LIGHTING BY INCANDESCENCE. 691 



1246. For the same expenditure of energy incandescent lamps 

 give far more light when the difference of potential at the terminals 

 is increased, but they waste more rapidly. In conditions which 

 are near those practically used, the luminosity is nearly proportional 

 to the 6th power of the difference of potential V at the terminals, 

 and the waste is proportional to the 25th power of V.* 



Let H be the number of hours that a lamp lasts, L its luminous 

 intensity in carcels, and W the energy expended per hour; if we 

 assume that these different quantities are proportional to powers 

 of V, we may put generally 



If P is the price of the lamp, and Q the price of unit of elec- 

 trical work, taking into account the fuel or the consumption 

 of products, according as we deal with mechanical electromotors, 



or batteries, together with the sinking fund for the installation, 



p 

 and the yield. The expense per carcel-hour is p = -^r~ on the 



QW iL 



part of the lamp, and q = - for the electromotor ; the total 



I / 



expense 



is evidently a minimum for conditions which make the differential 

 of the second member in respect of V null that is to say, when 

 we have 



The ratio of the expense of the lamps to the total expense is then 



The exponent y will be equal to 2, if the resistance of the 

 carbon were constant ; it is really greater, and we shall have a higher 



* FLEMING. Phil. Mag. [5], Vol. xix., p. 368. 1885. 



Y Y 2 



