Hx^-,^-^^ (2) 



Mr. W. H. Preece on the Electric Light. 31 



5. Confining our attention for the present to the heat gene- 

 rated (H), this will be distributed throughout the circuit ; and 

 that in the resistance (I) will be 



p+r+l~ (p + r + l)' 



Now if we suppose n resistances in circuit joined up in series, 

 then the total heat generated will be 



_ H '=(^W • • • • • (*> 



If we differentiate this fraction with respect to nl and put it 

 equal to nothing, we can find when the heat generated in 

 these resistances becomes a maximum ; that is, 



whence 



p + r + nl=2nl ; 

 that is, 



p-\-r=nl; 



or the greatest heat is generated in the resistances when the value 

 of the latter equals the resistances of the rest of the circuit. 



6. Let us now assume the n resistances to be connected up 



in multiple arc ; then the joint resistance will become -,and 



n 



the heat generated will be 



E 2 - 



and the maximum amount of heat will occur ; as before, when 



, I 

 p + r= - 

 ' n 



7. Now, in the first case, if the internal resistance of the 

 battery and of the connecting wires be very small compared 

 with nl, we may neglect them ; so that by putting jO + r=0, 

 equation (3) becomes 



11 nV 



or the total amount of heat generated in the resistances will vary 

 inversely as the number of the latter in circuit. 



8. In the second case, we cannot neglect p ■+■ r; for here the 



