626 LENZ ON ELECTRO-MAGNETISM. 
In the same manner we find, if three series have not a more power- 
ful action than two 
c=3(y =P), 
i.e. this happens when the length of the free ends is half as great as 
half the sum of the differences between the length of the first series and 
the lengths of the second and third series. 
Having thus proved that by increasing the series of convolutions we 
never obtain a maximum of the electric current, and therefore that a 
greater increase would only do harm, we proceed to the general consi- 
deration of the subject. 
We therefore suppose the convolutions of a series of the bespun me- 
tallic wire to lie thick on one another. Let the length of the space on 
which the convolutions may be wound up be = a, the thickness of the 
wire = 0b; let the thickness of the wire covered with silk surpass the 
thickness of the uncovered wire by the excess 6, so that it be = 6 + £, 
the length of a convolution be = ec, the lengths of the free ends of the 
wire = m; the number of convolutions then which can be wound in 
one series upon the armature is = Pat 3 and the length of the wire 
.c, and the whole length which the elec- 
of these convolutions = —“ 
56+ 6 
tricity has to run through tor one series of convolutions 
c+m. 
Le eed 
SOE BY 
If we assume the resistance offered by a wire of the same substance, 
whose length = 1, and whose thickness = 1, as unity, the resistance 
for one series of convolutions becomes 
oe _ac+(b+B)m 
TiMepATS IT Bee Bye 
Further, let the electromotive power produced in one convolution, 
which, according to the second and third of our laws above proved, 
remains the same for every magnitude of the convolutions and for 
every thickness of the wire, be called f; the electromotive power pro- 
duced in a series of convolutions is therefore, according to the first of 
the above laws, 
“tape 
and consequently the power of the electric current for a series of con- 
volutions, or 
abe f 
ac+(b+6)m 
We must now for our purpose express the length of a convolution or ¢ 
Pai a 
