[1] Rhind was appointed midshipman on September 3, 1838,[3] and between 1839 and 1841 he served in the Mediterranean Squadron aboard the frigate Ohio and the sloop-of-war Cyane.

[1] He then served aboard the sloop-of-war Warren in the West Indies in 1842–1843, then on the frigate Macedonian off the coast of Africa in 1843–1844, before attending the Philadelphia Naval School in 1844–1845.

He then served aboard the sloop-of-war St. Mary's in the East Indies in 1850–1851, before returning to the U.S. Coast Survey, where he remained until 1854,[4] receiving promotion to the rank of master on April 30, 1853.

[5] Rhind was commissioned as a lieutenant on February 17, 1854,[5] and served on the sloop-of-war John Adams in the Pacific Squadron,[1] but in May 1855[6] was court-martialed after a disagreement with his commanding officer, and left the Navy in September 1855.

[3] Later, after commanding the gunboat Paul Jones and the screw frigate Wabash, he assumed command of the sidewheel gunboat Agawam in the North Atlantic Blockading Squadron on October 23, 1863, and earned praise from Rear Admiral Samuel Phillips Lee for the "gallantry and endurance displayed" by hiss crew and him during an engagement with three Confederate artillery batteries at Deep Bottom on August 13, 1864.

[3] Rear Admiral David Dixon Porter, in his official report to the Navy Department, wrote; The American Civil War ended in April 1865.