I 



TRANSACTIONS OF SECTION A. 527 



yet begun to appear in the City price-lists. If 10/. were taken as the par value of 

 a horse-power night and day for a year, and allowing for the actual value being 

 greater or less (it might be very much greater or very much less) according to cir- 

 cumstances, it was easy to estimate the right quantity of metal to be put into the 

 conductor to convey a current of any stated strength, such as the ordinary strength 

 of current for the powerful arc light, or the tenfold strength current (of 240 webers) 

 which the author had referred to in his address as practically suitable for deliver- 

 ing 21,000 horse-power of Niagara at 300 miles from the fall. 



He remarked that (contrary to a very prevalent impression and belief) the 

 gauge to be chosen for the conductor does not depend on the length of it through 

 which the energy is to be transmitted. It depends solely on the strength of the 

 current to be used, supposing the cost of the metal and of a unit of energy to be 

 determined. 



Let A be the sectional area of the conductor ; s the specific resistance (accord- 

 ing to bulk) of the metal ; and c the strength of the current to be used. The 

 energy converted into heat and so lost, per second per centimetre, is scrjA ergs. 



Let p be the proportion of the whole time during which, in the course of a 

 year, this current is kept flowing. There being 31^ million seconds in a year, the 

 loss of energy per annum is 



31-5 X Wpsc^'IA ergs (1) 



The cost of this, if U be the cost of an erg, is 



31-5 X 10^ ^sc- i:iA (2) 



Let V be the money value of the metal per cubic centimetre, the cost of pos- 

 sessing it, per centimetre of length of the wire, at 5 per cent, per annum, is 



VAI20 (3) 



Hence the whole annual cost, by interest on the value of the metal, and by loss- 

 of energy in it, is 



20 A (*) 



The amount of A to make this a minimum (which is also that which makes the 

 two constituents of the loss equal) is as follows : — 



A = ^(si-5.10'psc''i:Q 



= c^/(63.10>^/F) (5) 



Taking 701. per ton as the price of copper of high conductivity (known as 

 'conductivity copper' in the metal market), we have -00007/. as the price of a 

 gramme. Multiplying this by 8-9 (the specific gravity of copper), we find, as the 

 price of a cubic centimetre, 



r= -00062/. (6) 



and the assumption of 101. as the par value of one horse-power day and night for 

 365 days, gives, as the price of an erg, 



• m/(.3Hxl0«x74xl0«) = ^g-l^^ofU . . .(7) 



Supposing the actual price to be at the rate of e x 10/. per year, per horse-power 

 we have 



^=237W*''^^^- (8) 



Lastly, for the specific resistance of copper we have 



s = 1640 ^9) 



Using (8) and (9) in (5) we find, 



J „ / 63x]0^xl6 40xpc , pe 



^°^^ 23 k 10'^ X ■00062 = '^rM • • (10) 



Suppose, for example, p = -5 (that is, electric work through the conductor 

 for twelve hours of every day of the year to be provided for), and e = l. These 



