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, medi?val mariners before the pregnant period about92 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.
Fig. 9.—Scaph.

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(Back.)

Fig. 10.—Astrolabe.
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 under93 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.
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 Fran?ois 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 elevations94 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 with95 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 to96 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.
Fig. 13.—Davis’s Back-staff.
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.

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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 the98 trigonometrical survey of England and Wales, which was begun in 1784.
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 his99 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; and101 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 abo............