are considering we 
shall consider P to be a constant. Then = is the cost of the 
power in making one candle-light for one hour, and the 
total cost of getting one candle-light for one hour is 
iP 
zat. 
* “ On Potential-difference, &c.”’ 
2D2 
fy 
