He was the son of William B. Davidson, an artillery officer in the United States Army, and Elizabeth Chapman Hunter.

[9] During the 1850s, Davidson was stationed on the USS Dale as part of the Africa Squadron and Atlantic Anti-Slavery Operations of the United States to suppress the slave trade.

[12][11] In the 1850s, Davidson was also assigned duty for several years with the Coast Survey, a predecessor of what became the National Oceanic and Atmospheric Administration.

In 1856, Davidson was one of the officers selected to return the exploration vessel HMS Resolute to Queen Victoria and the Royal Navy.

[22][23] The organization was tasked with enforcing the state's oyster-harvesting laws and served as the predecessor of the modern Maryland Natural Resources Police.

[1][7] In the role, he conducted the first detailed hydrographic surveys of Argentine waterways, including the Bahia Blanca Estuary and Iguazu River.