630 LENZ ON ELECTRO-MAGNETISM. 



maximum of the current at somewhat about thirteen series of convo- 

 lutions, and the current then becomes about 115 times stronger than 

 when produced by one convolution. 



We will here separately consider the case in which m-=- o, i. e. 

 where the spirals have no free ends, but close in themselves. If we 

 put m = o in the expression of the current for one convolution, for one 

 series of convolutions, and for n series of convolutions, we shall then 



for a single convolution = i- 



2y7r+Tr(6 + ^) 



for a series of convolutions = J- 



2 97r+7r(6 + /3) 



for n series of convolutions = ^ 



whence it follows that here the current in one convolution is just as 

 strong as in a series consisting of any number of convolutions ; and 

 that in both these cases it is stronger than when several series of con- 

 volutions cross one another (for n is quite a positive number). The 

 expression of the current for a convolution may moreover be exhibited 

 thus / 



(2q + b+J)^ 

 b°~ 



i. e. it is equal to the electromotive power, divided by the resistance 

 offered by a convolution ; and in effect it is evident that in this case of 

 m z= a series of convolutions must act just in the same manner as a 

 single convolution; for with the increase of the number of convolutions 

 the electromotive power and the resistance become increased in the 

 same proportion, consequently the quotient of the one by the other, or 

 the electric current remains unchanged. It is also now evident that in 

 effect a second series of convolutions can only weaken the current, 

 since in the second series the electromotive power increases as in the 

 first, with the increase of the number of convolutions ; while, on the 

 contrary, the resistance is greater in the two series than double the 

 same in one series, on account of the enlarged diameter. 



But there is one phaenomenon of electro-magnetism to which all the 

 above positions however cannot yet be applied, namely, to the pro- 

 duction of the spark. This occurs then only, when the metallic con- 

 ductor of the current is disturbed at some place; there enters therefore 

 into the circular passage of the current an intermediate conductor, 

 whose length is almost indefinitely small, but whose resistance is almost 

 indefinitely great. We must therefore, in order to apply the above- 

 developed formulae, first be in a condition to reduce this intermediate 

 conductor to a certain length of wire, with the diameter of the wire 

 given, and thus to determine m ; — but for this reduction we are yet in 

 want of the data. 



INDEX. 



