The geographical ideas which bear on this question depend, of course, upon the sphericity of the earth.[79] This was entertained by the leading cosmographical thinkers of that age,—who were far however from being in accord in respect to the size of the globe. Going back to antiquity, Aristotle and Strabo had both taught in their respective times the spherical theory; but they too were widely divergent upon the question of size,—Aristotle’s ball being but mean in comparison with that of Strabo, who was not far wrong when he contended that the world then known was something more than one third of the actual circumference of the whole, or one hundred and twenty-nine degrees, as he put it; while Marinus, the Tyrian, of the opposing school, and the most eminent geographer before Ptolemy, held that the extent of the then known world spanned as much as two hundred and twenty-five degrees, or about one hundred degrees too much.[80] Columbus’ calculations were all on the side of this insufficient size.[81] He wrote to Queen Isabella in 1503 that “the earth is smaller than people suppose.” He thought but one seventh of it was water. In sailing a direct western course his expectation was to reach Cipango after having gone about three thousand miles. This would actually have brought him within a hundred miles or so of Cape Henlopen, or the neighboring coast; while if no land had intervened he would have gone nine thousand eight hundred miles to reach Japan, the modern Cipango.[82] Thus Columbus’ earth was something like two thirds of the actual magnitude.[83] It can readily be understood how the lesser distance was helpful in inducing a crew to accompany Columbus, and in strengthening his own determination. Whatever the size of the earth, there was far less palpable reason to determine it than to settle the question of its sphericity. The phenomena which convince the ordinary mind to-day, weighed with Columbus as they had weighed in earlier ages. These were the hulling down of ships at sea, and the curved shadow of the earth on the moon in an eclipse. The law of gravity was not yet proclaimed, indeed; but it had been observed that the men on two ships, however far apart, stood perpendicular to their decks at rest.