Mr. E. H. M. Bosanquet on Electromagnets. 341 



used by Maxwell and the best writers. For conductivity I 



write either - or cy, 



P . 



Having the magnetic resistances of the magnets with pole- 

 pieces mentioned above, we can obtain their conductivities ; 



B> 



The formula known as Frolich's may be obtained by 

 assuming that the conductivity of the magnet is proportioned 

 to its defect of saturation. (See my letter to i The Electrician/ 

 vol. xvi. p. 247, February 1886 ; and Prof. S. P. Thompson, 

 Phil. Mag. xxii. p. 290, Sept. 1886.) If we measure the mag- 

 netism as % (magnetic induction), we may write this, 



Conductivity = k ( U w - %), 



which represents a straight line on the scheme of conduc- 

 tivities and inductions ; see figs. 1 & 2. 



For the sake of clearness I have drawn on fig. 1 the 

 permeabilities of Rowland's table i., and of my ring E, and 

 also the average conductivities of plain bars and bars with 

 pole-pieces, deduced from the magnetic resistances given in my 

 paper first above cited ; also both in figs. 1 & 2 the applica- 

 tion of Frolich's law to the bars with pole-pieces. 



It will be seen that, if a real state of things be represented 

 by any curve, a tangent drawn to that curve at any point will 

 represent a Frolich's law, which will be true only so far as the 

 curve and the tangent coincide. In the present case there 

 appears to be a point of inflexion on the curve just before 

 approaching the region of what I may call super-saturation 

 (tendency of 3$ to increase without actual limit ; see paper 

 first cited) . The tangent drawn through this point of inflexion 

 coincides with the curve for a considerable distance in the 

 neighbourhood of IS = 15.000 ; and I shall show later that the 

 excitation in the cores of a dynamo with such magnets may 

 be confined in actual practice within very moderate limits on 

 either side of this value. 



The use of Frolich's law to deduce consequences where 

 wide variations of the magnetic intensity take place, as, for 

 instance, where the magnetism is supposed to be reduced to 

 half its maximum value, appears to be fallacious in such cases 

 as the present. 



The curve in fig. 2 is the same as the curve marked " Bars 

 with PP " in fig. 1, but drawn to a larger vertical scale. 



