Port view of a small two masted vessel with fore and aft rig on both masts, the fore mast also having square rig top sails. The Union Jack is flying from the main mast yard. A small tender is tied to the stern. Nine people are visible on the deck. The Hornet is at anchor. The coastline is visible in the background and there is a stern view of another vessel to the left of the image. The Hornet appears to have 4 guns as there are 2 gun ports on the port side - this helps to identify the vessel as the 4-gun ex-Dutch hoy of 1794 rather than the 6-gun schooner of 1831 (see below).
The inscription on the back of the portrait suggests the Hornet was a schooner of 4 guns. However, the 4-gun Hornet was a 60-ton Dutch hoy, purchased by the Navy in 1794 as a gunboat but broken up at Sheerness in 1795. The schooner HM Hornet was 181 tons, had 6 guns and was launched at Chatham in 1831. This vessel was used for coastguard service before being broken up at Chatham in 1845.
Sources:
Lecky, H.S. (1914), The King's Ships, Vol.III, p.292
Jones, R. (nd), Rupert Jones List, H-M, p.706
Winfield, R. (2005), British Warships in the Age of Sail 1793-1817, p.324