226 THE MAGNETIC CIRCUIT [ART. 66 



computation of their performance, provided that he adapts the 

 numerical values of the unit permeances to each individual case, 

 on the basis of his previous experience. Many authors have 

 given theoretical formulae for the leakage inductance of induction 

 machines. 1 These formulae, curves, and methods, while useful 

 in accurate work, are too elaborate to be quoted here; at any rate 

 they are of interest only to a specialist in design. Two examples 

 of the theoretical calculation of leakage inductance are given 

 below, in order to show the student the general method used, 

 and thus introduce him into the literature on the subject. 



(a) A Theoretical Calculation of the Slot Leakage Permeance. 

 We shall calculate the equivalent permeance for the half closed 

 slot (Fig. 55), an open slot being a special case of it. With 

 the notation shown in sketch, and with S PP slots per pole per 

 phase, we have: 



&c = M&2/2 + &3/*3 + b 4 '/s 4 ]/S PP ; dffi P ' = pdx/ (s 4 S PP ) , 

 and n x =C PP x/b 4 . Hence 



and 



. . (152) 



The equivalent permeance of one slot, per unit of the semi- 

 net axial length of the machine is 



This shows that the slot permeance depends only upon the 

 proportions of the slot and not upon its absolute dimensions. 



(6) A Theoretical Calculation of the Zigzag Leakage Permeance. 

 The calculation of the zigzag leakage permeance is simple only 



1 C. A. Adams, loc. cit.; also Trans. Amer. Inst. Elec. Engrs., Vol. 24 

 (1905), p. 338; ibid., Vol. 26 (1907), p. 1488. Hobart, Electric Motors, 

 (1910), Chap, xxi; Arnold, Wechselstromtechnik, Vol. 5, part 1 (1909), pp. 

 49-54; R. Goldschmidt, Appendix to his book on The Alternating Current 

 Commutator Motor (1909); R. E. Hellmund, Practische Berechnung des 

 Streuungskoeffizienten in Induktionsmotoren, \Elektrotechnische Zeitschrift, 

 Vol. 31 (1910), p. 1111 and 1140; W. Rogowski, Zur Streuung des Dreh- 

 strommotors, ibid., pp. 356, 1292, and 1316. See also an extensive series 

 of articles by J. Rezelman in La Lumicre Electrique, 1909-1911, and in 

 the (London) Electrician. 



