Davidson was educated at Marischal College, where he studied second and third year classes from 1819-1821,[2] including lectures from Professor Patrick Copland.

Davidson staged an exhibition of electrical machinery at Aberdeen, Scotland, and in Edinburgh, where it was viewed on 12 February 1842 by the young James Clerk Maxwell.

[2] Among the machines shown were his locomotive, an electrically driven lathe and printing press, and an electromagnet capable of lifting 2 tons.

He designed his own chemical batteries to provide power and, being a practical man, was enthusiastic about the potential of electromagnetism to drive machinery.

By 1839 he had designed a printing press, a turning lathe and a four-wheeled car that all used Davidson's batteries and rudimentary electric motor.

He built a full size locomotive, Galvani of 1842, which was a four-wheeled machine, 16 feet long and powered by Davidson's batteries.

[2] In 1840, the Aberdeen Banner had predicted that the type of machinery he was producing "will in no distant date supplant steam"; however, it was only when electric locomotives were introduced in the 1890s that the media came to recognize what he had done.