To sum up the geographical knowledge of the ancients, we have first, the sphericity of the earth surmised, although its size was vaguely conceived and underrated; secondly, the positive knowledge of Europeans limited to the unshaded portion of the map on page 73; thirdly, divers theories respecting the conformation of southern Africa; fourthly, a _mare oceanum_ stretching westward to the unknown Asiatic shore, with hypothetical islands intervening, and expressed opinions that this sea was navigable, and that possibly India might be reached by sailing westward. These ideas, vague as they seem, were held only by the learned few; the world of the ignorant reached scarcely beyond the horizon of their actual experience. Not until long after its actual circumnavigation, in the sixteenth century, was the popular mind able to grasp the idea of the earth's sphericity. * * * * * We come now to mediæval times, when from the fifth to the fifteenth century the cosmographical as well as all other knowledge of the ancients lay well-nigh dormant; to the people a land of darkness as well as a sea, though in some few colleges and convents these things were thought of. "Ces ténèbres," says Humboldt, _Exam. Crit._, tom. i. p. 59, "s'étendaient sans doute sur les masses; mais, dans les couvens et les colléges quelques individus conservaient les traditions de l'antiquité." Upon this world of darkness light first broke from the far north, the voyages of the Scandinavians from the ninth to the twelfth centuries being the _aurora borealis_ of maritime discovery. These Northmen, as in their expeditions Danes, Norwegians, and Swedes were indiscriminately called, by their warlike propensities made themselves known and feared along the shores of Europe at an early date; but their western discoveries were known only to themselves; at all events, no trace of distant voyages to the west are found in the records of their neighbors. It is only quite recently that the sagas of the Northmen were brought to the attention of European scholars; and when the Danish bishop, Müller, published his bibliography of the sagas, 3 vols., Copenhagen, 1817-1820, these narratives were held to be more fiction than fact. Even so late a writer as George Bancroft, _History of the United States_, vol. i. pp. 5, 6, says that the story of colonization by the Northmen "rests on narratives, mythological in form, and obscure in meaning; ancient, yet not contemporary," and that "no clear historic evidence establishes the natural probability that they accomplished the passage." Irving, _Columbus_, vol. iii. pp. 432-5, considers the matter "still to be wrapped in much doubt and obscurity." Both of these authors, however, seem to have considered only the evidence presented by Malte-Brun and Forster. Since their time proofs beyond question have established the authenticity of these voyages of the Northmen. The sagas on American discoveries are preserved in the