and Surfaces of Incandescence Lamps. 369 
therefrom. The difficulty of the full and complete discussion 
of this subject is the absence of sufficiently prolonged experi- 
ments to give statistics reliable for this purpose. These can 
only be obtained at great expense and by experiments lasting 
over a considerable time; but the results to hand make a 
preliminary investigation interesting on the connection which 
exists between the life of incandescence lamps and other 
correlated quantities. 
The manufacture of incandescence lamps has now advanced 
to such a condition that the accidents of manufacture are 
greatly under control. The conditions necessary to get a 
good lamp are fairly well understood, and the physical actions 
going on in the lamp are also to a great extent known. We 
now know that the expectations of earlier investigators of 
getting an absolutely unalterable carbon incandescence lam 
are not destined to be fulfilled; but we know that the gradual 
destruction of the filament is an operation dependent upon 
several causes, which may be greatly delayed by attention to, 
and success in, certain operations of manufacture. 
The gradual destruction of the carbon filament in a vacuum 
lamp is a kind of erosion taking place at one or more points. 
Observation seems to show that in a single loop-filament this 
cutting through takes place most generally near the negative 
side. The determining cause of breakage is, however, tem- 
perature ; and carbon filaments which present such inequalities 
of resistance as to give rise to spots of higher temperature 
might, other things being equal, be expected to be doomed to 
a short career. Lamp-filaments are therefore like human 
lives: some come into the world with a taint of disease upon 
them, in the shape of irregularity of structure, which pre- 
disposes to an early death ; but nevertheless, as even in the 
case of suicide, the great law of averages overrides particular 
instances, and gives us, in the case of a sufficiently extended 
series of observations, a law connecting the average behaviour 
under fixed circumstances. 
Experience gained during three years of commercial manu- 
facture and use of incandescence lamps has demonstrated that 
when a large number of filaments are prepared with identical 
care, and the lamps made with them sorted out into batches, 
and worked with varying electromotive force, there is a very 
constant relation between the average efficiency or candles 
per horse-power and the average duration or life, and the 
working potential or volts of the lamp. Now, in a general 
way we do not know what the form of the function is that 
connects these three quantities, or any two of them, but there 
have been a large number of observations on the relation of 
