MEASUREMENT, CARTOGRAPHY, AND THEORY, 1500–1800
It is characteristic of our history that a gap, almost entirely
unbridged, exists between the early period and the sixteenth century
in the story of the development of methods of precision in determining
geographical position. We have already referred to early efforts to
estimate the size of the earth, and in this connection have mentioned
that simple instrument of unknown origin, the gnomon. Aristarchus
improved upon the mere upright rod whose shadow was measured, by
setting one upright in a bowl, the length of the rod and the radius of
the bowl being equal; by means of this instrument, which was called
the scaph, the angle of altitude could be read on a scale of circles
inscribed on the inside of the bowl. Among other early instruments were
the astrolabe, an invention attributed to Hipparchus, which served
mariners and others down to the seventeenth century; the diopter, which
appears to have resembled an alidade mounted on a stand, and may be
regarded as a prototype of the theodolite; and Ptolemy’s rods, or the
triquetum, in which a rod working upon two others, one vertical while
the other pointed to the observed object, enabled the angular zenith
distance to be read. It is true that some additions to this list of
instruments were made by, or for the benefit of, mediæval mariners
before the pregnant period about the beginning of the sixteenth
century. Thus the less cumbrous quadrant was early brought into use,
to the partial displacement of the circle of the astrolabe. The
cross-staff, for measuring the angle between the horizon and the sun,
is first described, so far as is known, in 1342.
[Illustration: Fig. 9.--Scaph.]
[Illustration: (Front.) (Back.)
Fig. 10.--Astrolabe.]
[Illustration: Fig. 11.--Quadrant.]
But it was not until the sixteenth century that the study of the
earth’s size and figure began again to attract attention. The fact
that it did so, and the interest that was thereafter maintained in
this investigation, stand in the first instance to the honour of
French science. The Spanish and Portuguese congress which attempted
in 1524 to lay down the boundary fixed under the Pope’s award as
separating the areas of Spanish and Portuguese dominion in the new
world--a line lying 370 leagues west of the Cape Verd Islands--failed
utterly; the length neither of a degree nor of a league could be agreed
upon. Jean Fernel (1497–1558) in France, however, made measurements
by calculation from the revolutions of a carriage wheel and by means
of quadrant observations, and reached a fair estimate of a degree. A
Dutchman, Willibrord Snell, who published his results in 1617, laid the
foundation of modern methods of survey by applying to the measurement
of an arc between Alkmaar and Bergen-op-Zoom the system of a series
of triangles and the trigonometrical computation of the distance.
During the century which intervened between the labours of Fernel and
of Snell, it is clear that interest was waking in the development of
precise methods of land-surveying, for the compass was probably first
applied to this work at the beginning of the period; in 1571 we find
Leonard Digges introducing in England an instrument which represented
the theodolite at an early stage; and Jean Pretorius at Wittenberg
in 1590, and Philip Danfrie in France in 1597, with his graphometer,
foreshadowed that most valued equipment for detailed survey work, the
plane-table.
[Illustration: Fig. 12.--Cross-staff.]
An arc was measured and the length of the degree calculated in
England by Richard Norwood in 1633–37. Important improvements in
instruments appear about this time. Thus François Vernier introduced
in 1630 the microscopic attachment named after him the vernier,
through which close and accurate reading of scales may be made. In
1643 appeared Torricelli’s barometer, and in 1648 Pascal, in France,
applied the principle of the difference of atmospheric pressure at
different elevations to the measurement of height above sea-level.
