1 82 ALTERNATING CURRENTS 



the various phases waves whose superposition gives rise, as we have 

 seen ( 20), to a rotating wave of magnetic flux in . the air-gap we 

 considered only those lines of induction which actually cross the gap 

 and penetrate into the rotor core, there becoming linked with the rotor 

 conductors. In addition to such effective or useful lines, however, 

 there will be others which simply become linked with the stator 

 windings, without undergoing any linkage with the rotor windings. 

 All such lines, which do not contribute anything towards the 

 magnetic link connecting the two sets of windings, are spoken of 

 as leakage lines, and the corresponding flux as leakage flux. Out of 

 the total maximum flux Lili linked with the primary, a certain 

 proportion, MIi, will become linked with the secondary, and the 

 remainder will form the primary leakage flux. We may term M the 

 virtual mutual inductance of the two windings. 



The currents circulating in the secondary similarly give rise to a 

 flux Lglg in each phase, an amount MI 2 becoming linked with the 

 primary, and the remainder forming the secondary leakage flux.* 



The ratios vi = ^ and v z = vf are termed the Hopkinson leakage 

 M M 



coefficients. They were first introduced by A. Blondel.t 



The reciprocals of the Hopkinson leakage coefficients, viz. 



vi = = T and V2 = = ^ are known as Behrend's leakage 



Vl LI V. 2 L 2 



coefficients. 



The ratios n = ^ and r 2 = if? of the leakage flux to 



the useful flux in the two windings are known as Heyland's leakage 

 coefficients. 



Lastly, a very important coefficient, which has been used by 

 Heyland, Behrend, Blondel, Hobart, and many other writers, and 

 which is known as the dispersion coefficient, is the ratio 



M 2 1 



S- = ri + r 2 + TITS = VM - = - 



In the special case under consideration, in which the stator and 



* In the special case under consideration, in which the primary and secondary 

 windings are supposed to be identical in every respect, L, = L 2 ; this, however, would 

 not hold generally. 



t It must be clearly understood that the definitions v, = -.? and v 2 = .r* are based 



on the assumption of equal numbers of turns in the stator and rotor windings. If the 

 turns are different, we must imagine the rotor winding replaced by one having the same 

 number of turns as the stator winding. 



J Behn-Eschenburg uses or in a slightly different sense, viz. a = Jl ," T (Journal 



lv, Lo 



of the Institution of Electrical Engineers, vol. xxxiii. p. 239). 



