346 Mr. K. H. M. Bosanquet on Electromagnets. 



where / may be called the coefficient of efficiency ; it will 

 depend on the build of the machine, and may probably range 

 from J to ^o or less. Nothing in the theory depends on it, so 

 far as our present purpose is concerned. We neglect varia- 

 tions of distribution, which would give rise to change of/. 



We then put E = CR, from Ohm's electrical law in the 

 circuit, and the equation stands 



CR = 4nAf% •. (3) 



The next step is to express % in terms of the magnetizing 

 current. If we make here the usual assumption, 



% = conductivity x magnetizing force, 



~ 47rm0 , . x 



or % = cy x — j— , (4) 



and substitute in (3), the current disappears from the equation, 

 and we have 



ZR = 16irmn A/ x cy ; . . . . (5) 



a relation between the coefficients for a given value of the 

 conductivity, which is not without use, but does not help us 

 in the general problem. 



The assumption (4) is not, however, called for by the nature 

 of things, for it is clear that IS is not generally proportional 

 to the magnetizing current. And our present treatment will 

 be founded on the assumption that, so long as the conditions 

 of the machine vary but little, there must be some power of 

 the magnetizing current or of its magnetic potential to which 

 3$ may be regarded as proportional. Assume, then, a general 

 form of law which can be fitted to any part of the range of 

 magnetization, 



% = KO (6) 



Substitute this in (3), and gather up the constants into the 

 coefficient; then, 



or C = K 2 ^y; (7) 



which expresses the current as a power of the velocity of 

 rotation. 



Here we may conveniently put #= = _ and assume C and 



n to be a pair of corresponding values differing little from C 

 and n, so that 



£-©' "> 



By means of this formula we can determine the value of x 



