478 The Vector Properties of Alternating Currents, tyc. 



It will be evident that the same process is equally applicable when 

 the currents are no longer of a simple sinuous character, provided 

 only that the network representing one particular case can be pro- 

 perly drawn ; for, however complicated the network may become 

 when it represents several such cases, it is obtained from the original 

 network by increasing some of the vectors to correspond with the 

 changes in the conductors. If we have a current, C, passing through 

 (1) a wire of resistance R, (2) a coil of self-induction L, or (3) a 

 condenser of capacity K, the voltages at the ends of these conductors 

 are given respectively by the expressions 



RC ' and ~k\ ° dt > 



o 



and hence the vectors representing them are proportional respec- 

 tively to 



R, L, and 1/K, 



and the effect of an alteration in R, L, or K can generally be easily 

 indicated on the network figure. 



It may, therefore, be taken as established that the vector method 

 of representing alternate current quantities is as applicable when 

 the currents and potentials vary in a manner widely different from 

 the sine law as when they are simply sinuous. But it is desirable in 

 this connexion to repeat and emphasise an old warning about the 

 continued use of coefficients of self and mutual induction in the 

 theoretical investigations of alternate current problems. These co- 

 efficients may be of service in connexion with coils not possessing 

 iron cores, but they are very misleading in commercial cases in which 

 iron is present. By no choice of the value of these coefficients is it 

 possible to represent the phenomena of hysteresis. The presence of 

 the latter implies that the current has a different law of variation 

 from that of the voltage, while the assumption of constant induction 

 coefficients necessitates that if either the current or potential follows 

 a sine law the other must also. Again, constant self-induction in- 

 volves the assumption that there is no loss of energy in the magnetic 

 changes going on in the iron, an assumption which is not only known 

 to be wrong, but one which involves an error of serious practical 

 importance. It has already* been pointed out that the difficulty of 

 reconciling theoretical formulae with experimental results does not 

 arise so much from assuming that the currents vary according to a 

 simple sine law, as from the quite unjustifiable assumption and use 

 of constant coefficients of induction. 



* See 'Electrician,' June 5 1891, "Alternate Current Theory," by Dr. W. E. 

 Sunipner. 



