390 Prof. Ayrton and Mr. Medley on 



as to lamp renewals and the cost as to power, the first being 

 equal to the price of a lamp divided by the product of its life 

 into its candle-power, and the second to the price of one watt- 

 hour multiplied by the watts per candle. So that, if L(v) , 

 C(v), and W(y) were the life in hours, the candle-power, and 

 the watts per candle respectively expressed as functions of the 

 pressure in volts kept constantly on the lamp, and if p were 

 the price of a lamp and H the price of one watt-hour, then the 

 cost per hour per candle equalled 



L(u) x C(t') v n 



and the value of v which made this expression a minimum, 

 they showed, was the proper P.D. to employ with the par- 

 ticular type of lamp. 



The authors gave two methods of solving this problem 

 defined by their equation of cost — the one a graphical method, 

 and the other an analytical one. The graphical method con- 

 sisted in drawing curves from the best experimental results 

 then available to represent L(i?), C(v), and W(v) respectively 

 in terms of v, and from these three curves finding the values 

 of L(t>), C(v), and W(v) for many values of v, then, by sub- 

 stitution in the cost equation, data were obtained from which a 

 last curve showing the relation between potential difference 

 and cost per hour per candle could be drawn. 



The curves on p. 45, Proc. Phys. Soc. vol. vii. 1885*, showed 

 the results obtained when this method was applied to the case 

 of 16 C.P. 100-volt Edison lamps, using as experimental data 

 the results of tests, made at the Finsbury Technical College, 

 on the relations between candles, volts, and watts, and the 

 values of the life of this type of lamp when run at different 

 pressures, as published by M. Foussat. 



The curve AAA showed the cost per candle for lamp 

 renewals during 560 hours when the price of a new lamp 

 was five shillings ; BBB the cost per candle for power during 

 the same period, one horse-power for 560 hours being reckoned 

 at £5, and CCC gave the total cost per candle for 560 hours. 

 The ordinate of this latter curve had a minimum at about 

 101*4 volts. 



With the analytical method, on the other hand, empirical 

 equations were first found to represent as nearly as possible 

 the experimental results. Thus it was found that 



1 AO-07545 v -11-697 



and L W + C(,)-° 



WO) = 3- 7 + lO 8 - 007 - ' 07667 v ; 



* Phil. Mag. torn, cit. p. 308, 



