588 Lord Rayleigh on the Induction- Coil. 



as the magnetism diminished, eddy -currents would tend to be 

 formed, and their importance for our purpose depends upon 

 their duration. If this be short, compared with the time- 

 constants of the secondary circuit, their influence may be 

 neglected. Otherwise the electromotive force of the falling 

 magnetism lags, and acts to less advantage. The time- 

 constant, viz., the time in which the current falls in the ratio 

 e : 1, for the principal eddy-current in a cylinder of radius R 

 is given by 



4tt^CR2 



(2-404) 2 ' W 



where C represents the conductivity and /x the permeability*. 

 If d be the thickness of a thin sheet having the same time- 

 constant as the wire of radius It, it is easily shown in the 

 same way that 



d : E=tt : 2*404. 



If we take for iron in C.G.S. measure 



0=1/9611, f* = 500, 



we get approximately 



T-^B'j ...... (?) 



so that for a wire of 1 mm. diameter t= ? J () - 5 - second. It 

 may be doubted whether this would be small enough to 

 prevent the eddy-currents reacting injuriously upon the 

 secondary circuit. 



We will now consider the third of the causes which impose 

 a limit upon the secondary spark, viz. want of suddenness in 

 the break, supposed for the present 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 depends 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 

 ideal, 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 equation of such a vibrator is, as 

 usual, 



_. + *_+A=U ; .... (10) 



and the solution corresponding to u = (no charge), du/dt = j 

 * Brit. Assoc. Bep. p. 446 (1882) ; Scientific Papers, ii. p. 128. 



