much more accurate measurement of a number of short lines,
or bases. Similarly, instead of determining direction by observ-
ing the position of a shadow at midday, or of a constellation in
the night sky, or even of a steady wind, use was made of
terrestrial magnetism through the magnetic compass, and
instruments were evolved which enabled horizontal angles to
be measured with great accuracy. Meanwhile the astronomers
showed that the earth is spherical, and that the position of any
place on its surface could be expressed by its angular distances
from the Equator (latitude) and a prime meridian (longitude),
though for many centuries an accurate and practical method
of finding longitude baffled the scientists.

The application of these astronomical conceptions, and the
extension of the knowledge of the world through exploration
and intercourse, encouraged attempts to map the known
world--but this introduced another problem: how to map a
spherical surface on a flat sheet. The mathematician came to
the rescue again--with his system of projections, by which
some, but not all, spatial properties of the earth's surface can
be preserved on a single map. Then the astronomers dis-
covered that the earth is not a perfect sphere, but is flattened
slightly at the Poles; this introduced further refinements, such
as the conception of geodetic as opposed to astronomical
latitudes, into the mapping of large areas, and great lines of
triangulation were run north and south across the continents
to determine the true 'figure of the earth', and to provide
bases for their accurate mapping.

Meanwhile, increasing demands were being made on the
map maker. The traveller or the merchant ceased to be the sole
user of maps. The soldier, especially after the introduction of
artillery, and the problems of range, field of fire, and dead
ground which it raised, demanded an accurate representation
of the surface features, in place of the earlier conventional or
pictorial delineation, and a solution in any degree satisfactory
was not reached until the contour was invented. This again
adds to the task of the surveyor who must run lines of levels
and sometimes go to the extent of pegging out the contour
lines on the ground. Then the archaeologist, the historian, and
much later, the modern geographer had their own special

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