220 THE MAGNETIC CIRCUIT [ART. 65 



of the corresponding parts of the armature coils. Since all these 

 permeances are in parallel, (Peq is equal to their sum, or 



e .... (149) 



Here the letter I denotes the lengths in cm. of the coil, or, what 

 is the same thing, the width of the paths of flux. The subscripts 

 i, a, and e refer to the iron, the air-ducts, and the end-connections 

 respectively. Thus, Z; is the semi-net length of the core, that is, 

 the length exclusive of ducts but inclusive of the space between 

 the laminations. 1 The corresponding permeance per centimeter is 

 0Y. The sign "prime " signifies that the corresponding (P's refer 

 to one centimeter width of path. 



The coefficient a is equal to 1 when the end-connections 

 are arranged as in Fig. 52, and a=J when they are arranged 

 according to Fig. 53. Namely, in the first case the number of 

 conductors C e per group of the end-connections is equal to the 

 number C PP in the embedded part. In the second case C e is 

 equal to JC PP . In the first case there are as many groups of 

 end-connections per phase as there are poles; in the second 

 case there are twice as many groups per phase as there are poles, 

 so that two groups (one pointing to the right and one to the left) 

 must be counted per pole. Thus, with undivided end-con- 

 nections, the inductance is Cpp 2 (P e 'le, while with divided end- 

 connections it is (iCpp) 2 <?y.2Z e =Cpp 2 . \(Pele- This accounts for 

 the value of a = i, in formula (149), and shows that the inductance 

 due to the end-connections is reduced twice by subdividing 

 them into two groups. When estimating the leakage reactance 

 it is therefore necessary to know the exact arrangement of the 

 end-connections. 



In preliminary calculations, before the armature coils are 

 drawn to scale, the length l e of the end-connections in a full- 

 pitch winding is usually assumed to be equal to about 1.5r, where 

 T is the pole pitch. For fractional-pitch windings, l e varies 

 roughly as the winding-pitch, or l e = 1.5r (see Art. 29). 



1 The semi-net length is used in getting the leakage permeance in the 

 slot, tecause the flux spreads as it comes out of the iron almost immediately. 

 The spaces between the laminations do not affect the density in the air 

 because they are so small as compared to the dimensions of the slot. 



