He probably entered the King's or Marischal College, Aberdeen, in 1808, and received a Bengal cadetship in 1812.
Most of his service was regimental, part of it attached to the hill corps, of which his brother James Gilbert was surgeon, the 1st Nusseerabad battalion.
469–88, meteorological observations made hourly for the space of nearly two years; of ‘Account of the Climate and Agriculture of Subathoo and Kotguhr’ in ‘Edinburgh Journal of Science’ (1828), ix.
A joint paper by Alexander and Patrick, entitled ‘Account of a Journey through the Himalaya Mountains,’ appeared in ‘Edinburgh Philos.
‘A Journal of Meteorological Observations made in India from 1817 to 1829,’ by Patrick, forms British Museum Addit.