688 INDUSTRIAL APPLICATIONS. 



are equal. In this case the cost of interest and of redemption 

 represent a sum which is equal to the expense for the energy lost, 

 and we have 



IOoNKP/0-' 



It will be seen that, for a total minimum expense, the density 

 of the current /=- only depends on the metal and the cost of 



o 



the energy, and that the relative expense for the same current is 

 independent of the section of the wire. 



With two different metals, the prices of which per kilogramme 

 are respectively k and ', the densities d and d', and the rates of 

 redemption t and /', the ratio of the densities of the current / and *', 

 and that of the corresponding expenditures D and D' are 



)/ o-'_ / Y^dt a-' 



r 7 "Vicwr o- ' 



It may be estimated that, for equal volumes, the price of 

 copper of good quality is 10 times the cost of iron. If, in the 

 preceding expressions, 



Q K</ 



= =10, 



Q' 



and, assuming that the redemption is the same in both cases, we 

 find 



/ D 



- =I ' 2 99> = 774 ' 



The density of the current will therefore be a little greater 

 with copper than with iron, but the expense is much greater. We 

 may, however, remark that for the same current the sections of 

 wires are inversely as the values of * and /'; the weight of iron 



