LENZ ON ELECTRO-MAGNETISM. 629 
is attained by the current, 
P(maximum) a(3q ry pa IE =) Mis . . (E.) 
This expression again shows : 
1. That the maximum of the current stands in direct proportion to 
f, i. e., to the power of the magnet, or rather to the strength of the 
magnetism which is produced in the armature by the placing on of the 
magnet, and which again vanishes. 
2. The maximum is more powerful for a thick wire than for a slender 
one, for we can bring its expression to the form 
wy 2 
ss ned 
BTS 
which shows that the whole expression increases with the increase of 6. 
3. The maximum decreases with g, i. e. it becomes so much the 
smaller according to the greatness of the cylinder on which the first 
series of convolutions is wound, it being assumed that the armature 
does not on that account become greater. 
4. It becomes smaller with the increase of m, i. e. the greater the 
free connecting ends of the spirals are, the smaller-is the ultimate at- 
tainable maximum of the current. 
5. Finally, the maximum increases when a increases, i. e. when the 
space of the armature upon which a series of convolutions can be 
wound becomes greater. 
We shall consider the power of the current of a single convolution 
wound round the armature to be the same as m, then as soon as we 
put in the general expression (D.) for the current zm = 1,anda =6 + 6, 
we find hes of 
P (a convolution) R09 4b 2 OPaD (2 q + b+ B ) ae 
If we divide the expression for the maximum of the current (E.) by 
this, we may designate the quotients as the maximum of increase, and. 
find that 
2¢+(6+8) += a 
the maximum of the increase is ——————__,~—___—__ 
2q+2(b+ DT (= my 
_If I propose to find, for instance, with how many series of convolutions 
I attain the maximum of the current for my magnet and armature, 
when I take a length of 850 English inches for the wire of the multi- 
plier and the connecting wires together, I have 
a =1°6,b + B = 0:065 (wire No. 4) g = 0°335, m = 850. 
The formula x = / = gives for n = 13:07, and the formula (F.) 
a 
gives the maximum of increase = 114°8. We shall obtain therefore the 
