ON THE INDUCTION-COIL. 



190 



loss of energy at break — the energy of the primary spark — is 



vanishing when the primary and second ary circuits are closely inter- 

 twined — the case of no „magnetic leakage. 1 ' 



If we maintain the suppositions as to the behaviour of the iron and 

 the suddenness of the break, the above calculated secondary current 

 may be supposed to be instantaneously formed, even although the 

 secondary circuit be not closed. This is most easily seen when a con- 

 denser, such as a leyden-jar, is associated with the ends of the secondary. 

 Even when no jar is applied, the capacity of the secondary itself acts 

 in the same direction and allows the formation of the current. Whether 

 partly due to a jar or not, it will be convenient for the présent to regard 

 the capacity as associated with the terminais only of the secondary wire. 

 Under thèse circums tances the secondary current folio ws the laws laid 

 down by Kelvin in 1853, the same in fact as govern ail vibrations in 

 which there is but one degree of freedom. [f the résistance is not too 

 high, the current is oscillatory. After the lapse of one quarter of a 

 complète period of thèse oscillations, the current vanishes, and the 

 whole remaining energy is the pôtential energy of electric charge. If 

 the résistance of the secondary wire can be neglected (so far as its in- 

 fluence during this short time is concerned), the pôtential energy of 

 charge is the équivalent of the original energy of the secondary current 

 at the moment after the break. In the case of no magnetic leakage, 

 this is again the same as the energy of the primary current before 

 break. 



On thèse principles it is easy to calculate a limit for the maximum 

 potential-difference at the terminais of the secondary, or for the spark- 

 length, so far as this is determined by the potential-difference. For if 

 q be the capacity at the secondary terminais, V the maximum potential- 

 difference, the energy of the charge is \q V 2 , and this can never exceed 

 the energy of the primary current before break, viz., ^Lc 1 . The limit 

 to the value of V is accordingly 



\ 



(4) 



and it is proportional to the primary current. 



