32 Mr. W. H. Preece on the Electric Light. 



greater we make n, the smaller - becomes with respect to p + r ; 

 so that if eventually - becomes very small, we may neglect it 

 in the denominator of the fraction. Then 



W n m 



W — = (*>\ 



~(p + r) 2 .n{p + ry ' ' ' * ." W 



so that in this case also the total heat generated in the resistances 

 will vary inversely as the number of the latter in circuit. 



9. Now it must be observed that in each of these cases the 

 total heat is distributed over n resistances ; and therefore, as 

 compared with one resistance, the heat generated in each is 



only -j of that generated in one. So that, joined up either in 



series or in multiple arc, the heat generated in each of a number 

 of resistances varies inversely as the square of their number. 



10. With respect to the light emitted, if the amount of heat 

 generated represented exactly the amount of light emitted, 

 then the above equations would indicate the effects produced 

 by multiplying the lights or subdividing the current when a 

 constant battery is employed. But this is not so. The light 

 obtained is not proportional to the heat generated. Below a 

 certain limit the production of heat is not accompanied by 

 light at all. In the case of incandescence, if the heat be dis- 

 tributed over two wires instead of one, inasmuch as the mass 

 to be heated in the one case is double that in the other, the 

 actual temperature to which each of the wires will be heated 

 will be only one quarter of that obtained with one wire, and 

 the total light emitted will be half what it was before. In 

 the case of the arc a similar result probably takes place : the 

 incandescent matter, which is heated by the current and which 

 gives out the light, is increased by the addition of each lamp, 

 and therefore diminishes the actual temperature of each arc, 

 and consequently diminishes the light given out in direct pro- 

 portion to the number of lights. 



11. Moreover, in the arc the actual disintegration of the 

 carbons and the transference of matter across the air-space, 

 represent an amount of work done which must be deducted 

 from that converted into heat, and which again tends to dimi- 

 nish the amount of light emitted. If, therefore, the lamps be 

 joined up in series or in multiple arc, the light emitted by each 

 lamp will vary inversely in a greater ratio than the square of 

 the number in circuit. 



12. We have assumed E to be constant; but if the current 



