PEIRCE. — MANNER OP GROWTH OF A CURRENT. 517 



In order to determine the manner of growth of the current in the coil 

 of the solenoid when the circuit is suddenly closed, it will be well to 

 follow the usual procedure in treating analogous problems in heat con- 

 duction, and inquire first how the coil current would decay if, after the 

 core has been uniformly magnetized by a steady coil current, the electro- 

 motive force were suddenly cut out of the coil without opening the circuit. 

 The solution of this problem furnishes immediately the solution of the 

 one first stated. Heaviside 1° has treated by this method a solenoid with 

 iron core 2 centimeters in diameter. If the coil is fairly thin, so that 

 substantially the whole flux of induction which threads its turns is the 

 flux in the core itself, we need not distinguish between L and L x in 

 equation (1 1) and since there is no electromotive force in the coil 



and by virtue of (3) 



The constant s is to be determined from the constants of the solenoid and 

 of the core, and we shall find it instructive to study the effect of a change 

 in s in a problem otherwise given. We will assume at first that JV, the 

 number of turns of wire in the coil per centimeter of the length of the core, 

 and w, the resistance in absolute units of the coil per centimeter of its 

 length, are such as to make s unity ; in the second case the value of s 

 shall be 2.5. The first is somewhat less, the second much greater than 

 the value which would most closely correspond to the magnet shown in 

 Figure 1. The field intensity, H, in the core must satisfy equations (6) 

 and (23) at every instant, and, when t = 0, must be equal to If for all 

 values of r. 



The special solution, 



of (G), in which 



A e-* 2 * • J (n r), (24) 



2 p ( n a Y 



Arrfjia 



2 ' 



10 Heaviside, Electrical Papers, 1, 394. 



