In Search of the Castaways - Jules Verne

The book tells the story of the quest for Captain Grant of the Britannia. After finding a bottle cast into the ocean by the captain himself after the Britannia is shipwrecked, Lord and Lady Glenarvan of Scotland decide to launch a rescue expedition. The main difficulty is that the coordinates of the wreckage are mostly erased, and only the latitude (37 degrees) is known.
Lord Glenarvan makes it his quest to find Grant; together with his wife, Grant's children and the crew of his yacht the Duncan they set off for South America. An unexpected passenger in the form of French geographer Jacques Paganel joins the search. They explore Patagonia, Tristan da Cunha Island, Amsterdam Island, Australia and New Zealand in their search for the castaways. (summary from Wikipedia).