Potential-difference to employ with Incandescent Lamps. 3095 
of Edison lamps had been made with 55-, 108-, and 110-volt 
lamps. As, however, he had no such results, and as his tests 
of lives are the only ones that we now have, and possibly may 
have, until the completion of the excellent work at present 
being carried out by the Hlectric-Lighting Jury of the Health 
Exhibition, we commenced this investigation by endeavouring 
to combine the lives given by M. Foussat with the results 
previously published for efficiency. ‘To enable us to do this, 
we assumed that the life of 1000 hours given by M. Foussat 
for his 100-volt lamps when used with a potential-difference 
of 100 volts would be the same as that for our 108-volt lamp 
when employed with a potential-difference of 108 volts ; or, in 
other words, we regarded lives given by him as applicable to 
our 108-volt Edison lamps when each of his potential-differ- 
ences was multiplied by mae 
To ascertain the most economic potential-differences, we 
must proceed as follows :—Let /(v) be the life in hours as a 
function of the number of volts constantly kept on the lamps, 
@(v) the number of candles emitted by one lamp as a function 
of the potential-difference in volts employed, let p be the 
price in pounds paid for one lamp, and n the number of 
hours per year that a lamp is kept burning ; then 
pxn 
Fe) x Hv) 
stands for the cost per year per candle, as far as the renewal 
of lamps is concerned. 
Next, let H stand for the cost in pounds of an electric 
horse-power per year for the number of hours an electric 
horse-power is employed. It is often assumed that H is pro- 
portional to the number of hours per day that the power is 
used, or that the yearly bill for power should be based on the 
horse-power hours, or total energy consumed ; but this idea, 
which runs even through the Hlectric Lighting Act, is quite 
an erroneous one. H will be of the form 4+F(n), where A 
is a constant independent of the number of hours and depending 
on the rent of the site, capital expended upon engines, dynamos, 
leads, &c.; and F(7) is some function of the number of hours 
during which electric power is required,and depends on the cost 
of coal, superintendence, &c. If the light were only required 
for one or two hours in a district where rent was very high, 
h would be the all-important term and F(7) would be unim- 
portant; whereas if the electric power were required for various 
_ purposes, for, say, 15 or 20 hours out of the 24, in a place 
where rent was low but coal dear, (7) would be the important 
item in the yearly bill for electric power supplied. 
