528 BEPORT — 1881. 



-suppositions correspond fairly well to ordinary electric transmission of energy 

 iin towns for light, according to present arrangements. We have — 



'That is to say, the sectional area of the wire in centimetres ought to he ahout a fiftieth 

 of the strength of the current in webers. Thus, for a powerful arc-light current 

 of 21 webers, the sectional area of the leading wire should be -4 of a square centi- 

 metre, and therefore its diameter (if it is a solid round wire) should be '71 of a 

 centimetre. 



If we take e = -^.j:, which corresponds to 1,9001. a year as the cost of 5,250 

 horse-power (see Presidential Address, Section A, p. 518), and if we takep = 1, that is 

 reckon for continued night and day electric work through the conductor, we have — 



J _ c . c 

 ~ ^381 ^ 19-5 ■ 



and if c = 24, ^ = 1-24, which makes the diameter 1"26 centimetres, or half an 

 inch (as stated in the Presidential Address). But even at Niagara it is not pro- 

 bable that the cost of an erg can be as small as 7;\- of what we have taken as the 

 par value for England ; and probably therefore a larger diameter for the wire than 

 \ inch will be better economy if- so large a current as 240 webers is to be con- 

 ducted by it. 



6. On the proper Proportions of "Resistance in the Working Coils, the Elec- 

 tro-Magnets, and the External Circuits of Dynamos. JBy Professor 

 Sir WiLLUM Thomsok, M.A., F.B.S. 



For the electro-magnet; 



Let L be the length of the wire, 



■£ -,, bulk of the whole space occupied by wire and insulation, 

 w „ ratio of this whole space to the bulk of the copper alone (that is, 



let - B he the bulk of the copper), 

 n 



A „ the sectional area of wire and insulator, 



i2 „ the resistance of the wire. 

 For thaworking coil, let the corresponding quantities be i', £', n', B.'. Lastly, let 

 s be the specific resistance of the copper. We have — 



B = AL 



T> L B 



R = m- = ns-^^. 



TT A a/(w S B) K /T \ 



Hence, . ^^/bT T/R ^ •* 



and similarly, . A' = ^^^^, ^^ ^^^ 



where K and K' denote constants. 



Now, let c be the current through the magnet coil, and c' that through the 

 working coil, and let v be the velocity of any chosen point of the working coil. 

 Denoting by p the average, electro-motive force between the two ends of the 

 working coil, we have — 



where Jis a quantity depending on the forms, magnitudes, and relative positions of 

 B and B', an^ on the magnetic susceptibility of iron ; diminishing as the suscepti- 

 bility diminishes with increased strength of current, or with any change of B and 

 B' which gives increase of magnetising force. 



In the single-circuit dynamo (that is, the ordinary dynamo) c' is equal to e, 



