Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/210

the electromagnetic system of units, this factor does not occur in the equations here given.

544.] Helmholtz also deduces the current of induction when a conducting circuit and a circuit carrying a constant current are made to move relatively to one another.

Let $R_{1}$, $R_{2}$ be the resistances, $I_{1}$, $I_{2}$ the currents, $A_{1}$, $A_{2}$ the external electromotive forces, and $V$ the potential of the one circuit on the other due to unit current in each, then we have, as before,

If we suppose $I_{1}$ to be the primary current, and $I_{2}$ so much less than $I_{1}$, that it does not by its induction produce any sensible alteration in $I_{1}$, so that we may put $I_{1}={\frac {A_{1}}{R_{1}}}$, then

a result which may be interpreted exactly as in the case of the magnet. If we suppose $I_{2}$ to be the primary current, and $I_{1}$ to be very much smaller than $I_{2}$, we get for $I_{1}$,

This shews that for equal currents the electromotive force of the first circuit on the second is equal to that of the second on the first, whatever be the forms of the circuits.

Helmholtz does not in this memoir discuss the case of induction due to the strengthening or weakening of the primary current, or the induction of a current on itself. Thomson^[1] applied the same principle to the determination of the mechanical value of a current, and pointed out that when work is done by the mutual action of two constant currents, their mechanical value is increased by the same amount, so that the battery has to supply double that amount of work, in addition to that required to maintain the currents against the resistance of the circuits^[2].

545.] The introduction, by W. Weber, of a system of absolute

1. Mechanical Theory of Electrolysis, Phil. Mag., Dec., 1851.
2. Nichol's Cyclopaedia of Physical Science, ed. 1860, Article 'Magnetism, Dynamical Relations of,' and Reprint, § 571