Mr. K. H. M. Bosanquet on Electromagnets. 345 



Thus the tangent and Frolich's laws, upon one or other of 

 which almost all treatment of the theory of dynamo machines 

 has been based, are shown to be far from representing the 

 true laws which govern electromagnets. 



In a paper by the Messrs. Hopkinson, reprinted in i The 

 Electrician/ Nov. 19th, 1886, we have an example of another 

 way in which it has been attempted to fit Froliclr's law to 

 represent the law of magnetization. The intersection of the 

 Frolich law with the true law in diagram A there given is 

 made to take place at about $3 = 5500. If the case be 

 represented by a scheme of conductivity and induction, the 

 straight line representing Frolich's law crosses the curve of 

 the true law at a considerable angle, and by the end of the 

 representation in about $3 = 11,000 the two diverge widely. 



Now it seems unlikely that Froliclr's law, so used, can have 

 any bearing upon the action of the dynamo machine. The 

 advantage of the law is that, being easily manipulated, it can 

 be made to coincide exactly with the true law in the part of 

 the dynamo range in actual use. Such a case is represented 

 by a tangent drawn to the curve in my scheme. It is very 

 unlikely, however, that any dynamic action, such as to be of 

 practical utility, could take place in the region of 33 = 5000. 



I shall now proceed to a few propositions, suitable for 

 application to the true laws of electromagnets as embodied in 

 series of numbers rather than in formulae, founded chiefly on 

 the dynamic action itself. 



The outlines of the theory have been explained to some 

 extent in my paper on Self-regulating Dynamo machines, 

 Phil. Mag. [5] xv. p. 275. But the application to laws 

 expressed numerically, and the line of reasoning now adopted 

 are new. 



For the present I confine myself to the series dynamo. 



According to the mode of statement now usually adopted, 

 the E.M.F. developed in an armature at n revolutions is 



E = 4nA33 A , (1) 



where 13 A is the field-intensity within the coils of the armature. 

 This differs only in arrangement of units from the formula 

 adopted in my previous paper. 



The first thing is to express 23 A in terms of the 13 developed 

 in the field-magnets. We have measures of the §3 across the 

 equatorial sections of the field-magnets, and can connect it to 

 some extent with the potential of the magnetizing current. 

 In the present approximate purpose we assume 



as A =/is, (2) 



