ON THE INDUCTION-COIL. 



205 



If we take for iron in c. g. s. measure 



C= 1/9611, fi = 500, 



we get approximately 



r = T L J ffi 2 ; (9) 



so that for a wire of 1 mm. diameter r = -çôVïï secon d. It inay be 

 doubted whether this would be small enongh to prevent the eddy- 

 currents reacting injnriously upon the secondary circuit. 



We will now consider the third of the causes whîch impose a limit 

 upon the secondary spark, viz. want of suddenness in the break, sup- 

 posed for the présent to be unprovided with a condenser. After the 

 cessation of metallic contact the primary current is prolonged by the 

 formation of a sort of arc. the duration of which dépends among other 

 things, such as the character of the metals, upon the magnitude of the 

 current itself. If we again suppose the behaviour of the iron to be 

 idéal, we may treat the secondary circuit as a simple vibrator, upon 

 which acts a force ( U) proportional to the rate of fall of the primary 

 current. The équation of such a vibrator is, as usual, 



d 2 u du ' . ; 



_ + + (10) 



and the solution corresponding to u = 0 (no charge), dujdt = 0 (no 

 current), when t = 0, is ] ) 



u= 1 7 f e~ )*in ri (/— t') . Udt' (11) 



where 



n' = V{^—\f) (12) 



The various éléments of (11) represent in fact the effects at time t of 

 the velocities U dt' communicated [t — t') earlier. In the présent case we 

 are to suppose that U is positive throughout, and that f U dt' is given. 



The intégral simplifies in the case of % = 0, that is of evanescent 

 secondary résistance. We hâve then ri = n, and 



u == — I sin n (t — t ) . U dt' 



(13) 



') „Theory of Sound," vol. I, § 66. 



