PEIRCE. — CHANGES IN INDUCTANCES OF ELECTRIC CIRCUITS. 573 



dH 



dt 



P 



47ryu, 





*f) 



(34) 



When there are no eddy currents in the core, the intensity (//) of 

 the ma<,'netic field has at every point of the iron the boundary value 

 ffg = AttNC, but in general Ovaries from point to point. The flux 

 of magnetic induction through the turns of the coil per centimeter of 



TIME. 



Figure 34. Two electromagnets were placed in series with each other and 

 with an oscillograph and a storage battery, and a shunt (S) of small resistance 

 was provided for one of the magnets. OZ shows the form of the battery cur- 

 rent when S was closed, QK the fall of this current when S was suddenly opened 

 after the original current had become steady, and FG the rise of the current 

 to its old value when the shunt is again closed. 



its length parallel to the z axis and N times the induction flux through 

 the core are practically equal, and we may write 



or, 



3 practically equal, and we may write 



TT -\T n r* f 'ATT •\1TT\ 



„_ w ■ Hs 



47ri\r' 



^ ^ wHs fipN 



4 ttN infji. 



J J [da- + ^ j^^^^' 



(35) 

 (36) 



where the integration extends over a cross-section of the core. 



The vector JI is always perpendicular to its curl, and the intensity 

 of the component of the current at any point in the iron, in any direc- 

 tion s, parallel to the a^i/ plane at any instant, is equal to 1/4 tt times 

 the value at that point, at that instant, of the derivative of ^ in a 

 direction parallel to the a'j/ plane, and 90° in counter clockwise rota- 

 tion ahead of s. 



