510 PROCEEDINGS OF THE AMERICAN ACADEMY. 



units, the mean total flux of induction, through each turn of the coils 

 of the magnet, for a given gap-width, corresponding to currents repre- 

 sented in amperes by the abscissas. These curves are specimens of a set 

 obtained experimentally : only half of each cycle — representing about 

 20 determined points, every one of which lies sensibly on the curve — is 

 given lest the complete diagrams prove confusing. Reckoned from the 

 top of the diagram, the curves correspond, respectively, to the gap-widths 

 1.6 mm., 4.7 mm., 9.7 mm., 19.7 mm., and 28.4 mm. Figure 4 shows a 

 similar cycle corresponding to a gap-width of about 1.6 mm. for a maxi- 

 mum current of about 6.2 amperes: the magnet was put repeatedly 

 through the cycle before the observations were made. The dotted curve 

 D P shows a rising branch of the cycle from D to P. 



It is evident that the manner of growth of a current in the coil of the 

 magnet is influenced by eddy currents in the core, by the residual effects 

 of past magnetic experiences and the corresponding form of a hysteresis 

 cycle for rapid changes of the magnetizing field, and by magnetic lag, if 

 such there be, as well as by the causes enumerated above. It is always 

 difficult to distinguish between the effects of all these causes, and it will 

 be well to get such help as we can from a theoretical discussion of the 

 effect of eddy currents alone in a core of definite constant permeability. 



Eddy Currents in a Core of Fixed Permeability within 

 a Long Solenoid. 



Several writers have discussed the application of Maxwell's general 

 equations 4 to the determination of the growth of currents in coils of wire 

 which surround solid metal cores of various forms, and Heaviside printed 

 more than twenty years ago 5 an extremely interesting series of fifteen 

 papers on problems connected with the induction of currents in the solid 

 core of a long solenoid. Although it is practically impossible to subject 

 to accurate computation the growth and the decay, under given conditions, 

 of currents in the coils of a magnet like that shown in Figure 1, it will be 

 instructive to consider some analogous problems in the case of a long 

 solenoid, the solid core of which is supposed to have a fixed permeability, 

 and to be of the same diameter as that of the iron cylinders within the 

 coils of the magnet in question. To facilitate comparison between the 

 numerical results of this paper and those obtained in similar cases by 

 Heaviside, it will be convenient to use his notation, at least in part. 



* Treatise on Electricity and Magnetism, 2, ch. ix. 



6 The Electrician, 1884-85 ; Electrical Papers, 1, 353-416. 



