348 Mr. R. H. M. Bosanquet on Electromagnets. 



where x is that power of the velocity with which the current 

 varies, in the given state of the machine. 



We immediately infer some propositions of interest with 

 regard to x. 



x — 1 can only he finite and positive so long as the conduc- 

 tivity diminishes as §3 increases. 



It is infinite when the conductivity is constant. It is 

 negative when % and the conductivity increase together. 



Following the course of the changes usual in electromag- 

 nets, which we may illustrate by fig. 2, we then have 



x — 1. 33. Conductivity. 



— ... up to about 5000 increasing. 



> . . . 5000 to about 7000 maximum. 



+ GO J 



+ ... above 7000 diminishing. 



Limit at saturation 18,000 to 20,000. 



Thus the range of possible dynamic equilibrium is from 

 about % = 7000 upwards. In the lower part of this x is great, 

 or the current changes violently for small changes in the 

 velocity. In the saturation region x approximates to 1, and 

 the current is more nearly proportional to the velocity. 



I have calculated the values of x given by the successive 

 pairs of numbers on which fig. 2 is based (bars with pole- 

 pieces). ■ These- are : — 



28. x. 



8,500 22-2 



9,500 14-6 



, , 10,500. 8-95 



11,500 5-00 



12,500 3-00 



13,500 2-15 



14,500 1-47 



15,500 1*24 



16,500 1-15 



Plotting these on a scale, I took out the values of % corre- 

 sponding to those of x obtained from the Gramme machine. 

 And from the experimental conductivities (fig. 2) I calculated 

 the magnetizing forces which would be required by magnets 

 such as ours to produce this condition. These are : — 



