484 Mr. 0. Heaviside on Resistance 



If the mean magnetic energy preponderates, the effective 

 inductance is positive, and the permittance negative ; and 

 conversely, if the electric energy preponderates. If there be 

 no condensers, the comparison with a coil is obviously most 

 suitable, and if there be no magnetic energy we should natu- 

 rally use the comparison with a condenser ; but when both 

 energies coexist, which method of representation to adopt is 

 purely a matter of convenience in the special application 

 concerned. 



If the mean energies, electric and magnetic, be equal, then 



17 = = 8', R'K' = 1, 



I = R' J 



=kJ • • • • < 16 > 



That is, by equalizing the mean energies we bring the cur- 

 rent and potential-difference into the same phase, annihilate 

 the effective inductance (and also permittance), and make the 

 effective conductance the reciprocal of the effective resistance, 

 which now equals the impedance itself. It should be noted 

 that the vanishing of the energy-difference only refers to the 

 mean value. The two energies are not equal and do not 

 vanish simultaneously. Sometimes, however, their sum is 

 constant at every moment, but this is exceptional. [Example, 

 a coil and a condenser in sequence.] 



5. Passing now to the second class referred to in § 2. 

 imagine, first, the combination to be electromagnetic, and 

 that V is steady, producing a steady C, dividing in the 

 system in a manner solely settled by the distribution of con- 

 ductivity. Although we cannot treat the combination as a 

 coil as regards the way the current varies when the impressed 

 force is put on, we may do so as regards the integral effect 

 at the terminals produced by the magnetic energy. This last 

 is the well-known quadratic function of the currents in different 

 parts of the system, 



T = iL 1 C 1 2 + MC 1 C 2 + iL 2 C 2 2 + (17) 



Now put every one of these C's in terms of the C, the total 

 current at the terminals, which may be done by Ohm's law. 

 This reduces T to 



T=iL C 2 , (18) 



where L is a function of the real inductances, self and mutual, 

 of the parts of the system, and of their resistances. This L 

 may be called the impulsive inductance of the system. For 

 although it is, in a sense, the effective steady inductance, 

 taking the current C at the terminals as a basis, being, in 

 fact, the value of the sinusoidal inductance 1/ at zero fre- 



