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PROCEEDINGS OF THE AMERICAN ACADEMY. 



in the electromotive force applied to it, the change in the current and 

 therefore the change in the field in the iron caused by the current can- 

 not be made instantaneous, even if eddy currents be wholly shut out, 

 and, though dividing up the core has its effects, we cannot expect them 

 to be so striking as in the case where the exciting circuit is open. 



Let us consider a very long, uniformly wound solenoid consisting of 

 N turns of insulated copper wire per centimeter of its length, wound 

 closely upon a long, soft iron prism of square cross-section (2 a X 2 a) 



— & 



TIME 



Figure 33. The toroid (DN) and the electromagnet (TP), with its jaws 

 separated by a gap of about eight centimeters, were placed in parallel across 

 the poles of a storage battery, with an oscillograph in the electromagnet branch. 

 OJY shows the manner of growth of the current in TP and DCZ the manner 

 of decay of the current when the battery circuit was suddenly broken. If, 

 after the ciu"rents in the circuit have become steady, a block of iron was sud- 

 denly dropped into the gap in the core of the electromagnet, the induced cur- 

 rent took the form GT. 



built up compactly of a large number of straight, varnished filaments or 

 " wires " of square cross-section (c X c), with their axes parallel to that 

 of the prism, which shall be used as the z axis. The electric resistance 

 of the solenoid per centimeter of its length parallel to the z axis shall 

 be w, the constant applied electromotive force per centimeter of the 

 axis shall be -E, and the intensity of the current in the coil shall be 

 C.^ Within the core, the magnetic field (H) will have everywhere 

 and always the direction of the axis of the prism, and if q is the cur- 

 rent flux at any instant at any point in the iron, p the specific resis- 

 tance of the metal, and fi its magnetic permeability, which for the 

 present purpose shall be regarded as having a fixed uniform value, 

 gx = 0, qy = 0, H^ = (\ ff, = (), Hz=H, 4 7r^ = Curl^, 



■* Peirce, These Proceedings, 43, 5, 1907. 



