630 LENZ ON ELECTRO-MAGNETISM. 
maximum of the current at somewhat about thirteen series of convo- 
lutions, and the current then becomes about 115 timés 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 x series of convolutions, we shall then 
Serta: for a single convolution = CS QUnE ae 
2qr +7(b +B) 
of 
Iqu+a(O+B) 
bf 
2qr+n7r(b+ B) 
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 7 is quite a positive number). The 
expression of the current for a convolution may moreover be exhibited 
thus 
for a series of convolutions = 
for n series of convolutions = 
(2g+6+ /)7 
Be 
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 =o 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 phenomenon 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 formule, 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. 
