312 Potential-difference to employ with Incandescent Lamps. 
This is a minimum when 
pe eOG 571 lees 
pn 
Hence taking p=0°25, n=560, H=£5, we find 
v=101°15 volts. 
Using (7) and (2), we should find in the same way that the 
minimum is obtained when : 
v=101°46 volts ; 
and these minimum values of v agree very closely with that 
previously determined graphically. 
One very important problem in connection with incandescent 
lamps, and one that cannot yet be regarded as solved, is the 
determination of the life of a lamp for any given number of 
volts, from experiments made either on the efficiencies at 
several different potentials, or from experiments on the life 
made at so high a potential-difference that the life will be 
short, and the experiment made therefore in a comparatively 
short time. 
If, however, an expression of the form 
fe) =10-" 
can be regarded as representing with sufficient accuracy the 
law of life for all types of incandescent lamps, then if sufficient 
experiments be made with a number of lamps at each of two 
different potential-differences to enable us to determine the 
average life at each of these potential-differences, the constants 
a and 6 can be calculated from the equation, and hence the 
value of /(v), the life, calculated for any other potential- 
difference. 
In connection with this investigation we have endeavoured, 
with the aid of one of our Assistants, Mr. Walmsley, to ascer- 
tain whether some form of ordinary cheap candle could be 
used, at any rate for rough photometric measurements, in 
place of the much dearer standard-candles, and, as far as the 
following results obtained with seven candles selected at 
random from a packet of No. 8 sperm-candles go, it would 
seem that these candles do not differ so very much more in 
intensity from one another than standard candles are said to 
do. Of course many more experiments on this subject must 
be made before the possibility of using cheap candles as a 
rough standard can be decided on, but in the meantime the 
following experiments may be interesting. 
This particular type of candle, No. 8 sperm, and costing 
11d. per pound, was selected, because such candles were found 
to resemble in thickness the standard candles that we have 
been accustomed to use, and which cost 2s. 9d. per pound. 
