bbed and afterward fastened to
a straw so that it shall float upon the water, the needle will
instantly turn toward the pole-star; though the night be never so
dark, yet shall the mariner be able by the help of this needle to
steer his course aright. But no master-mariner," he adds, "dares
to use it lest he should fall under the imputation of being a
magician."[1] By the end of the 13th century the compass was coming
into general use; and when Columbus sailed he had an instrument
divided as in later times into 360 degrees and 32 points, as well as
a quadrant, sea-astrolabe, and other nautical devices. The astrolabe,
an instrument for determining latitude by measuring the altitude of
the sun or other heavenly body, was suspended from the finger by a
ring and held upright at noon till the shadow of the sun passed the
sights. The cross-staff, more frequently used for the same purpose
by sailors of the time, was a simpler affair less affected by the
ship's roll; it was held with the lower end of the cross-piece
level with the horizon and the upper adjusted to a point on a line
between the eye of the observer and the sun at the zenith. By these
various means the sailor could steer a fixed course and determine
latitude. He had, however, as yet no trustworthy means of reckoning
longitude and no accurate gauge of distance traveled. The log-line
was not invented until the 17th century, and accurate chronometers
for determining longitude did not come into use until still later.
A common practice of navigators, adopted by Columbus, was to steer
first north or south along the coast and then due west on the parallel
thought to lead to the destination sought.

[Footnote 1: Dante's tutor Brunetto Latini, quoted in THE DISCOVERY
OF AMERICA, Fiske, Vol. I, p. 314.]

[Illustration: THE KNOWN AND UNKNOWN WORLD IN 1450, SHOWING THE
VOYAGES OF COLUMBUS, VASCO DE GAMA, MAGELLAN, AND DRAKE]

With the revival of classical learning in the Renaissance, geographical
theories also became less wildly imaginative than in the medieval
period, the charts of which, though beautifully colored and highly
decorated with fauna and flora, show no such accurate knowledge
even of the old world as do those of the great geographer Ptolemy,
who lived a thousand years before. Ptolemy (200 A.D.), in company
with the majority of learned men since Aristotle, had declared
the earth to be round and had even estimated its circumference
with substantial accuracy, th