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ELECTROMAGNETIC INDUCTION

Oersted's discovery of the compass deflection by the electric current had great theoretical importance. In the hands of Ampere, Gauss and Ohm it led to the under­standing of the magnetic fields produced by currents and the way they flowed through conductors. Electricity could now become a quantitative science and take over all the mathematical apparatus of mechanics. Nevertheless, in one important and puzzling respect the new laws differed from those of Newton. All the forces between .bodies, that he considered, acted along the line joining their centres; but here a magnetic pole moved at right angles to the line joining it to the current-carrying^wire. This was the first break from the simple scalar field theory, and opened the way to a more inclusive vector theory, where direction as well as distance counted. It was these physical discoveries that were to give a new impetus to mathematics.

Before the full interaction of electricity could be un­derstood still one more decisive step had to be taken. It had been shown how electric currents produced mag­netism; it remained to show how magnetjsm could pro­duce electric currents. This discovery, though it had to wait for another ten years, was not, like Oersted's, acci­dental. It was the result of a deliberately planned re-

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