CHAP. I] FLUX AND MAGNETOMOTIVE FORCE 17 



One of the reasons for which calculations are as a rule more 

 involved and less accurate in the magnetic than in the electric cir- 

 cuit is that there is no magnetic insulation known, and therefore the 

 paths of the flux in a great majority of cases cannot be shaped and 

 confined at will. The student will appreciate, therefore, the reason 

 for selecting a toroidal ring as the simplest magnetic circuit. If 

 the winding is distributed uniformly there is no tendency 'for mag- 

 netic leakage, except for a very small amount in and around each 

 wire. With almost any other arrangement of a magnetic circuit 

 there is a difference of magnetic potential, or an m.m.f. between 

 various parts of the circuit, and part of the flux passes directly 

 through the path of the least resistance, in parallel with the useful 

 path. A familiar example of this is the magnetic leakage between 

 the adjacent pole-tips of an electrical machine (Fig.29), or between 

 the coils of a transformer (Fig. 50) . 



The conditions in a magnetic circuit are similar to those 

 in an imperfectly insulated electric circuit, when it, together with 

 its sources of e.m.f ., is immersed in a conducting liquid. Part of 

 the current finds its path through the liquid instead of through 

 the conductors; the current is different in different parts of the 

 circuit, and the calculations are much more involved and less 

 accurate, because the paths of the current in an unlimited medium 

 can be estimated only approximately. 



In order to prevent or to minimize leakage the exciting ampere- 

 turns should be distributed over the whole magnetic circuit, to 

 each part in proportion to its reluctance. Then the m.m.f. is con- 

 sumed where it is applied, and no free m.m.f. is left for leakage. 

 Unfortunately, such an arrangement is impracticable in most 

 cases, though it ought to be approached as nearly as possible (see 

 Prob. 17 below). 



If there were a magnetic insulator, that is, a substance or a 

 combination the permeability of which was many times lower than 

 that of the air, it would be a great boon to the electrical industry. 

 It would then be possible to avoid magnetic leakage by insula- 

 ting magnetic circuits as perfectly as elect He circuits are insulated. 

 The absence of leakage would allow a reduction in the size of the 

 fi Id frames and exciting coils of direct- and alternating-current 

 machines. It would also permit us to improve the voltage regula- 

 tinn <>! LH-IK Tutors and transformers, to raise the power factor of 

 induct inn motors, and to increase considerably their 



