290 ELEMENTS OF ELECTRICAL ENGINEERING. 



turned off and on. Therefore, if the voltage at the end lamp is 

 to be kept within, say, 3 per cent, of its normal value, , which 

 is the value when all the lamps are in operation, then the voltage- 

 drop in the wires must not exceed 3 per cent of E when all the 

 lamps are in operation. 



To secure a specified drop out to the end lamp, Z, when all 

 the lamps are in operation, with the minimum weight of copper 

 in the wires, the sectional area of each portion, <z, b y c an.d d, 

 Fig. 163, of the wires must be * proportional to the square root 

 of the current in that portion. f Thus, if each lamp in Fig. 163 

 takes the same amount of current, then the current values in 

 the portions a, b, c and d, are as 4 : 3 : 2 : i, and the sec- 

 tional areas of the respective portions of the wires should be as 

 1/4 11/3: 1/2 : i/ 1 in order to give a minimum voltage-drop at 

 the end lamp, L, with a given amount of copper, or to give a min- 

 imum amount of copper for a specified voltage-drop at the end 

 lamp, L. 



In laying out street mains to supply a group of scattered cus- 

 tomers it is generally advisable, on account of the large amount 

 of copper involved, to taper the mains in steps in going farther 

 and farther from the center of distribution ; but, as a rule, the 

 successive steps should be made longer than the distance between 

 adjacent customers, in order to avoid an excessive number of 

 joints in the mains. 



In laying out service wires to supply current to a scattered 

 group of lamps, it is generally not advisable to taper the wires in 

 steps, because the amount of copper involved may not be large ; 

 whereas the expense of making many joints, together with the 



* It should be kept in mind that the fundamental condition here is a minimum 

 amount of copper for a given voltage-drop. A minimum amount of copper for given 

 watts lost in the line requires the sectional area of the wires to be proportional to the 

 current at each point ; that is, the number of circular mils per ampere must be the 

 same throughout the system to give a minimum amount of copper for a given loss of 

 power in watts. 



f The general proof of this proposition involves the highly elaborate methods of 

 the calculus of variations and therefore the proof of the proposition is not given here. 



