Potential-difference to employ with Incandescent Lamps. 309 
volts constantly at the terminals, then the lamp renewals 
represent, in our particular case, nearly one third of the 
yearly expenditure, and consequently any change in the price 
of lamps becomes extremely important. 
We find that the simplest expression for the candle-power 
of this incandescent lamp in terms of volts is 
ej (O— 8) eS ACE) 
Thus, for example, it will be found that if the cube roots of 
the values of @(v), given in the preceding table, are plotted 
with the corresponding values of v as coordinates of points on 
squared paper, the points lie in no regular curve so nearly as 
in a straight line, discrepancies being apparently due to 
errors of observation, and these errors of observation follow 
a periodic law which may be of interest physiologically. Or 
it may be that there really is a point of inflexion in the curve. 
For the particular lamp in question we find that 
a=0-0002621, 
b=62'12 ; 
or, if the law remains true for a less number of volts than 84, 
the lowest used in this experiment, then when v=62°12, the 
candle-power is zero. 
We do not, however, find that the cube roots of the candle- 
owers of all sorts of incandescent lamps follow a line-function 
of the difference of potential at their terminals ; for on exami- 
ning the results of experiments that have been made with 
various types of lamps, we find that with the first five of the 
following set of lamps the law 
V7 O(v) xv—b 
is very nearly true. 
1. A Lane-Fox lamp . .. . . from 50 to 80 volts. 
2. A British Electric Light Co.’s lamp ,, 50 to 68 
8. An Edison “7B” 8-candle lamp. ,, 45 to 63 
eam ald Swanlamp. .. .. «= sj; 40 to 64_,,, 
5. A low-resistance 8-candle Swan lamp ,, 16 to 40_,, 
Whereas with the next five lamps it is not so true, although 
for half the range the law might be regarded as true in all 
the cases. 
oo Maan lamp... .  . |. from 42 to 57 volts: 
7. A Maxim lamp . eee tee) Ny yy Oho ROR 
8. An old form Swan lamp . 37 20 to 54 
9. A high-resistance Swan lamp » 45 t0 90° ,, 
10. An Kdison B 8-candle lamp . . ,, 36 to 85 ,, 
We may here mention that we have found the following plan 
very useful in helping us to draw correctly a curve at a place 
” 
oP) 
) 
