INDUCTION COILS. 743 



1286. If a series of similar apparatus are arranged on the same 

 primary circuit, the problem will be determined, like the preceding, 

 by the aid of a series of differential equations (540) relative to each 

 of the transformers, and which should be satisfied at the same time : 



- 



at at 



M 2 + L' 2 -^ + R;i; = 0, etc. 



Instead of treating the general case, we may suppose simply that 

 all the transformers are identical, and that each of them has the 

 same useless resistance. 



The shunt-currents being equal, the result is the same as if all 

 the induced circuits were joined in series, without the addition of 

 fresh resistances. The expression for the efficiency is the same 

 as above, provided we consider b' and x as representing, in the 

 secondary wires, the total resistances of the transformers and of 

 the useful work. 



The effects are really more complicated, for we should consider 

 the coefficients of induction as functions of the intensities. 



1287. INDUCTION COILS. The induction coil is a true trans- 

 former, by which we endeavour to obtain, in the induced wire, 

 considerable electromotive forces, capable of producing long sparks, 

 of charging batteries, and reproducing the phenomena which are 

 realised by means of electrostatic machines. The primary current 

 is furnished by a constant electromotive force, and the induced 

 currents by the opening or closing of the primary circuit. 



These coils, as we know, are formed of a central cylinder of iron 

 wire, on which is coiled a stout wire, through which the primary 

 current passes, and then a secondary wire of far smaller diameter, 

 in which are formed the induced currents, and the windings of 

 which are carefully insulated, and terminate in two binding screws 

 forming the poles. 



The induced currents depend specially on the coefficient of 

 mutual induction M. We have seen (554) that the best conditions 

 are when the radius x of the core, the external radius y of the 

 primary circuit, and the radius z of the secondary circuit are to 



