[187 ] 
XXVII. On the Size of Conductors for the Distribution of 
Electric Energy. By Thomas Gbay, B.Sc, F.R.S.E* 
THE principal questions which have to be considered in 
the determination of the proper size of conductors for 
the distribution of electric energy are : — 
(1) Economy t, or the amount of metal which must be put 
into the conductor in order that the sum of the annual cost 
for interest on capital, for depreciation, and for energy lost in 
consequence of heat generated in the conductor by the 
current may be a minimum. 
(2) Safety, or the amount of metal necessary to prevent 
excessive heating. 
(3) Regulation, or the amount of metal required to prevent 
too great a variation of potential along the leads. 
In the consideration of the question of economy, let I be 
the fraction of the original cost of the conductors to be 
allowed annually for interest and depreciation combined, let P 
be the price per unit volume of the conductor, A its sectional 
area, and I its length. Then the cost per annum of possess- 
ing the conductor is 
6 IPAZ. 
Again, if E be taken as the cost of one erg of electric 
energy, c the current flowing in the conductor at any time t, 
and S the specific resistance of the material, the energy lost 
in heat will cost per annum 
where T is the number of seconds in a year. In most cases c 
will be a complicated and somewhat uncertain function of t, in 
consequence of which it may only be possible to form a rough 
estimate of the value of the integral. Let C be such a 
quantity that 
7 f t 7 
ES-M c 2 ^=EC 2 s4-T, 
AJo A 
and we get for the total annual expenditure due to the con- 
ductors the expression 
IPAZ + EC 2 s|t ( a ) 
* Communicated by the Author. 
t This problem for the case of a constant current flowing during the 
same portion of each day, has already been treated by Sir William Thom- 
son, in a paper communicated to the British Association at the York 
Meeting 1881, and printed in 'Nature' for September 1881. 
