of commerce during the same
period, direct our attention to the state of geographical science in the
sixteenth and seventeenth centuries.

We have already stated that the astrolobe, which had been previously
applied only to astronomical purposes, was accommodated to the use of
mariners by Martin Behaim, towards the end of the fifteenth century. He was
a scholar of Muller, of Koningsberg, better known under the name of
Regiomontanus, who published the Almagest of Ptolemy. The Germans were at
this time the best mathematicians of Europe. Walther, who was of that
nation, and the friend and disciple of Regiomontanus, was the first who
made use of clocks in his astronomical observations. He was succeeded by
Werner, of Nuremberg, who published a translation of Ptolemy's Geography,
with a commentary, in which he explains the method of finding the longitude
at sea by the distance of a fixed star from the moon. The astronomical
instruments hitherto used were, with the exception of the astrolobe, those
which had been employed by Ptolemy and the Arabians. The quadrant of
Ptolemy resembled the mural quadrant of later times; which, however, was
improved by the Arabians, who, at the end of the tenth century, employed a
quadrant twenty-one feet and eight inches radius, and a sextant fifty-seven
feet nine inches radius, and divided into seconds. The use of the sextant
seems to have been forgotten after this time; for Tycho Brahe is said to
have re-invented it, and to have employed it for measuring the distances of
the planets from the stars. The quadrant was about the same time improved
by a method of subdividing its limbs by the diagonal scale, and by the
Vernier. The telescope was invented in the year 1609, and telescopic sights
were added to the quadrant in the year 1668. Picard, who was one of the
first astronomers who applied telescopes to quadrants, determined the
earth's diameter in 1669, by measuring a degree of the meridian in France.
The observation made at Cayenne, that a pendulum which beat seconds there,
must be shorter than one which beat seconds at Paris, was explained by
Huygens, to arise from the diminution of gravity at the equator, and from
this fact he inferred the spheroidal form of the earth. The application of
the pendulum to clocks, one of the most beautiful and useful acquisitions
which astronomy, and consequently navigation and geography have made, was
owing to the ingenuity of Huygens. These are the principal di