482 • Mr. 0. Heaviside on Resistance 



perty p 2 = —?i 2 ; which substitution, made in Z and Y, reduces 

 them to the forms 



Z = R' + I/p, (3) 



Y=K' + &'p; (4) 



where B/, IV r , K? } S / are functions of the electrical constants 

 and of n 2 y and are therefore constants at a given frequency. 



In the first case we compare the combination to a coil 

 whose resistance is B/ and inductance I/, so that E/ and 1/ 

 are the effective resistance and inductance of the combination, 

 originally introduced by Lord Bayleigh* for electromagnetic 

 combinations. In my papers, however, there is no limitation 

 to cases of magnetic energy onlyt, and it would be highly 

 inconvenient to make a distinction. 



In a similar way, in the second case we compare the com- 

 bination to a condenser, and we may then call K7 the effective 

 conductance and S' the effective permittance at the given 

 frequency. E/ reduces to Z , and K7 to Y at zero frequency. 

 But it is important to remember that the two comparisons are 

 of widely different natures : and that the effective resistance 

 is not the reciprocal of the effective conductance. 



Y and Z in (3) and (4) are reciprocal, or YZ = 1, just as 

 the general Y and Z of (1) and (2) are reciprocal. 



If (V) and (C) denote the amplitudes of V and C, we have, 

 by (3) and (4), 



(V)/(C) = (R' 2 + L'V)s = I,say, ... (5) 



(C)/(V)=(K'* + SV)W,say. ... (6) 



I and J are also reciprocal. The former, I, being the ratio of 

 the force to the flux (amplitudes), is the impedance of the 

 combination. It is naturally suggested to call J the " admit- 

 tance " of the combination. But it is not to be anticipated 

 that this will meet with so favourable a reception as impe- 

 dance, which term is now considerably used, because the 

 methods of representation (1), (3), and (5) are more useful 

 practically than (2), (4), and (6) ; although theoretically the 

 two sets are of equal importance J. 



* Phil. Mag. May 1886. 



t In Part V. of " On the Self-induction of Wires " I have given a few 

 examples of mixed cases of an elementary nature, in connexion with the 

 problem of finding the effect of an impressed force in a telegraph circuit. 



X The necessity of the term impedance (or some equivalent) to take the 

 place of the various utterly misleading expressions that have been used, 

 has come about through the wonderful popularization of electromagnetic 

 knowledge due to the dynamo, and its adoption to Sir W. Thomson's 

 approval of it and of one or two other terms. 



