If we now change the number of elements in the battery E, the current intensity 7, measured by the galvanometer (?, will be altered according to Ohm's law,
where E is the potential difference between the anode and cathode, and R is the electrical resistance of the solution in
the trough. According to the ordinary laws of electric forces
++ the positively charged Zn ions pass from places at higher
potential to places at lower potential, and the negatively
charged SO4 ions travel in the opposite direction.
According to the doctrine of potential, the motive force for
a substance carrying unit charge is the fall of potential per
E unit of length -v, where I is the distance between the electrodes.
For an ion with the charge e, the motive force is therefore
Ee
~Y (compare p. 6). Let us assume for the moment that the
SO4 ions remain at rest, and that only the Zn ions trans- port electricity. If JF is doubled, the quantity of elec- tricity transported through the cross section Y in unit of time, will also be doubled. The quantity of electricity passing through the section Y of the electrolyte is bound to the zinc ions which travel in the direction from A to B. If, therefore, using the first current, all the zinc ions, which at time are between section Y and Y\, after one second — is, at time 1 — have wandered through the cross. section F, then, using the second current, double as many zinc ions must have passed across the section Y after one second, i.e. all the zinc ions which at time were contaiaed between the cross sections Y% and Y, if the distance F2F = 2FiF. In other words, in the first case the zinc ions which at time lie at Fa have passed in one second from Fa to Fi, in the second case from Fa to F. The velocity of the zinc ions is therefore
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