ON FARADAY'S LINES OF FORCE. 225 



Putting T for JV (# + 1^) we &&& 



y a 

 I= 7t( l ~* T )' 



/ Of 



r F n ~ 

 #/i 



The primary current increases very rapidly from to -^ , and the secondary 

 commences at -f - an( ^ speedily vanishes, owing to the value of r being 



.ft 71 



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 



fOO 



PRdt. 

 Jo 



The total quantity of current is 



" Idt. 



1 o 

 For the secondary current we find 



i 1 4' J, Rn 2* 



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

 if a current of quantity F = jrr- had passed through the wire for a time T, where 



'_ v i 71 



T = 



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 subse- 

 quent time 



a r /?' a 



/-TV 7 /- _ e ~T 



' "~7P e 



VOL. I. 29 



