22 Mr. 0. Heaviside on the 



wherein G and H contain only constants belonging to the 

 apparatus at z = 0, and G^ and H 1 those belonging to z=l, 

 besides the line-constants. Only one of the four need be 

 written ; thus 



V=l + pi ( p + Q 2 ) J o 2 + 2P ( R ' R o' + L'L 'n 2 ) + 2Qn(R 'L'-R'L ')l • (206) 



From this get H by changing the signs of P and Q. 

 Then, to obtain G-j and H l5 the corresponding functions for the 

 z = l end, change E ' to E,' and L ; to L/. These functions 

 have the value unity when the line is short-circuited at the " 

 ends, (Z = 0, Zi = 0). They may therefore be referred to as 

 the terminal functions. Their form is invariable. We only 

 require to find the R/ and L', or the effective resistance and 

 inductance of the terminal arrangements, and insert in (206 ) 

 and its companions. 



Thus, let the two conductors at the z=l end be joined 

 through a coil. Then R/ is its resistance, IV its inductance, 

 the steady-flow values, and the accents may be dropped, ex- 

 cept under very unusual circumstances, and I x is its impe- 

 dance at the given frequency, when on short circuit. But if 

 the coil contain a core, especially if it be of iron, neither R x 

 nor Lj can have the steady-flow values, on account of the 

 induction of currents in the core. Their approximate values 

 at a given frequency may be experimentally determined by 

 means of the Wheatstone bridge. Of course R x and L x are 

 really somewhat changed in a similar manner by allowing any 

 induction between the coil and external conductors, the brass 

 parts of a galvanometer, for instance; L going down and R 

 going up, though this does not materially affect I. 



If, instead of a coil, it be a condenser of capacity Si that 

 is inserted at z—l ; then, since 



C = Sxt = $ lP Y, 

 we have 



Z 1 =(S tf )- = -^/(S 1 » 2 ). 

 Therefore take 



R/rzrO, and Li's-OSjn*)- 1 . 



The condenser behaves, so far as the current is concerned, as 

 a coil of no resistance and negative inductance, the latter 

 decreasing as the frequency is raised, and as the capacity is 

 increased ; tending to become equivalent to a short circuit, 

 though this would require a great speed in general, as the 

 g^cm-negative inductance is large. [Thus n=100, S = 10 -15 

 (one microfarad), makes IV = — 10 11 . To get the inductance 

 of a coil to be 10 11 it must contain a very large number 

 of turns of fine wire.] Thus, whilst the condenser stops 



