Experiments with Alternating Currents, 249 



When 2 = 0, z 2 = ?" 0? substituting and manipulating, 



r 2 — kJj 

 Finally (7) becomes 



It will now be necessary to prove that i\ is a possible 

 function of t. It is needless to give the details, but it can 

 readily be shown that 



fi= ±r + -e Kt + -j — — <A W . . . (9) 



r 2 — k,u i KL — r 2 



Let k> ^, then an examination of (9) shows that r x is 



initially equal to — and continually increases with t. 



We may now, with safety, study the nature of the solution 



4) L \-ict , MqL .^. 



r 2 — «L r 2 — /eL 



differentiating, 



di 2 _ K 2 i ~L _ kt _ r 2 fcioL ~r± t 

 dt r 2 — k L L (r 2 — /cL ) 



When *=0, 



di 2 _ « 2 / L /ci r 2 



dt r 2 — kJj r 2 — kW 



the value of this when k is very great is approximately 



io r 2 

 — /e? H — y-. 



This result shows that if k is very great, i 2 initially diminishes 

 very rapidly. 



It is useless to give the details, but it can be shown that 

 the minimum value of i 2 is 



r 2 —tch r 2 —tcL 



If k=oo , the above becomes an indeterminate expression 

 the limiting value of which is zero, showing that if the coil (1) 

 is completely and rapidly broken, the current in coil (2) is, 

 under the given conditions, instantaneously diminished to 

 zero. 



