372 Dr. J. A. Fleming on the Characteristic Curves 
the limits of the values of electromotive force v, for which 
lamps are incandescent. We have, however, certain values 
for / corresponding to values of v not lying far on either side 
of the ordinary so-called “ marked volts’ of the lamp. When 
the writer was in America he was shown a large number of 
observations, made with the view of determining the relation 
between average life and electromotive force, not far on either 
side of 100 volts, taken for the Edison 108-volt A lamp. For 
this lamp the life-pressure curve at or near the working- 
pressure is approximately a logarithmic curve whose -equa- 
tion is 
=e 
where A and e@ are constants; and for the Edison 16-candle 
105-volt lamp « is nearly 25; and, accordingly, life varies 
inversely as the 25th power, roughly, of the electromotive 
force. In the figures shown to the writer the life-pressure 
curve had been drawn for pressures corresponding to lives far 
in excess of what could actually have been observed during 
the time filament-lamps have been made, reaching up to 
11,793 hours. ‘This is obviously improper: we do not know 
that « is not itself a function of v, and for pressures departing 
far from the ordinary working-pressure the variation of 
average life and pressure is not probably expressed by so 
simple a relation; and we cannot go fairly beyond the limits 
of actually observed lives. M. Foussat has recently communi- 
cated to a scientific journal the results of observations on the 
life of French Edison lamps. 
TABLe [. 
Volts. Life. log, (volts). | log,, (life). 
95 3595 197772 3°55570 
96 2751 1:98227 3°43949 
97 2135 1:98677 332940 
98 1645 1:99123 321617 
99 1277 1:99564 3°10619 
100 1000 200000 300000 
101 785 2-00432 2°89487 
102 601 2-00860 2°77887 
103 477 201284 2°67852 
104 375 2°01703 257403 
105 284 2°02119 2°45332 
Now the figures given by M. G. Foussat on p. 246 of ‘ The 
Electrician ’ for 1885, stated to be the result of a large number 
of observations on the relation of average life and pressure at 
or near 100 volts, conform approximately to the above law. 
Taking M. Foussat’s numbers for life and electromotive force, 
