Global Positioning System Reference
In-Depth Information
Great Circles
Another product of the school of navigation in Portugal during this period
was Pedro Nunes, a great mathematician who wrote the first mathematical
treatise on navigation—in the same decade that Frisius was contemplating
longitude. Frisius's student Mercator realized that the sailors of his day
were wrong in assuming that a straight line (shortest-distance) path across
the oceans required following a fixed compass course. Nunes had described
the
shape
of the fixed-compass course, the so-called rhumb line, or lox-
odrome:
18
it spiraled toward the poles because of the converging merid-
ians. In 1594 John Davis (the same Davis who has a quadrant named after
him) showed how mariners could sail a great circle route—the true short-
est path between two points on the surface of a sphere—by constantly
adjusting their bearings. This technique is obviously much more di≈cult to
implement in practice than simply following loxodromes, which were
straight lines on a Mercator map.
19
Some explorers may have known how to follow a great circle route
before Davis formally outlined the method. For example, Sebastian Cabot
seems to have followed such a route a century earlier in his explorations in
the North Atlantic.
20
(At the high latitudes of his expedition, great circle
routes can di√er markedly from rhumb lines.) Davis's achievement was to
publicize the method so that everyone could take advantage of it. By the
last decade of the sixteenth century, the mathematics of Mercator projec-
tions, rhumb lines, and great circles had been worked out, so that all
navigators knew how to change bearing depending upon their position and
thus follow a great circle, the shortest route between
A
and
B
.
Navigation was changing, moving from an art to a science. Navigational
instruments would follow a parallel course, from being the products of a
craft tradition to being the products of precision engineering. All the time,
empirical knowledge was being systematically built up. Now the French
got in on the act by developing
routiers
, known to the English as
rutters
—a
18. Technically,
rhumb line
refers to the course and
loxodrome
to the mathematical curve.
19. Mercator knew of Nunes's work, which appeared in a 1537 treatise, and studied it in
detail at Louvain. Edwin Wright, who was from the next generation of navigation theorists
and provided the mathematical underpinning for the Mercator projection, was also much
influenced by Nunes.
20. Sebastian Cabot was the son of John Cabot, the o≈cial European discoverer of North
America, in 1497. John Cabot also returned to his home port of Bristol, in southwest
England, with confirmation of the existence of rich fishing grounds—the Grand Banks o√
Newfoundland.
