and the Theory of the Induction-balance. 137 



of a and /3, viz. 



while 



and accordingly we get as the value of the primary curreni(26), 



'-SO+^K^***'^}- (32) 



The last term in these brackets decreases at a nearly infinite 

 rate ; hence the primary current jumps almost suddenly from 



IT 1 

 the value ^> to the value 



BV+8' {66) 



and then increases (or decreases, as the case may be) at a 

 more moderate pace, its subsequent values being given by 

 the equation 



The form of expression (32) when S is made very great is 

 noticeable, as it shows that the primary current in a wire coiled 

 up with a closed secondary is able to stop nearly as dead as if 

 the primary were doubled upon itself (6). It is 



E s t 

 *'=S«~ S (35) 



The value of the induced current under the same circum- 

 stances (viz. when the two circuits are coiled close together) 

 is easily obtained from (27), and is 



. E(S-E) __rs_t 



j=w+$y l{r+S) (36) 



If S = co , this is the current at instantaneous break, viz. 



i=r~ f< > (37) 



the same as (29) would have given; but if E=oo , it is the 

 current at make, viz. 



E _JL.t* 



