This type of chair is often referred to as a Naval Chair.
Indeed Treve Rosoman discusses almost identical chairs, that belonged to Admiral Boscawen, in Some Aspects of Eighteenth Century Naval Furniture, published in Furniture History Vol. XXXIII, 1997. Added to this Nelson had a similar set of chairs on the Victory. This mahogany chair works by a concertina action. The side rails and stretchers are hinged in the middle so that when the caned seat, which is hinged to the back, is lifted the front rail of the chair will push flush to the back. As this is done the side rails and stretchers fold in towards the middle of the chair giving a folded depth of only 4 inches. The speed with which this type of chair can packed made it ideal for the Navy where it was necessary to clear the decks quickly in order to bring the guns into action. Whatever couldn't be moved quickly was often thrown overboard. Third to last quarter 18th century.
Dimensions set up are given.