382 Dr. J. A. Fleming on the Characteristic Curves 
Ei increases, until the filament breaks. Then 
is an expression which has the following properties :— 
If H=Hy, then R=R); 
pS Co" ee avers 
The above formula is otherwise written 
log (R—r)=log (Ryp—7r)—A(H—E,). 
This formula has been tested for an Edison 8-candle lamp of 
which the resistance was measured over a considerable range 
by Professor Jamieson, and the resistance-pressure curve 
given in his paper. For this lamp luminosity commenced 
at 28°7 volts, and at this pressure it had a resistance of 73°4 
ohms; its resistance gradually decreased with increasing pres- 
sure until it became apparently constant and equal to 53°5 
ohms. ‘Taking A equal to 34, we have 
50 log (R—53°5) + (H — 28-7) =50 log (73°4 —53°'5) = 64°945. 
Calculating R by this formula for various values of electro- 
motive force H, we have the following table of observed and 
calculated resistances:— 
Hdison 8-candle Lamp. 
| Resistance Resistance 
Resistance | calculated Resistance | calculated 
Bold observed. | by above EME. observed. | by above 
formula. formula. 
28°7 73°4 734 48°3 62:7 61:57 
32°7 plen 70:05 51°9 61 60:34 
36°1 68:1 67°65 53 60:6 60 
39°7 66°4 65°49 56:2 59°3 59°13 
43:1 64:7 63°78 58 58:4 58°66 
45:9 63°7 62°51 61-1 57°8 57°98 
46°7 63°3 62:19 63:1 57 57°58 
The accordance between the observed and calculated resist- 
ances is fairly close. It seems very probable, from an inspection 
of the values at very low electromotive forces, that the resist- 
ance is a function of the electromotive force, reckoned from 
the pressure 6, at which the lamp-filament begins to be bright © 
red, and that of R is the resistance corresponding to any 
electromotive force, EH, and r is the minimum resistance to 
which the lamp tends. Then 
log (R—r) =A+B(H—8) +C(H—B)?+ &., 
where A BC, &e. are constants. If this should be the case, 
then it may be possible to express the life, candles per horse- 
power, candle-power, and resistance of a lamp, all as similar 
functions of the electromotive force, knowing certain constants 