A little later follows the application of the telescope to surveying
instruments. In 1669 Jean Picard, measuring an arc in France, used a
quadrant fitted with a telescope in which crossed wires were inserted,
providing lines and a point (the intersection of the wires) in the
field of observation, for the purpose of ensuring accuracy. Meanwhile,
in 1657, Christian Huygens, a Dutch scientist, introduced (if he did
not actually invent) the pendulum clock; and Jean Richer, using one
in the course of astronomical work undertaken in South America for
the French Academy of Sciences, found that the pendulum regulated to
beat seconds in Paris failed to do so in Cayenne. This opened up the
problem of the deviation of the earth’s figure from the true sphere;
Sir Isaac Newton had argued such deviation to exist from mathematical
theory associated with the rotation of the earth, and Huygens himself
also investigated the question. Their conclusions, and that to be drawn
from Richer’s pendulum observation, represented the earth as an oblate
spheroid, or (in simpler expression) as somewhat flattened at the
poles, the polar diameter being shorter than the equatorial. On this
showing, a degree measured, let us say, in the north should be longer
than one measured nearer the equator; but J. and D. Cassini, in the
course of an extensive triangulation in France in 1684–1718, obtained
an opposite result. Their measurements were subsequently proved
inaccurate, but not before much controversy had arisen as to whether
the earth is a prolate spheroid (as their results would go to prove),
or oblate, as held by Newton and Huygens; and the French Academy had
despatched expeditions to Peru and to Lappland, there to measure
arcs for comparison. The Peruvian arc was measured by Pierre Bouguer
and Charles de la Condamine in 1735–45, in the face of difficulties
sufficiently reflected by the length of time occupied and by the fact
that they fell out over the work and published separate accounts of it;
the Lappland arc was worked out by P. L. M. de Maupertuis and his party
in 1736–37.
[Illustration: Fig. 13.--Davis’s Back-staff.]
[Illustration: Fig. 14.--Pretonius’s Plane-table.]
It may be noticed that the difficulties of Bouguer and De la Condamine
included troubles with untrustworthy instruments; but during the
following half-century, while geodetic work proceeded apace in France,
and was also carried on by measurements in South Africa, North America,
and Italy, instruments making for greater precision were being
designed.
[Illustration: Fig. 15.--Ramsden’s Theodolite.]
The instruments and data available during the sixteenth and
seventeenth centuries had been fairly effective in skilled hands for
the observation of latitude, but observations for longitude remained
very difficult. Regiomontanus had prepared ephemerides for 1474–1506,
and Columbus used them; Peter Apianus made a series for 1521–70, but
the results continued to be far from accurate till the appearance of
Kepler’s Rudolphine Tables in 1526. Harrison’s work on the chronometer
had been anticipated as early as 1530 by Gemma Frisius, who indicated
the possibility of using a clock in determining longitude; but even
Huygens’s clock was not found effective for this purpose. In 1735,
however, John Harrison’s first chronometer appeared, and afforded
the accurate measurement of time under varying conditions which is
essential to the calculation of longitude. About 1737 Jonathan Sission
produced a theodolite, and later in the century Ramsden’s greatly
improved theodolite (actually a pioneer instrument, greatly though its
type was afterwards modified in detail) was constructed and brought
into use in the trigonometrical survey of England and Wales, which was
begun in 1784.
[Illustration: Fig. 16.--Modern five-inch transit Theodolite.]
Meanwhile in this period cartography underwent an evolution from
ancient to modern methods. It is impossible here to attempt any
catalogue of even the principal cartographers, and the work of a few
must be taken as typical. In the earlier part of the period (sixteenth
century) the marine chart was still the most generally valuable of
the cartographer’s wares; but he was already extending his stock in
other directions. Thus Gerhard Kremer (1512–94), more famous under the
name of Mercator, is principally known for his chart of the world
on the familiar rectangular projection which bears his name; but his
other activities, besides the production of an atlas, included that
of maps of various special areas; and he carried out survey work
himself in Flanders as the basis of a map of that territory, which
he produced in 1540. Not only the projection named after him, but
also the secant conical, are usually attributed to Mercator. Edward
Wright, a mathematician of Cambridge, produced the first English
map on Mercator’s projection, which indeed has been stated to be
actually Wright’s own invention; on this map we should observe the
omission of various imaginary and erroneous details common to maps of
the period--notably the southern continent. But the renewal of the
study of map-projection was mainly owing to German mathematicians,
such as Werner of Nuremberg, and Apianus, in the first two decades
of the century. In Mercator’s work there are to be observed various
tendencies towards modern practice, such as the abolition of the old
small sketches or miniatures representing towns and divers other
subjects, and the introduction of symbols. On the other hand, the
period of the application of criticism by the cartographer to the data
before him was not yet come. Mercator was content to supplement data,
where imperfect, by imagination; and that tendency is to be observed
in other work of the period, as, for example, in the astonishing
conception of the hydrography of Africa set forth by F. Pigafetta in
1591. However, the application of criticism and prompt attention to
new sources of information soon became recognized as cartographers’
duties. Thus, Nicolas Sanson of Abbeville, who founded a famous
map-making establishment in 1627, made a common practice of citing
his authorities; and again, promptly upon the work of Jean Picard
(noticed above) and others, in the determination of positions from 1669
to the end of the century, there followed the production of a map of
France corrected according to these observations, which were also used
in other French publications. On some of these appears--first about
1674--the earliest rude representation of relief by hachures, though
the old practice of the cartographer, of drawing relief in a species
of perspective, and thereby making a molehill on his map out of a
mountain in nature, was by no means yet superseded. It was more than
half-a-century later that the cartographers hit upon the contour-line.
