1887.] On the llieory of the Alternate Current Dynamo. 167 



Fig. 3. 



resulting relations of potential in the secondary and the time will be 

 indicated by the dotted line HIJKOLMNTQ. The mean square 

 observed will be proportional to ML. a/LP ; but ML. LP is proportional 

 to EL, hence the potential observed will vary inversely as \/LP, even 

 though the maximum induction remain constant. If then the maxi- 

 mum induction be deduced on the assumption that the induction is a 

 simple harmonic function of the time, results may readily be obtained 

 vastly in excess of the truth. 



II. "Note on the Theory of the Alternate Current Dynamo." 

 By John Hopkinson, M.A., D.Sc, F.RS. Received Feb- 

 ruary 17, 1887. 



According to the accepted theory of the alternate current dynamo, 

 the equation of electric current in the armature is <yy + ~Ry = periodic 

 function of t, where 7 is a constant coefficient of self-induction. This 

 equation is not strictly true, inasmuch as 7 is not in general constant,* 

 but it is a most useful approximation. My present purpose is to 

 indicate how the values of 7 and of the periodic function representing 

 the electromotive force can be calculated in a machine of given con- 

 figuration. 



To fix ideas, we will suppose the machine considered to have its 

 magnet cores arranged parallel to the axis of rotation, that the cores 

 are of uniform section, also that the armature bobbins have iron cores, 

 so that we regard all the lines of induction as passing either through 

 an armature coil, or else between adjacent poles entirely outside the 

 armature. The sketch shows a development of the machine con- 

 sidered. The iron is supposed to be so arranged that the currents 



* "On the Theory of Alternating Currents," 'Telegr. Engin. Journ.,' vol. 13, 

 1884, p. 496. 



