PEIRCE. — BEHAVIOR OF THE CORE OF AN ELECTROMAGNET. 105 



will have an asymptote, CY, parallel to the axis of abscissas, at a dis- 

 tance, KC, from it corresponding to E/r amperes, and, if OK represents 

 the time t h and OL the time t 2 , the area FGDC, or A U2 , expressed 

 in square centimeters, is equal to 



Im f (/ x - dt, (8) 



so that iVi.a = - 7 = — j : • (9) 



im Im ■ * w 



In practice N usually differs from n <£, where <£ is the induction flux 

 through the iron core of the electromagnet alone, by only a small frac- 

 tion of itself, and, if a is the area of the cross section of the core at 

 any point, a certain average value of B, the induction, can be obtained 

 from the expression N~/na, though in such cores as are used in large 

 transformers, H, and therefore B, would probably have very different 

 values at different points of the section. Really N is greater than n <£ 

 by the amount of the magnetic flux, in the air about the core, through 

 the turns of the exciting coil, caused by the current in the coil itself 

 or by neighboring currents, if there are such. 



Using this theory, a good many persons have studied at various times 

 the magnetic properties of different large masses of iron, and in 1893 

 Professor Thomas Gray of Terre Haute published in the Philosophical 

 Transactions of the Royal Society a long series of very beautiful 

 current curves, 6 obtained, with simple apparatus handled with great 

 skill, from a 40 K. W. transformer belonging to the Rose Polytechnic 

 Institute. A number of diagrams 7 showing the manner of growth of 

 currents in the exciting coils of large electromagnets with solid cores 

 have been printed within the last dozen years ; of these the curves 

 given by Dr. "W. M. Thornton are especially interesting. 



If to the coil of an electromagnet, in series with a rheostat of 

 resistance r, a given electromotive force be applied, and if r be then 

 reduced by steps, at intervals so long that one is sure that the final 

 current belonging to each stage has been practically attained, the 

 curve which has elapsed times for abscissas and the corresponding 



6 T. Gray, Phil. Trans., 184, 1808. 



7 Hopkinson and Wilson, Journal of the Institute of Electrical Engineers, 24, 

 1895. Thornton, Electrical Engineer, 29, 1902 ; Phil. Mag., 8, 1904 ; Electrician, 

 1903 Peirce, These Proceedings, 41, 1906. Several figures from this last paper 

 are here reproduced. 