M. S. Cruquius adopted this method of showing relief on a chart of the
Merwede in 1728; P. Buache similarly showed the depths of the English
Channel in 1737; J. G. Lehmann used contours as the proper scientific
basis of hachuring in 1783, and a contoured map of France was produced
in 1791 by Dupain-Triel. The atlas of Germany, begun by a famous
cartographer of Nuremberg, Homann, and published in 1753, illustrates
successive stages in the evolution of hill-shading; for the earliest
map in the series, dating from thirty-five years earlier, shows the
first endeavour to differentiate the shading according to the steepness
of slope. In the meantime the use of maps had already been recognized
in some of the many special departments of geographical science from
which they are now inseparable. For example, the variation of the
compass had been mapped by C. Burrus early in the seventeenth century,
and was more effectively worked out by the famous astronomer E. Halley
in 1683. A. Kircher, again, took an early step in the department of
oceanography by mapping currents and other features of the oceans in
1665.
[Illustration: Fig. 17.--The World according to Mercator (1587).]
From what has been written above, it may be inferred, and justly so,
that Holland and France led the way in the development of cartography
from the sixteenth to the eighteenth century. But by the end of the
sixteenth century and throughout the seventeenth the mapping of most
of the western European countries was rapidly extended, as in Germany,
Austria, Switzerland, and Italy, in Denmark and Scandinavia, and in
the British Isles. German local mapping ranked high, as appears from
the collection in Ortelius’s Theatrum Orbis (1570) and from Mercator’s
map of Germany (1585), both of which show the superiority of the
cartographical material available for Germany. A large number of maps
were based on original survey work. As early as 1566 a map of Bavaria
by Philip Bienewitz, on a scale approximating (in terms of our survey)
to two and a quarter miles to an inch, gave the results of a regular
survey of remarkable accuracy for the period. Such was also the case
(to select an example at home) with Christopher Saxton’s atlas of
England and Wales (1574–79), in which the maps are about an inch to
three miles in scale. This work marked the beginning of an important
period in the history of British maps; Timothy Pont’s maps of Scotland
appeared about 1608, and John Speed’s, of the British Isles on about
the same scale as Saxton’s, in 1610. Hollar adopted a smaller scale
(about five miles to the inch) in his maps of England and Wales dated
1644. These were of service in the Civil War, and the importance of
military requirements in furthering the extension of organized survey
work--which will appear in its subsequent history--is early exemplified
in a survey of Ireland made under an Act of 1653; though this, the
first British cadastral survey, was not a preliminary but a result of
military operations, for it was made in connection with the parcelling
of Irish lands among those who took part in the suppression of Irish
rebellion. Again, the Scottish rebellion of 1745 led directly to a
survey under Captain (afterwards General) Roy in 1747. It may be added
here that in later cadastral work Ireland again took precedence of
Great Britain: the six-inch survey begun in the former country in 1825
was nearly finished when that of Great Britain was undertaken in 1840.
France continued to lead the way in cartography in the eighteenth
century. The maps of G. Delisle (1675–1726) and of J. B. B. D’Anville
(1697–1782) were not merely confined to local work; they also included
the presentation of cartographical material for distant lands selected
according to truer scientific criteria. Thus D’Anville’s map of Africa,
though preserving a few old inaccuracies, did away with details which
were purely imaginary, and boldly revealed the then practically
complete ignorance of the interior by representing it almost wholly
as a blank. We may contrast this with earlier maps of the continent.
Thus Waldseemüller (1516) showed waterways running parallel with the
west coast, from north to south, and showed no conception of the Congo.
Gastaldi (1564) marked the Zaire (Congo); but this and an east-flowing
river and a branch of the Nile all flowed from a great central lake,
Zembere. Mercator established a definite parting of the Nile, the
Zaire, and the east-flowing system, though his ideas were still far
from the truth.
