LENZ ON ELECTRO-MAGNETISM. 613 
In order now to find the resistance which the electric current suffers 
in its passage through the different wires, I first reduce their lengths 
all to one diagonal, and indeed to that of the wire of the multiplier, 
on the principle that two wires of the same metal offer then the same 
resistance to conduction when their lengths are in the same proportion 
as their diagonals (See Ohm’s G'alvanic Chain). In this case therefore 
the reduced lengths of the wires express their resistance to conduction: 
to have therefore a general idea of the problem, I suppose the mul- 
tiplier, the conducting wires, and the electromotive spirals (with their 
free ends) to have the three reduced lengths, L, ¢, and X, and the elec- 
tromotive power produced in the spirals to be represented by 2, then 
—__"_____ will be in effect the current which takes place, and we 
Ty) he 
therefore have 
x : 
P+TLA TP ain La 
x=(Let b+ A)tprsin. dam «6 oe (A) 
If we now consider the electromotive power in a convolution of the 
wire as unity, representing the unknown deviation produced by a con- 
volution by £, and its reduced length by (A); then granting the pro- 
bable hypothesis, that at one and the same distance of the convolutions 
the electromotive force is directly as the number of convolutions, the 
following relation will take place for the number 2, and for the reduced 
lengths ,, belonging to it (this is not necessarily 2 A, because the free 
ends of the spirals need not increase in the same ratio for every num- 
ber of convolutions) 
—(L +! + ())p'sin 3 & 
~ (L+l+4+2,) p'sin. da 
ath 
n 
therefore : 
: ee sins bE Pe 4:1) 
In the experiments just mentioned / + A continued of the same 
magnitude for every number of convolutions, as the conducting and 
spiral wire consisted of one piece, besides L remains the same, we 
therefore have L + 7 + (A) = L +7 + 2, and the equation B be- 
comes changed into the following : 
BSL he re SN ah Sis ath” oid (as! Sa 
If we now put instead of 4 « the values contained in the last column of 
our table of experiments, we obtain eleven equations, from which after 
the method of the least square, we shall be able to determine £, and if 
we bring this value of £ into the equation (C.), we shall find the devi- 
ations a belonging to the number of convolutions, and the differences 
between this and the observed values will show whether the assumed 
272 
- I = . 
sin. 5% = 2 
