The list of instruments given by Davis as necessary to a skilful seaman comprises the sea compass, cross-staff, chart, quadrant, astrolabe, an “instrument magnetical” for finding the variation of the compass, a horizontal plane sphere, a globe and a paradoxical compass. The first three are said to be sufficient for use at sea, the astrolabe and quadrant being uncertain for sea observations. The importance of knowing the times of the tides when approaching tidal or barred harbours is clearly pointed out, also the mode of ascertaining them by the moon’s age. A table of the sun’s declination is given for noon each day during four years 1593–1597, from the ephemerides of J. Stadius. The greatest given value is 23° 28′. Several courses and distances, with the resulting difference of latitude and departure, are correctly worked out. A specimen log-book provides one line only for each day, but the columns are arranged similarly to those of a modern log. Under the head of remarks after leaving Brazil, we read, “the compass varied 9°, the south point westward.” He states that the first meridian passed through St Michael, because there was no variation at that place, and therefore that this meridian passed through the magnetic pole as well as the pole of the earth. He makes no mention of Mercator’s chart by name nor of Cortes or other writers on navigation. Rules are given for finding the latitude by two altitudes of the sun and intermediate azimuth, also by two fixed stars, using a globe. There is a drawing of a quadrant, with a plumb line, for measuring the zenith distance, and one of a modification of a cross-staff using which the observer stands with his back to the sun, looking at the horizon through a sight on the end of the staff, while the shadow of the top of a movable projection, falls on the sight; this, known as the back-staff, was an improvement on the cross-staff. It was fitted with a reflector, and was thus the first rough idea of the principle of the quadrant and sextant. This remained in common use till superseded in 1731 by Hadley’s quadrant. The eighth edition of Davis’s work was printed in 1657.
Edward Wright, of Caius College, Cambridge, published in 1599 a valuable work entitled Certain Errors in Navigation Detected and Corrected. One part is a translation from Roderico Zamorano; there is a chapter from Cortes and one from Nunez. A year later appeared his chart of the world, upon which both capes and the recent discoveries in the East Indies and America are laid down truthfully and scientifically, as well as his knowledge of their latitudes and longitudes would admit. Just the northern extremity of Australia is shown.
Wright said of himself that he had striven beyond his ability to mend the errors in chart, compass, cross-staff and declination of sun and stars. He considered that the instruments which had then recently come in use “could hardly be amended,” as they were growing to “perfection”—especially the sea chart and the compass, though he expresses a hope that the latter may be “freed from that rude and gross manner of handling in the making.” He gives a table of magnetic declinations (variation) and explains its geometrical construction. He states that Medina utterly denied the existence of variation, and attributed it to bad construction and bad observations. Wright expresses a hope that a right understanding of the dip of the needle would lead to a knowledge of the latitude, “as the variation did of the longitude.” He gives a table of declination of the sun for the use of English mariners during four years—the greatest given value being 23° 31′ 30″. The latitude of London he made 51° 32′. For these determinations a quadrant over 6 ft. in radius was used. He also treats of the “dip” of the sea horizon, refraction, parallax and the sun’s motions. With all this knowledge the earth is still considered as stationary—although Wright alludes to Copernicus, and says that he omitted to allow for parallax. Wright ascertained the declinations of thirty-two stars, and made many improvements or additions to the art of navigation, considering that all the problems could be performed trigonometrically, without globe or chart. He devised sea rings for taking observations, and a sea quadrant to be used by two persons, which is in some respects similar to that by Davis. While deploring the neglected state which navigation had been in, he rejoices that the worshipful society at the Trinity House (which had been established in 1514), under the favour of the king (Henry VIII.), had removed “many gross and dangerous enormities.” He joins the brethren of the Trinity House in the desire that a lectureship should be established on navigation, as at Seville and Cadiz; also that a grand pilot should be appointed, as Sebastian Cabot had been in Spain, to examine pilots (i.e. mates) and navigators. Wright’s desire was partially fulfilled in 1845, when an Act of Parliament paved the way for the compulsory qualification of masters and mates of merchant ships; but such was the opposition by shipowners that it was even then left voluntary for a few years. England was in this respect more than a century behind Holland. It has been said that Wright accompanied the earl of Cumberland to the Azores in 1589, and that he was allowed £50 a year by the East India Company as lecturer on navigation at Gresham College, Tower Street.