English cartographers of the eighteenth century were inspired by the
over-sea expansion of the empire to much good work beyond the home
shores. Thus J. F. W. Desbarres in 1774–79 made use of the nautical
surveys of James Cook and others in his Atlantic and North-American
work. Thomas Jefferys produced West Indian and American atlases at
the same time, and Aaron Arrowsmith founded a famous cartographical
establishment, the work of which was carried on for a century. Mention
is also due here of the work of Major James Rennell, who became
surveyor-general of Bengal in 1763, and covered that territory in
his atlas of Bengal (1779) on a scale of five miles to one inch, the
work depending mainly upon route surveys and being, of its kind,
extraordinarily good. The trigonometrical survey of England and Wales,
already referred to as begun in 1784, owed its origin to French
inspiration; for Cassini de Thury, who in 1740 had re-measured and
found incorrect the work of J. and D. Cassini in France, represented
the desirability of establishing a geodetic connection between Paris
and Greenwich, and General William Roy was appointed to supervize the
English work.
The revival of interest in earth-measurement and survey led directly to
the furthering of the study of theoretical geography. We have happened
already upon the names of Peter Apianus and Gemma Frisius in the
history of the mathematical branch of geography; these two--Apianus by
publishing in 1524 his _Cosmographicus Liber_, and Frisius by editing
and expanding that work under the title of _Cosmographia_--re-founded
the science on a mathematical basis, though they remained bound to
the Ptolemaic view of a sharp distinction between geography, the
general description of the world, and chorography, the particular
description of a region. There is, perhaps, something characteristic
in the insistence on this curiously arbitrary distinction; there has
been sometimes a tendency to narrow the view of the field of “pure”
geography on the part of workers labouring in one corner of it and
turning their backs upon the rest. Indeed, at this very period is
found another _Cosmographia_, to which its author added the epithet
“universalis,” wherein the now familiar view of geography as a human
and political field of study appeared, to the no less familiar
exclusion of the mathematical aspect; for Sebastian Münster, in his
work published in 1544, neglected the mathematical side entirely,
modelling his work on that of Strabo. Philip Cluverius, again, in his
_Introduction to Universal Geography_ (1624), preserves the distinction
between geography and chorography, albeit but one out of his six
books deals with the earth at large, while in the rest countries are
treated in detail, the human aspect being closely studied. Nathanael
Carpenter of Oxford, however, threw over the distinction in so far
as he recognized that neither geography, as distinguished by earlier
writers from chorography, nor chorography itself, nor topography
(under which term were classified the closer descriptions of smaller
areas than those which belonged to chorography), was anything more
than a part of a whole. Therefore, he divided his _Geography_ (1625)
into “spherical” and “topical” parts, the first dealing with the
mathematical side, the second with different divisions of the earth
according to physical, not political, considerations; his work is thus
notable as indicating his realization of the function of geographical
study which follows from those of measurement and description--namely,
that of the correlation of phenomena. In 1650 appeared the _Geographia
Generalis_ of Bernhard Varenius, who died, still a young man, in that
year. He laid down a broad division of the subject into general and
special parts. His general part was sub-divided so as to include,
firstly, the shape, size, and general physical characteristics of the
earth, the distribution of land and water, land forms and hydrography;
secondly, the astronomical and mathematical aspects, such as zones,
latitude and longitude, the investigation of which was carried further
in the third sub-division, which was comparative, dealing in this
manner with data previously adduced. Varenius did not himself take up
the special part of geography, though he defined it as also falling
into three sub-divisions, the first of which should deal with the
position, boundaries, physical features, and natural products of a
country, the second with celestial and atmospheric conditions, and the
third with the human element. This last was (as it still is) a popular
branch of the subject which, for his own part, he would not have
admitted; he held pure geography to be a matter apart from political
and social considerations. But here was a geographical framework which,
as H. R. Mill has pointed out, “was capable of accommodating itself
to new facts, and was indeed far in advance of the knowledge of the
period.” Being so, its worth was by no means generally recognized at
first, although in 1672 Sir Isaac Newton put forth an annotated English
edition for use in connection with lectures of his own. “The method
included a recognition of the causes and effects of phenomena, as
well as the mere fact of their occurrence, and for the first time the
importance of the vertical relief of the land was fairly recognized.”
The work found its place in time; the French and Dutch geographers,
as well as the English, had it in their own tongues, and it became a
standard, not only for the century of its original production, but for
the next also.