William Thomson (Lord Kelvin) mathematically demonstrates that the discharge of a capacitor (a Leyden jar) through a circuit with self-inductance produces an oscillating current, and defines the resonant-frequency equation of an LC circuit. This formulation underlies every tuned circuit built afterward, including spark and arc radio transmitters. In 1858, Berend Wilhelm Feddersen photographed the oscillatory sparks predicted by this theory using a rotating mirror, providing the first direct visual evidence of the oscillatory nature of the discharge — an intermediate step Hertz would draw on in 1887 to build his spark oscillator.