THE MAGNETIC CIRCUIT ELECTROMAGNETS 27 



which, if the dimensions are in centimeters, will be the leakage 

 flux in maxwells; and this is seen to be merely the product, 

 average value of m.m.f. X permeance. 



It is evident that this formula can be applied to case (d) in 

 order to calculate the leakage flux in the space occupied by the 

 coil, and so obtain the total leakage flux inside a magnet of the 

 type illustrated, where the coils do not occupy the whole of the 

 annular air space between the core and the cylinder forming the 

 return path. 



Case (/). Parallel Cylinders. The permeance of the air paths 

 between the sides of two parallel cylinders of diameter d and 



FIG. 11. Permeance between parallel cylinders. 



length I which are shown in section in Fig. 11 cannot be 

 calculated so easily as in the examples previously considered; 

 but the following formula may be used, 1 



irl 



(b + d-yv + zbd) 



P = 



It will be observed that the logarithm in this and previous 

 equations is to the base e, and although the formula could be 

 rewritten to permit of the direct use of tables of logarithms to 

 the base 10, there appears to be no good reason for doing so. If 

 a table of hyperbolic logarithms is not available, the quantity 

 log t can always be obtained by using a table of common logarithms 

 and multiplying the result by the constant 2.303. 



6. Flux Leakage in Similar Designs. In all the above formulas 

 it will be seen that the permeance, P, remains unaltered per 

 unit length measured perpendicularly to the cross-section shown 



1 This formula can be developed mathematically in the same manner as 

 the better-known formulas giving the electrostatic capacity between parallel 

 Wires, 



