Archibald Lang joined the Royal Navy in 1804. He was appointed Surgeon to the Cornelia in 1808  and obtained a degree in medicine in 1816.....
The following gentlemen have obtained the degree of Doctor in Medicine from the University of Glasgow, within the last twelve months: - Messrs. Thomas Nelson, Morrice Alexander, George Montgomery, and Archibald Lang, from Scotland; John Johnston, and Christopher Thornton, from Ireland; Andrew Dick, from Scotland; William Owens Allen, from Ireland. 
Archibald Lang was employed as Surgeon Superintendent on the Lord Sidmouth in 1819. The Lord Sidmouth departed England on 27 September 1818 and arrived in Port Jackson 11 March 1819.
He died while serving at the Royal Naval Hospital, Jamaica on 21 April 1826, from having accidentally punctured his finger dissecting a dead body in the hospital.
Archibald Lang's Grave
Robert Baird a friend from Lang's youth visited his grave twenty years later -
In addition to the desire to see the Government works at Port Royal, I had this other inducement, that I anxiously wished to visit the spot where lie the remains of one of the best and earliest friends of my youth—the remains of the excellent and able Dr. Archibald Lang, M. D., for several years surgeon of the naval hospital at Port Royal; of whom it is truly said on the beautiful tablet erected to his memory by the naval and military officers then on the West Indian station, in Port Royal church, that -
He was the good Samaritan, the sick man's Comforter, and the poor man's friend.'
By one of those contingencies which strike the mind from their infrequency, I had, without any pre-arrangement, visited Lang's grave on the anniversary of his death. That day twenty years he had been called by his Maker to give an account of his stewardship, having died in consequence of a wound received in the discharge of his duty as hospital surgeon; and now, twenty years afterwards, I, who had in early life enjoyed much of his favour and well-remembered kindness, stood by his gravestone for the first time. Good, worthy, excellent Dr. Lang! it required not the anecdotes still told in this far-off place of your labours and repose; nor the flattering tribute to your worth and memory in the Naval Reminiscences of Captain Scott; nor even the handsome testimonial which your brother officers, of both services, have inscribed on your tombstone within the hospital gates, and again on the marble tablet on the walls of the church; to inform me of the fact that you were indeed one of the Pilgrims of Mercy, or that 'Of first-rate talent in the healing art, Unwearied zeal, benevolence of heart; For rich, for poor, alike for high and low, Your philanthropic heart felt pity's glow. But it was delightful to know that your character was so justly estimated by those who had the means of knowing, and the capacity for appreciating, your many and varied excellences of head and heart. 
Archibald Lang, M.D., Several Years Surgeon of the Naval Hospital, Port Royal, Died 21 Apl., 1826 - Erected by Vice Admiral Sir Lawrence W. Halsted, K.C.B., Commander in Chief and the Captains and Officers Employed Under His Command on the Jamaica Station - Commissioner T.G. Sutherland and Officers of the Civil Department R.N.,