CHAP. V] EXCITING AMPERE-TURNS 89 



This picture of the flux distribution follows directly from the 

 fundamental law of the magnetic circuit, the flux density being 

 higher at the places where the permeance of the path is higher. 

 The actual flux distribution is such that the total permeance of all 

 the paths is a maximum, as compared to any other possible distri- 

 bution. In other other words, the flux distributes itself in such a 

 way, that with a given m.m.f . the total flux is a maximum, or with 

 a given flux the required m.m.f. is a minimum. This is confirmed 

 by the beautiful experiments of Professor Hele-Shaw and his col- 

 laborators, 1 who have obtained photographs of the stream lines of a 

 fluid flowing through an arrangement which imitated the shape 

 and the relative permeances of the air-gap and of the teeth in an 

 electric machine. 



Let & a be the total permeance in perms of the air-gap between 

 the surface of the pole shoe and the teeth, and let be the useful 

 flux per pole, in maxwells, which is supposed to be given. Then, 

 according to eq. (2), Art. 5, the number of ampere-turns required 

 for the air-gap is 



(44) 



The problem is to calculate the permeance of the gap from the 

 drawing of the machine. 



One of the usual practical methods is to calculate (P under cer- 

 tain simplifying assumptions and then multiply the result by an 

 empirical coefficient determined from tests on similar machines. 

 The simplest assumptions are (Fig. 25) : (a) that the armature has 

 a smooth surface, the slots being filled with iron of the same per- 

 meability as that of the teeth; (6) that the external surface of the 

 pole shoes is concentric with that of the armature; (c) that the 

 equivalent air-gap a^ is equal to two-thirds of the minimum air- 

 gap plus one-third of the maximum air-gap of the actual machine; 

 (d) that the ventilating ducts are filled wit h iron; (<) that the paths 

 of the fringing flux at the edges of the pole shoe are straight lines, 

 and extend longitudinally to the edge of the armature surface and 

 laterally for a distance equal to the equivalent air-gap on each 



1 For a detailed account of the experimental and theoretical investigations 

 on this robject, with nnim-mu^ n-fi-n-ncw, eee Hnwkina and Wnllia, Th* 

 Dynamo (1909), Vol. 1, Chapter XV. 



