118 PROCEEDINGS OF THE AMERICAN ACADEMY. 



"Electrodynamisches Potential/'^Oand 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 ^^ 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 iV 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, Zi, the ratio of N to the current, L^, and the ratio, to P, of 

 twice the contribution (7") made by the current to the energy when 

 there are no other currents in the neighborhood, Lz, so that 



T (fl 1,T T T T dN 



(15) 



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 Lx is the slope of the 

 curve or the tangent of the angle XKP ; the value of X2 at P is the 

 slope of the line OP or the tangent of the angle XOP; the value of Z3 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 N 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 



" Neumann, Abh. d. Berl. Akad., 1845. 

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



