118 PROCEEDINGS OF THE AMERICAN ACADEMY. 



"Electrodynamiscb.es Potential," 10 and that the different common defi- 

 nitions of self-induction, when applied to an electromagnet of the 

 usual form, really describe physical quantities which are widely 

 different from one another. The ambiguity in the use of the term 

 "self-induction" still exists, and it will be convenient in this paper to 

 adopt the notation used by Sumpner 11 in his article on " The Varia- 

 tions of the Coefficients of Induction." If, in absolute value, / is the 

 strength of a current growing in the coil of an electromagnet with 

 laminated core, if N is the total flux of magnetic induction through 

 the turns of the coil, and e the counter electromotive force of induc- 

 tion, we may call the ratio of e to the time rate of change of the 

 current, L iy the ratio of iV to the current, X 2 , and the ratio, to /", of 

 twice the contribution (T) made by the current to the energy when 

 there are no other currents in the neighborhood, L 3 , so that 



dl vr—TT t dN 



1 5 i 



If then for a particular magnetic journey, taken at a given speed, N is 

 given as a function of /in the form of a curve like OPQ in Figure 12, 

 the value, at any point P on the curve, of L x is the slope of the 

 curve or the tangent of the angle XKP ; the value of L 2 at P is the 

 slope of the line OP or the tangent of the angle XOP ; the value of X 3 is 

 the ratio of twice the curvilinear area OPD to the area of the square 

 erected on OJ. Similar definitions are sometimes given for such a 

 magnetic journey as is represented by the line MGPQ of Figure 13. 



In the paper just cited Sumpner gives a very interesting graphical 

 method of constructing a curve which shall show the manner of growth 

 of the current in the coil of the electromagnet when the curve which 

 connects iV T and / is given. 



The Electromagnets used in doing the Work 

 described below. 



A number of electromagnets were used in carrying on the experi- 

 mental work described in this paper. 



Though the investigation had to do primarily with magnets the 

 cores of which were laminated or otherwise finely divided so as to get 



10 Neumann, AMi. d. Berl. Akad., 1845. 



11 Sumpner, Phil. Mag., 25, 1888. 





