PEIRCE. — BEHAVIOR OF THE CORE OF AN ELECTROMAGNET. 129 



growth of a current in the coil of an electromagnet which has such a 

 core, with that of a current in a circuit of fixed inductance, without 

 attempting at the outset to account mathematically for the differences, 

 though it will be easy to do so later on. 



In the case of a simple circuit, without iron, of resistance r ohms 

 and constant inductance, L henries, which contains a constant electro- 

 motive force of E volts, the rise of the current / when the circuit is 

 suddenly closed follows the law 



/=^(l-e-X), 



(16) 



and attains the fractional part k of its final value {E/r) in the time 



t = loge (1 — Jc), 



(17) 



which is independent of the ultimate current strength and involves 

 only the time constant (X/r) of the circuit. If the circuit is made 



FiGUKE 22. 



Curves which show the manner of growth of currents in a coil of 1394 turns 

 belonging to the magnet Q, to a given final value, when the applied voltages 

 were 82, 41, and 20.5, nearly. In each case the core was neutral at the outset. 



up partly of non-inductively wound resistance wire, and partly of 

 helices, r may be kept constant, while L is changed, by changing the 

 relative proportions of the two parts ; or r may be altered while L is 

 constant, by increasing or decreasing the non-inductive portion of the 

 circuit. 



rOL. XLIII. — 9 



