The induction coil is a step-up transformer with a non-constant EMF applied to the primary. The standard 19th century technique was to use a DC source of EMF, interrupted by an electrotome or repeater.  "Clock-work Electrotome. For the purpose of interrupting the circuit rapidly ... the instrument represented [at the right] is very convenient. ... It consists essentially of a bent copper wire, which , by means of clockwork..., is made to vibrate rapidly, dipping its ends alternately into two glass cups, intended to contain mercury...."     (from the 1851 edition of the Manual of Magnetism, pg 244, where the cost was $6.00 to $7.00)

   The two electrotomes below, like the one above, are in the Smithsonian Institution collection. The design is by Charles Grafton Page, who described them in an article in American Journal of Science in 1839; he called them vibrating armatures. They are not listed in any Davis catalogue in my possession, but show typical Davis construction traits. The current passes through the wire helix forming the electromagnet and then though one of the moving contacts to a mercury bath. This causes the armature to twist, the circuit is broken, and the armature is no longer attracted to the electromagnet. It relaxes back to its original position, the mercury contact is restored and the cycle repeats itself.