378 Dr. J. A. Fleming on the Characteristic Curves 
Life. Candles per H. P. 
IVT OS eat teceitienss's ieee ete 100 
ALO itera: aap vs oo sislade 110 
BLO etree sete sis soy ais asia 120 
DOU ANE Prctiione veaciinaesisssis 130 
ZWD entesistarsicaie c'' on sisi « 0 140 
TAO eee ere eiise chau 4 scion 150 
HOO Oe recesses ccee 160 
(2iC Come e Rania. ¢ swine 170 
DOO | om deverctee teastaraiale's waloccie 180 
AO ee ere Malem mce de’ eietes 190 
3] eaneebocsee ousnsends 200 
ZO 5 doled aeeiisicts coo esie 210 
LQ ee seeecetuenssn tes 220 
The length of life, 11,793 hours, given as corresponding to 
an efficiency of 100 candles per horse-power, is nearly equal 
to four years of average burning in working hours, and could 
not have been the result of actual observation; but these 
numbers agree very closely with the law that 
iL 
lOc F595) 
where / represents life in hours and & candles per horse- 
power. Itis most probable that this law has been deduced 
from observations on the life lying within an observed range 
and then extended by calculation to efficiencies below those 
actually observed. In any case these observations are not in 
great discord with the above deductions made from the 
numbers furnished by M. Foussat on the connection between 
life and electromotive force, in conjunction with other observa- 
tions on the relation of efficiency to working pressure in the 
case of Hdison lamps. 
It is, however, far more probable that the connection between 
the candles per horse-power and the working pressure is 
expressible by a formula of this kind, 
logk=a+Pu+yv?+ Ke., 
where e«, 8, y are known constants ; and in this case we should 
have then both the life-pressure characteristic curve, and the 
efficiency-pressure characteristic curve expressed by analogous 
equations :— ; 
log l=a+bv+cov’ + &e., 
log k=a+ Bu+yv’+ &e. 
We have seen above that such a formula does fit in with 
observed values for one pair of variables. Further examina- 
tion of this point is desirable. 
