380 Dr. J. A. Fleming on the Characteristic Curves 
In these cases we see that the cube root of the candle-power 
is very-nearly proportional to the excess of the electromotive 
force above a certain point. Now, on examining a number of 
such cases, it appears that this constant is the value of that 
electromotive force at which the lamp just begins to give signs 
of incandescence. In the case of the 8-candle lamp above, 
Professor Jamieson marks in his table against the H. ME. 
28°7 “filament bright red.” It will be very interesting if 
further examination should give confirmation to this surmise ; 
but the above figures seem to indicate that the cube root of 
the candle-power is proportional to the electromotive force 
reckoned from the neighbourhood of that pressure at which 
the filament begins to give out light. If we call this excess 
pressure the “ effective volts,’ then we can state the rule that 
the cube root of the candle-power is proportional to the effec- 
tive volts. We have then, according to the observations of 
Professors Ayrton and Perry, in a certain number of cases 
an empirical law of this kind, 
/K=a(v—), 
in which K is the candle-power measured at a pressure v. 
This may be written 
4 log K=log a+log (v—b). 
By ordinary algebraic theory we have 
log a=a—1—4a—1°+4a—1°— &e.; 
“. if c=b+1, we can write log (v—d) as equal to the series 
vo—¢e—ho— 6 +h0—0 4+ Ke, 
and 
loo Ks A+ Bo—p+Co—c¢ + Divo + we 
If the supposition above made is correct, that b is a value not 
far from that pressure at which the lamp becomes incandes- 
cent, then & is seen to be an exponential function of the 
effective volts of a kind similar to that which has been found 
to reconcile very well the values of observed life and corre- 
sponding working electromotive force. 
Other observers have before now called attention to the 
fact, that within a certain range the candle-power of a lam mp 
varies approximately as the sixth power of the current passing”. 
In the case of the above-mentioned Hdison 16-candle lamp, 
* At the British-Association Meeting at Montreal, Mr. Preece read a 
note on this subject, confirming previous observations made in 1883, and 
showing, from observations of his own, Professor Kittler, and Captain 
Abney, that incandescence varies very nearly as sixth power of current. 