The great mark which Wright made was the discovery of a correct and uniform method of dividing the meridional line and making charts which are still called after the name of Mercator. He considered such charts as true as the globe itself; and so they were for all practical purposes. He commenced by dividing a meridional line, in the proportion of the secants of the latitude, for every ten minutes of arc, and in the edition of his work published in 1610 his calculations are for every minute. His method was based upon the fact that the radius bears the same proportion to the secant of the latitude as the difference of longitude does to the meridional difference of latitude—a rule strictly correct for small arcs only. One minute is taken as the unit upon the arc and 10,000 as the corresponding secant, 2′ becomes 20,000, 3′=30,000, &c., increasing uniformly till 49′, which is equal to 490,001; 1° is 600,012. The secant of 20° is 12,251,192, and for 20° 1′ it will be 12,251,192+10,642—practically the same as that used in modern tables.
The principle is simply explained by fig. 5, where b is the pole and bf the meridian. At any point a a minute of longitude: a min. of lat.: : ea (the semi-diameter of the parallel): kf (the radius). Again ea: kf: :kf:ki: :radius :sec. akf (sec. of lat). To keep this proportion on the chart, the distances between points of latitude must increase in the same proportion as the secants of the arc contained between those points and the equator, which was then to be done by the “canon of triangles.”
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Fig. 5. |
Wright gave the following excellent popular description of the principle of Mercator’s charts; “Suppose a spherical globe (representing the world) inscribed in a concave cylinder to swell like a bladder equally in every part (that is as much in longitude as in latitude) until it joins itself to the concave surface of the cylinder, each parallel increasing successively from the equator towards either pole until it is of equal diameter to the cylinder, and consequently the meridians widening apart until they are everywhere as distant from each other as they are at the equator. Such a spherical surface is thus by extension made cylindrical, and consequently a plane parallelogram surface, since the surface of a cylinder is nothing else but a plane parallelogram surface wound round it. Such a cylinder on being opened into a flat surface will have upon it a representation of a Mercator’s chart of the world.”
This great improvement in the principle of constructing charts was adopted slowly by seamen, who, putting it as they supposed to a practical test, found good reason to be disappointed. The positions of most places in the world had been originally laid down erroneously, by very rough courses and estimated distances upon the plane chart, and from this they were transferred to the new projection, so that errors in courses and distances, really due to erroneous positions, were wrongly attributed to the new and accurate form of chart.
When Napier’s Canon Mirificus appeared in 1614, Wright at once recognized the value of logarithms as an aid to navigation, and undertook a translation of the book, which he did not live to publish (see Napier). Gunter’s tables (1620) made the application of the new discovery to navigation possible, and this was done by Addison in his Arithmetical Navigation (1625), as Well as by Gunter in his tables of 1624 and 1636, which gave logarithmic sines and tangents, to a radius of 1,000,000, with directions for their use and application to astronomy and navigation, and also logarithms of numbers from 1 to 10,000. Several editions followed, and the work retained its reputation over a century. Gunter invented the sector, and introduced the meridional line upon it, in the just proportion of Mercator’s projection. The means of taking observations correctly, either at sea or on shore, was about this time greatly assisted by the invention bearing the name of Pierre Vernier, the description of which was published at Brussels in 1631. As Vernier’s quadrant was divided into half degrees only, the sector, as he called it, spread over 14% degrees, and that space carried thirty equal divisions, numbered from 0 to 30. As each division of the sector contained 29 min. of arc, the vernier could be read to minutes. The verniers now commonly adapted to sextants can be read to 10 secs. Shortly after the invention it was recommended for use by P. Bouguer and Jorge Juan, who describe it in a treatise entitled La Construction, &c., du quadrant nouveau. About this period Gascoigne applied the telescope to the quadrant as used on shore; and Hevelius invented the tangent screw, to give slow and steady motion when near the desired position. These
