Ah, Your John Arbuthnot Home was a military man!
http://discovery.nationalarchives.gov.uk/details/r/C12749409Reference: WO 69/143/357
Description: Statements of Service, Royal Artillery 7 Battalion Numbers 3422 to 3897.
This entry appears on opening 390; this number is imprinted at the top right of each opening.
Soldier's Number 3777: John Arbuthnot HOME. Born High Church, Edinburgh, Midlothian. Enlisted 1854 aged 24 years. Note: Transferred to 12 Battalion 1855.
Covering dates indicate enlistment year. Date: 1854
Added: Something not quite right with the dates here, Alan. John Arbuthnot Home married Margaret McNeillie 1843 Edinburgh (from the Edinburgh grave stone, I think this is the one you're looking for). But if the same person was 24 in 1854 when he enlisted???