374 Dr. J. A. Fleming on the Characteristic Curves 
failure showed that 
2 
log /=135—v— — _ 
10 log (=135—v 5000 
is a formula which gives very nearly correct results in calcu- 
lating the life of a lamp /, given the working-pressure v in 
volts. This may be expressed otherwise :— 
2 
ee GS Mi rae nee 
ee a9) 1 20 0007 
or 
[= 10)13'5—"10— "0000502 
Calculating by this formula, we get the following values 
for log J and J, ( being the average life in hours of the 100- 
volt Edison lamp as made in France :-— 
TaBLeE II. 
| 
Calculated by formula. | Observed. 
i. log 7. log Z. d. 
3939 35488 3°5D57 3595 
2749 3°4392 3°4395 | 2751 
2136 3°3296 3°3294 2135 
1658 3°2196 32167 1645 
1289 3°1100 3° 1062 | 1277 
i000 3°0000 3°0000 | 1000 
776 2°8900 278948 785 
602 2°7798 2-7788 601 
467 2°6698 * 26785 477 
362 2°5592 2°5740 379 
281 2°4488 2°4533 284. 
It is evident, then, that the simple exponential function 
does not give nearly so good results as a formula of this latter 
description; and there is no doubt but that by a suitable 
selection of constants a formula can be obtained expressing 
the life of the lamp as a function of electromotive force 
throughout an observed range, which shall be closely in 
accordance with observed facts*. Until, however, a much 
* Mr. F. M. Wright has given, in ‘The Electrician, p. 311 (1885), a : 
formula— 
L 
1000° 
This is equivalent to 9-09 log L= 127—V; 
ne ’ 
100—V=9-098218 log 
and Professors Ayrton and Perry have given 
Le 1914 —llv 
oF 10 log L=140 —1+12, 
both of which are nearly equivalent to the formula given in the text. 
