PEIRCE. — MANNER OP GROWTH OP A CURRENT. 519 



of t ; when t = 0, the function is in the core everywhere equal to ff , and 

 when t is infinite, it vanishes. It is easy to see, therefore, that a function 

 //defined by the equation 



where H^ is a given constant, satisfies equations 



H a + s[D r H] r=a =H^ 



and (6), is everywhere equal to zero when t = 0, and, when t is infinite, 

 is everywhere equal to H^. Siuce a function which satisfies these con- 

 ditions is unique, (33) represents the strength of the magnetic field within 

 the core of the solenoid while it is being magnetized from a neutral state 

 to the uniform intensity H^ by a current (6') in the coil due to an electro- 

 motive force impressed in it. If N h the number of turns of wire in the 

 coil, Eihe applied electromotive force in the coil circuit, and w = w 1 + w" 

 the resistance of the coil circuit, all three per centimeter of length of the 

 solenoid, the coil current is given (11) by the equation 



E 

 w 



w a ^*4 1 + s 2 n p 2 \ 



C= (34) 



It is possible to hasten the growth of a current of given final value in 

 a simple circuit with fixed inductance (L) independent of the current 

 strength, by increasing the applied electromotive force (E), and adding 

 to the circuit a corresponding amount of resistance wound nou-inductively ; 

 for this process decreases the time-constant Ljr without changing Ejr. 

 The same statement is true in practice for almost every sort of electro- 

 magnet. 12 It is not easy to see immediately from equation (34), how- 

 ever, just what the effect on C is of a given change in w, for both n 

 and a involve w implicitly through s. 



Since H^ = 4 it N C^, we may rewrite (34) in the form 



e - cf "L 1 "^S(i+.v)J" 



(35) 



12 After this paper was in type I became acquainted with the results of the 

 elaborate study made by Professor T. Gray into the manner of growth of currents 

 in the coils of electromagnets with finely divided cores. The beautiful curves 

 which he gives in Volume 184 of the Philosophical Transactions of the Royal 

 Society illustrate very strikingly the fact here mentioned. 



