The third voyage of Captain James Cook began on the 11th of June 1776. The map on the stamp shows the course of the expedition between March and October 1777. It is primarily concerned with the northern limits of his expedition.

March 7: Sighted New Albion, Drake's name for the west coast of  North America.
August 3: 62° 34´ N 192° 30´E
August 9: Named Cape Prince of Wales, 65° 46´N 191° 45´E, the extreme western extremity of the North American continent.
August 15: Named Icy Cap, 70° N 198° 20´ E
August 17: Crossed the Arctic Circle
September 4:  “...time to think of leaving these northern parts....”
October 26: Sailed for Hawaii

The longitudes above are Cook’s, which were measured East from Greenwich.