and Surfaces of Incandescence Lamps. 371 
whilst for very high electromotive force, life is zero and 
candles per horse-power or efficiency a maximum. Now the 
area of cross section which is a maximum for a certain value 
v3 of electromotive force represents the product of life and 
candles per horse-power, or the maximum candle-hours per 
horse-power it is possible to get; and the value of k/ is there- 
fore a very important quantity. I shall call this maximum 
vaiue of kl the principal modulus of the lamp, because the 
value of the lamp for commercial purposes is obtained by 
dividing the numeric representing this principal modulus by 
the price of the lamp, taking either the cost of manufacture 
or the selling-price, according as the question is considered 
from a manufacturer’s or purchaser’s point of view. 
Fig. 1, Diagram of the principal Characteristic Curves of a Lamp. 
= 
=V 
Gen, 
The product k/ is itself a function of the electromotive 
force, and the value of the electromotive force which makes 
this quantity a maximum is an important one to determine. 
It is the pressure at which the lamp should be worked in order 
to realize the greatest quantity of light for a given expenditure 
of energy in the lamp. 
Let us next consider the form of the function which ex- 
presses these characteristic curves. Take, for instance, the 
curve of life and electromotive force. We do not know 
whether this curve is a continuous curve, whether it is 
asymptotic to axis of y, or, in fact, how it behaves beyond 
