Welsh claim to the discovery of America—The story of Madoc—Believers in the tale—Origin of the traditions—Its first appearance—Early authorities for Madoc—Philological conjectures—Llwyd—Powel—Herbert—Were the Mexicans Welsh?—Stories of Welsh Indians—Morgan Jones—The Doegs—Stedman's figments—Griffiths—Evans—No Welsh Indians discovered—Antiquarian evidence lacking—Mexican rites—Explanation of the Madoc story—Madoc went to Ireland—Early navigation of the Welsh—Advance of English shipping—Relations with Norway—Scotland—Marco Polo and Mandeville—Trade with Iceland—Continuous intercourse—Did the English get further?—Macham discovers Madeira—Calamities befall him—First appearance of the story—Improbabilities—Nicholas of Lynn—The 'Inventio Fortunata"—The Ruysch map—The Zeni—"Zichmni," an Orkney man—Source of the Zeno story—The story—"Frislanda"—Nicolo Zeno, goes "Engroneland"—Tale of the fisherman—"Estotiland"—"Drogio"—Voyage of "Zichmni"—Difficulties of the narrative—Who was "Zichmni"?—Identification of names—"Frislanda" the Faröe Islands—Or Iceland—Mistakes of the younger Zeno—The people of Drogio—Identification of "Engroneland" difficult—The Zeno map—Its accuracy—A plagiarism—Evidence against the narrative.