Chapter VII.
The Mathematical Electricians of the Middle of the Nineteenth Century.
While Faraday was engaged in discovering the laws of induced currents in his own way, by use of the conception of lines of force, his contemporary Franz Neumann was attacking the same problem from a different point of view. Neumann preferred to take Ampère as his model; and in 1845 published a memoir,[1] in which the laws of induction of currents were deduced by the help of Ampère's analysis.
Among the assumptions on which Neumann based his work was a rule which had been formulated, not long after Faraday's original discovery, by Ennil Lenz,[2] and which may be enunciated as follows: when a conducting circuit is moved in a magnetic field, the induced current flows in such a direction that the ponderomotive forces on it tend to oppose the motion,
Let ds denote an element of the circuit which is in motion, and let Cds denote the component, taken in the direction of motion, of the ponderomotive force exerted by the inducing current on ds, when the latter is carrying unit current; so that the value of C is known from Ampère's theory. Then Lenz's rule requires that the product of O into the strength of the induced current should be negative. Neumann assumed that this is because it consists of a negative coefficient multiplying the square of C; that is, he assumed the induced electro- motive force to be proportional to C. He further assumed it to be proportional to the velocity v of the motion, and thus obtained for the electromotive force induced in ds the expression
,
where ε denotes a constant coefficient. By aid of this formula,
