From limited observations it seems that the average life of a carbon-filament lamp varies as the fifth or sixth power of the watts per candle-power. If V is the voltage at which the lamp is worked and L is its average life, then L varies roughly as the twenty-fifth power of the reciprocal of the voltage, or
L = aV−25.
A closer approximation to experience is given by the formula
| log10L = 13.5 − | V | − | V² | . |
| 10 | 20,000 |
(See J. A. Fleming, “Characteristic Curves of Incandescent Lamps,” Phil. Mag. May 1885).
All forms of incandescent or glow lamps are found to deteriorate in light-giving power with use. In the case of carbon filaments this is due to two causes. As already explained, carbon is scattered from the filament and deposited Ageing of lamps. upon the glass, and changes also take place in the filament which cause it to become reduced in temperature, even when subjected to the same terminal voltage. In many lamps it is found that the first effect of running the lamp is slightly to increase its candle-power, even although the voltage be kept constant; this is the result of a small decrease in the resistance of the filament. The heating to which it is subjected slightly increases the density of the carbon at the outset; this has the effect of making the filament lower in resistance, and therefore it takes more current at a constant voltage. The greater part, however, of the subsequent decay in candle-power is due to the deposit of carbon upon the bulb, as shown by the fact that if the filament is taken out of the bulb and put into a new clean bulb the candle-power in the majority of cases returns to its original value. For every lamp there is a certain point in its career which may be called the “smashing-point,” when the candle-power falls below a certain percentage of the original value, and when it is advantageous to replace it by a new one. Variations of pressure in the electric supply exercise a prejudicial effect upon the light-giving qualities of incandescent lamps. If glow lamps, nominally of 100 volts, are supplied from a public lighting-station, in the mains of which the pressure varies between 90 and 110 volts, their life will be greatly abbreviated, and they will become blackened much sooner than would be the case if the pressure were perfectly constant. Since the candle-power of the lamp varies very nearly as the fifth or sixth power of the voltage, it follows that a variation of 10% in the electromotive force creates a variation of nearly 50% in the candle-power. Thus a 16 candle-power glow lamp, marked for use at 100 volts, was found on test to give the following candle-powers at voltages varying between 90 and 105: At 105 volts it gave 22.8 c.p.; at 100 volts, 16.7 c.p.; at 95 volts, 12.2 c.p.; and at 90 volts, 8.7 c.p. Thus a variation of 25% in the candle-power was caused by a variation in voltage of only 5%. The same kind of variation in working voltage exercises also a marked effect upon the average duration of the lamp. The following figures show the results of some tests on typical 3.1 watt lamps run at voltages above the normal, taking the average life when worked at the marked volts (namely, 100) as 1000 hours:
| At | 101 | volts the | life was | 818 | hours. |
| ” | 102 | ” | ” | 681 | ” |
| ” | 103 | ” | ” | 662 | ” |
| ” | 104 | ” | ” | 452 | ” |
| ” | 105 | ” | ” | 374 | ” |
| ” | 106 | ” | ” | 310 | ” |
Self-acting regulators have been devised by which the voltage at the points of consumption is kept constant, even although it varies at the point of generation. If, however, Voltage regulators. such a device is to be effective, it must operate very quickly, as even the momentary effect of increased pressure is felt by the lamp. It is only therefore where the working pressure can be kept exceedingly constant that high-efficiency lamps can be advantageously employed, otherwise the cost of lamp renewals more than counterbalances the economy in the cost of power. The slow changes that occur in the resistance of the filament make themselves evident by an increase in the watts per candle-power. The following table shows some typical figures indicating the results of ageing in a 16 candle-power carbon-filament glow lamp:—
| Hours run. | Candle-Power. | Watts per Candle-Power. |
| 0 | 16.0 | 3.16 |
| 100 | 15.8 | 3.26 |
| 200 | 15.86 | 3.13 |
| 300 | 15.68 | 3.37 |
| 400 | 15.41 | 3.53 |
| 500 | 15.17 | 3.51 |
| 600 | 14.96 | 3.54 |
| 700 | 14.74 | 3.74 |
The gradual increase in watts per candle-power shown by this table does not imply necessarily an increase in the total power taken by the lamp, but is the consequence of the decay in candle-power produced by the blackening of the lamp. Therefore, to estimate the value of an incandescent lamp the user must take into account not merely the price of the lamp and the initial watts per candle-power, but the rate of decay of the lamp.