112 pkoceedings of the american academy. 



The Uses of Exploring Coils wound upon the Core of an 



Electromagnet. 



If an electromagnet, in addition to its exciting coil, has another 

 wound about its core, and if the observer has means of obtaining the 

 intensity (/') of the current induced in this secondary coil, for given 

 current changes in the exciting coil, as a function of the time, it is 

 easy to study the magnetic properties of the core under the circum- 

 stances of the experiment. Let there be n' turns in the secondary coil, 

 let the resistance of its circuit be r' ohms, and let N' be the total in- 

 duction flux, in maxwells, through the turns of the coil at the time t, 

 then if I' is measured in amperes 



dN' 



^ = -10.././'. (13) 



If ^' be plotted against the time in a curve in which V centimeters 

 parallel to the axis of abscissas represent one second and an ordinate 

 m' centimeters long one ampere, and if A' 1^2 represents the area 

 between the curve, the axis of abscissas and the ordinates correspond- 

 ing to the time ti, and t^, we have in absolute value, 



iV/ - N^ = 10« • r' fr ■ dt = ^^^'''j'/f'^' = c/ ■ A\„ (14) 



h 



where q' is a known constant. 



When the primary current (/) in the exciting coil is growing, the 

 current in the secondary coil has a direction opposite to that of /, and 

 it is often desirable to emphasize this fact in a diagram by drawing 

 the i, t and /', t curves on opposite sides of the axis of abscissas ; but if 

 the relative values of i and /' are alone to be considered, it is some- 

 times more convenient to disregard their relative directions. If in any 

 case the current in the exciting coil of an electromagnet be made to 

 grow in the manner indicated by curve U in Figure 4, the i', t diagram 

 will consist (Figure 9) of a set of detached areas on the t axis. The 

 sum of any number of these areas when multiplied by 10^ r'/l' m' 71' 

 gives approximately the whole change in the induction flux through 

 the core up to the corresponding time, from the outset. In the "step- 

 by-step " ballistic method of determining the permeability of a closed 

 ring of rather small cross section the areas represented by the shaded 

 portions of Figure 9 are determined by discharging the induced 

 current through a calibrated ballistic galvanometer of long period, and 

 assuming that the first elongations of the suspended system measure 



