28 On the Self-induction of Wires. 



pendently of the resistance of the coil. Taking PZ=10, this 



makes L 1 = R//20n, where RZ is the resistance of the line. 

 The relation (29 b) makes 



~ - 2PRj 2P 2 R* /OA7x 



Gi=i+ ~ir + ~~w^' • • - (305;) 



If the coil had no inductance, but the same resistance, G x would 

 have the same expression, but with 1 instead of -J- in (30 b). 

 The effect of the inductance has therefore increased the ampli- 

 tude of the current, and it is conceivable that Gr 1 could be 

 made less than unity, though not practicable. 



Now the G-j/Ri of (30 b) is a minimum, with Rj variable, 

 when R = 2PR 1 , and this will make Gi = 2, or the terminal 

 factor to be Gti~*='7. Now if we vary the number of turns 

 of wire in the coil, keeping it of the same size and shape, the 

 magnetic force will vary as (Rj/G)^, so it at first sight appears 

 that Ri = R/2P and Tj! = R/2Pn make the magnetic force a 

 maximum for a fixed size and shape of coil. There is, how- 

 ever, a fallacy here, because varying the size of the wire as 

 stated varies L x nearly in the same ratio as Rj, whilst (oOb) 

 assumes 1^ to be a constant, given by (29 b). It is perhaps 

 conceivable to keep Lj constant during the variation of R 1? 

 by means of iron, and so get (Rj/Gr)* to be a maximum; but 

 then, on account of the iron, this quantity will not represent 

 the magnetic force. 



If, on the other hand, we vary R x in the original G x of 

 (28£), keeping Lj/Rx constant (size and shape of coil fixed, 

 size of wire variable), Gi/Ri is made a minimum by 



R 1 2 + L J V = R 2 /2P 2 , (31b) 



giving a definite resistance to the coil of stated size and shape 

 to make the magnetic force a maximum. Now Gr x becomes 



2P 

 G 1 =2+^(R 1 -L 1 n), .... (324) 



where Li/Ri has been constant. If this constant have the 

 value n~\ we have G x = 2 again, and Rj, L x have the same 

 values as before. There is thus some magic about G x = 2. 



Again, if the terminal arrangement consist of a coil R 1? 

 Li and a condenser of capacity Si and conductance Ki joined 

 in sequence, we shall have 



V/C=(E 1 + L lP ) + (K 1 + 8^)- 1 , 



= B 1 ' + L/p, say, 



