In the above, Montezuma and his people looked upon themselves as the descendants of freemen and heroes who had not been subdued, who were the inhabitants of a small island in the north. The description very strikingly answers to the character, manners, and principles of the Welsh, and the place as the British Island. When Cortez came to their country, Montezuma was the eleventh emperor of Mexico in the Aztec line. Now, allowing an average reign to each emperor of twenty years, it will be found that Prince Madoc's arrival in this country will about coincide with the time of the establishment of this empire. This is also true with regard to the Peruvian empire. Atahualpa, who was treacherously and inhumanly put to death by the cruel and avaricious Pizarro, was the twelfth emperor of Peru in succession from Manco Capac. By the same method of calculation it will be seen that the dynasty of the Incas was established about the time of Madoc's arrival. In consequence of this, with many other proofs which cannot be introduced here, it has been maintained that he also was the founder of the Peruvian empire and civilization. John Williams, an author of no small repute, in his "Natural History of the Mineral Kingdom," vol. ii. p. 410, maintains that not only Mexico but Peru also was discovered by Madoc; that the few fair and white persons found there by the Spaniards were the descendants of Madoc's colony; and that Manco Capac and Mamma Ocello were Madoc and his wife. They are supposed to be the progenitors of the Peruvian Incas. As they were so different from the original natives in their complexions, they were thought to be the children of the sun; a sentiment which Manco might encourage for his own preservation. Mamma Ocello he thinks a corruption of Mamma Ichel, or Uchel, the Welsh for "high or stately mother." He gives it as his opinion that Madoc in his first voyage landed in the Gulf of Mexico, and that when he went back to his native country he promised those whom he left behind to return to them; but that in his second voyage he was driven by a storm from the north down as low as Brazil, and was shipwrecked near the mouth of the Amazon River; that he and his wife and the survivors sailed up that river; that after some time he arrived at Cuzco, the capital of the Peruvian empire; and that he never came to his first colony. He then assigns many reasons for his belief. It cannot be denied that some of those reasons are ingenious. The fact of Madoc or some of his followers having reached Peru is not denied; but they reached that country from the _western_, not the _eastern_, side of the continent. They went down the sea-coast west of Mexico to make explorations, or were carried against their choice by a storm to Peru, where they settled. Such a theory is in harmony with the foregoing pages, while it does not in any way conflict with the founding of that empire by Madoc.