The table below is compiled from three separate tables in the January 1840 Navy List: Medical Officers with the Dates of their Seniority; Alphabetical List of Medical Officers; and List of [the ships of] the Royal Navy, with their Present Positions. There is a (perhaps surprisingly small) number of inconsistencies between these tables; in these cases I have followed the last mentioned.

This list contains

• 11 Physicians (including the Physician General of the Navy, Sir William Burnett, whose title changed to Inspector-General of Naval Hospitals and Fleets on 25 January 1841, and to Director-General of the Medical Department of the Navy on 1 January 1844); as the Navy List does not give any position for eight of these Physicians, I assume these were all on half-pay
• 680 surgeons (111 in service afloat, 24 in service ashore, 248 on half-pay, 215 unfit for service, and 82 retired, of which 44 on a commuted allowance)
• 357 assistant surgeons (246 in service afloat, 29 in service ashore, 34 on half-pay, and 57 unfit for service)
• 8 dispensers (a defunct rank, now become a function performed by an Assistant Surgeon, or - at the larger hospitals - by a Surgeon, and often merged with that of medical storekeeper)
• 2 hospital mates (also a defunct rank, merged with that of assistant surgeon)

For a similar list for 1870 see here. That list reveals that of the 40 assistant surgeons who joined the Royal Navy in 1839, only 6 were still in service in 1870: one (John Davidson) had the rank of Inspector General, two that of Deputy Inspector General (Robert Pottinger and Henry Jones Domville); and three were Staff Surgeons (Frederick Harvey, David Lyall and William Loney; of which the last had the least seniority!).