Early on, he developed a talent for mechanical invention and construction, following which he was apprenticed to the trade of ship building with Matthew Van Dusen, while also studying mathematics with his brother George Davidson.

At one time during the Civil War he conducted repairs of 42 vessels, both large and small, at the Philadelphia Navy Yard, and also built several new ships.

His greatest feat was the building, in 70 days, of the Juniata (1,240 tons, 7 guns) from the frame of a Florida live-oak frigate that had been seasoned for 23 years.

[1] Davidson displayed his engineering abilities in the floating of the Monongahela, which had been driven inland on Santa Cruz Island during the earthquake of 18 November 1867, and left stranded 40 feet (12 m) high.

[1] Subsequently, he was ordered on duty at the bureau of construction in Washington, and was busy with plans for developing a navy of armored vessels, torpedo boats, and fast cruisers.