W Mr maxwell, ON FARADAY'S LINES OF FORCE. 



Putting A T for iV — - + -— we find • 



\R R I 



N n 



F 



The primary current increases very rapidly from to — , and the secondary commences at 



R 



F n 



- — , — and speedily vanishes, owing to the value of t being generally very small. 



The whole work done by either current in heating the wire or in any other kind of action 

 is found from the expression 



fPRdt 

 The total quantity of current is 



/ Idt. 

 For the secondary current we find 



Jo Rn" 4 Jg Rn 2 



The work done and the quantity of the current are therefore the same as if a current 



Fn 

 of quantity /' = ■ had passed through the wire for a time t, where 



T= 2iV 



In? n"^\ 



[-r^b)- 



This method of considering a variable current of short duration is due to Weber, whose 

 experimental methods render the determination of the equivalent current a matter of great 

 precision. 



Now let the electro-motive force F suddenly cease while the current in the primary wire 

 is /„ and in the secondary = 0. Then we shall have for the subsequent time 



R n 



p ' 



The equivalent currents axe. i /q and 4 ^o "Vv " > ^^^ their duration is t. 



K n 



When the communication with the source of the current is cut off, there will be a change 

 of R. This will produce a change in the value of r, so that if R be suddenly increased, the 

 strength of the secondary current will be increased, and its duration diminished. This is the 

 case in the ordinary coil-machines. The quantity N depends on the form of the machine, 

 and may be determined by experiment for a machine of any shape. 



