Lord Rayleigh on the Induction- Coil. 583- 



vanishing when the primary and secondary circuits are 

 closely intertwined — the case of no " magnetic leakage/'' 



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 condenser, 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 present to regard the capacity as associated 

 with the terminals only of the secondary wire. Under these 

 circumstances the secondary current follows the laws laid 

 down by Kelvin in 1853, the same in fact as govern all 

 vibrations in which there is but one degree of freedom. If 

 the resistance is not too high, the current is oscillatory. After 

 the lapse of one quarter of a complete period of these 

 oscillations, the current vanishes, and the whole remaining 

 energy is the potential energy of electric charge. If the 

 resistance of the secondary wire can be neglected (so far as 

 its influence during this short time is concerned), the 

 potential energy of charge is the equivalent 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 these principles it is easy to calculate a limit for the 

 maximum potential-difference at the terminals 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 

 terminals, V the maximum potential-difference, the energy of 

 the charge is i'yV 2 , and this can never exceed the energy 

 of the primary current before break, viz., JLc 2 . The limit 

 to the value of V is accordingly 



V=w(L/ 2 ), (4) 



and it is proportional to the primary current. 



So long as the iron can be treated as ideal, the above 

 formula holds good, and upon the supposition of a sufficiently 

 sudden break there seems to be no reason why it should not 

 afford a tolerable approximation to the actual maximum value 

 of V. The proportionality between spark-length and primary 

 current was found to hold good in Walter's experiments over 

 a considerable range. 



When the core is very long in proportion to its diameter, 

 or when it approximates to a closed circuit, the behaviour of 



2Q2 



