PEIRCE. — ESTABLISHMENT OF CURRENT IN COIL. 151 



one has a hysteresis diagram for a given magnetic journey of the core, 

 to predict accurately the form of a current curve corresponding to 

 this journey under given electric conditions. 



In the case of a commercial transformer, eddy currents in the lami- 

 nated core affect slightly the form of a current curve at the very be- 

 ginning, but nothing of the sort occurs in coils such as are used for 

 loading telephone circuits. I shall assume, therefore, that the form 

 of a current curve can be foretold if we have a permeability of the core 

 for the given magnetic path, in the cases of such induction coils as we 

 consider here. 



The theory and method of investigation here proposed applies 

 accurately to telephone loading coils with finely divided cores, and 

 gives good approximation to correct results with commercial closed- 

 core transformers. 



The investigation comprises two parts: Part One, the establish- 

 ment of the current in the primary coil of a transformer when the 

 secondary is open ; and Part Two, the growth of primary and second- 

 ary current, when the secondary is closed. 



PART I. SECONDARY OPEN. 



Theory. — Given a closed-core electromagnet of any form, perhaps 

 one like J shown in Figure 1, suppose that the manner of growth of the 

 flux of induction N in the core as the strength of the exciting current 

 is made to grow larger by steps has been determined when the condi- 

 tion of the core at the outset is a certain definite one. Let the flux N 

 be plotted against the ampere turns T of the exciting current, Curve 

 B A, Figure 2, and let one horizontal unit of the diagram represent a 

 ampere turns, and one vertical unit represent m Maxwells. If the 

 slope of the curve B A at any value T of ampere turns be ^ (T), then 



= 7rUN 

 K } a dT W 



If now an e. in. f. E be applied at the time t = to the exciting 

 circuit of resistance r, and if the exciting coil has n turns, and if the 

 strength of the exciting current be i, and if we neglect the flux in the 

 air through the turns of the coil, then 



