The following is the entry for Alexander Milne in William O'Byrnes 1849 'Naval Biographical Dictionary'.
MILNE. (Captain, 1839. f-p., 22; h-p., 8.)Alexander Milne, born in Nov. 1806, is second and youngest son of the late Admiral Sir David Milne, G.C.B., by his first wife, Grace, daughter of Sir Alex. Purves, Bart.
This officer entered the Royal Naval College 8 Feb. 1817; and embarked in 1819 on board the Leander 50, Capt. Edw. Chetham, bearing his father’s flag in North America. In June, 1820, we find him joining the Conway 26, Capt. Basil Hall; in which vessel, and in the Ramillies 74, and Ganges 84, both commanded by Capt. Edw. Brace, Albion 74, Capt. Sir Wm. Hoste, and Ganges again, Capts. Pat. Campbell and Sam. Hood Inglefield, bearing the flag for some time of Sir Robt. Waller Otway, he continued employed on the South American, West India, Home, and Brazilian stations, latterly as Mate and Acting-Lieutenant, until June, 1827. He then removed, in the capacity last mentioned, to the Cadmus 10, Capts. Chas. Gordon and Sir Thos. Raikes Trigge Thompson, also on the coast of Brazil; where he further served in that vessel (being confirmed to her by commission dated 8 Sept. 1827) until her return to England in April, 1830; on 25 Nov. in which year he was advanced to the rank of Commander. Obtaining an appointment, 26 Dec. 1836, to the Snake 16, Capt. Milne, on his arrival in that sloop in the West Indies, had the good fortune, during a cruize off the island of Cuba, to effect the capture, 23 Nov. 1837, of the Portuguese brigantine Arrogante having on board 406 slaves, and, 5 Dec. following, of the Matilda Spanish schooner, laden with 259 slaves. He was made Post, 30 Jan. 1839, into the Crocodile 26; and, in Nov. 1840, after having served in various parts of the North America and West India station (where he made prize of the Spanish slaver Mercedita, and had for some months charge of the Newfoundland and Labrador fisheries), he removed to the Cleopatra 26. In that vessel, when in the West Indies, he took, 27 Jan. 1841, the Secundo Rosario Spanish schooner, carrying 284 slaves. Returning, in the ensuing March, to the Crocodile, Capt. Milne continued in her, affording protection in the mean while to the fisheries in the river St. Lawrence, until paid off in Nov. of the same year. He was next, from 27 April, 1842, until April, 1845, employed in the Caledonia 120, as Flag-Captain to his father, Commander-in-Chief at Devonport: and from 7 Oct. 1846 until Dec. 1847 he officiated, in the St. Vincent 120, in a similar capacity under Sir Chas. Ogle, Port-Admiral at Portsmouth. Since the date last mentioned Capt. Milne has filled a seat at the Board of Admiralty. Agents – Messrs. Halford and Co.