CHOICE OF CONDUCTORS. , 687 



- , and the corresponding loss of energy per second is - 1 2 . Two 



o o 



conductors of different metals are therefore equivalent for the 



same current when the sections are proportional to the specific 



resistances. With iron and copper, for instance, these sections 

 should be in the ratio of 6 : i. 



We ought not, however, to conclude that in all cases the best 

 conducting metals and the greatest sections should be used, for 

 the price of the metal and the cost of establishing the wire play 

 an important part. 



In the case of bare conductors the most economical conditions 

 are furrn'shed by a given strength of current for each metal. Let 



P be the price of unit work in the conditions given by the 



chemical or mechanical electromotor, 

 n the number of seconds in a day (86400), 

 f the fraction of the time in which the current is utilised, 

 Q the price of unit volume of the metal, 

 / the rate at which the interest and the redemption of capital 



is estimated, 

 N the number of days in the year. 



The energy lost in heating the conductor per day, and for 

 unit length is equal to fn - 1 2 , and the corresponding expense 



o 



On the other hand, the price of unit length of the conductor 



is QS, and the cost per day QS . 



i oo.N 



The total expense D per day and unit length is then 



QS + ?/- 



looN S 



The section of the conductor which is adapted to reduce this 

 expense to a minimum is defined by the condition that the differential 

 of the second member is small that is to say, that the two terms 



