the altitude of the pole being found frequently, as the estimated
distance run was imperfect. He devised an instrument
whereby to tell the hour, the direction of the ship’s head, and
where the sun would set. A very correct table is given of the
distances between the meridians at every degree of latitude,
whereby a seaman could easily reduce the difference of longitude
to departure. In the rules for finding the latitude by the
pole star, that star is supposed to be 5° from the pole. Martin
Cortes attributes the tides entirely to the influence of the moon,
and gives instructions for finding the time of high water at Cadiz,
when by means of a card with the moon’s age on it, revolving
within a circle showing the hours and minutes, the time of high
water at any other place for which it was set would be indicated.
Directions are given for making a compass similar to those then
in common use, also for ascertaining and allowing for the variation.
The east is here spoken of as the principal point, and
marked by a cross.
The third part of Martin Cortes’s work is upon charts; he laments that wise men do not produce some that are correct, and that pilots and mariners will use plane charts which are not true. In the Mediterranean and “Channel of Flanders” the want of good charts is (he says) less inconvenient, as they do not navigate by the altitude of the pole.
As some subsequent writers have attributed to Cortes the credit of first thinking of the enlargement of the degrees of latitude on Mercator’s principle, his precise words may be cited. In making a chart, it is recommended to choose a well-known place near the centre of the intended chart, such as Cape St Vincent, which call 37°, “and from thence towards the Arctic pole the degrees increase; and from thence to the equinoctial line they go on decreasing, and from the line to the Antarctic pole increasing.” It would appear at first sight that this implied that the degrees increased in length as well as being called by a higher number, but a specimen chart in the book does not justify that conclusion. It is from 34° to 40°, and the divisions are unequal, but evidently by accident, as the highest and lowest are the longest. He states that the Spanish scale was formed by counting the Great Berling as 3° from Cape St Vincent (it is under 212°). Twenty English leagues are equal to 1712 Spanish or 25 French, and to 1° of latitude. Cortes was evidently at a loss to know the length of a degree, and consequently the circumference of the globe. The degrees of longitude are not laid down, but for a first meridian we are told to draw a vertical line “through the Azores, or nearer Spain, where the chart is less occupied.” it is impossible in such circumstances to understand or check the longitudes assigned to places at that period. Martin Cortes’s work was held in high estimation in England for many years, and appeared in several translations. A reprint, with additions, of Richard Eden’s (1561), by John Tapp and published in 1609, gives an improved table of the sun’s declination from 1609 to 1625—the maximum value being 23° to 30′. The declinations of the principal stars, the times of their passing the meridian, and other improved tables, are given, with a very poor traverse table for eight points. The cross-staff, he said, was in most common use; but he recommends Wright’s sea quadrant.
William Cuningham published in 1559 a book called his Astronomical Glass, in which he teaches the making of charts by a central meridional line divided into equal parts, with other meridians on each side, distant at top and bottom in proportion to the departure at the highest and lowest latitude, for which purpose a table of departures is given very correctly to the third place of sexagesimals. The chart would be excellent were it not that the parallels are drawn straight instead of being curved. In another example, which shows one-fourth of the sphere, the meridians and parallels are all curved; it would be good were it not that the former are too long. The hemisphere is also shown upon a projection approaching the stereographic; but the eighteen meridians cut the equator at equal distances apart instead of being nearer together towards the primitive. He gives the drawing of an instrument like an astrolabe placed horizontally, divided into 32 points and 360 degrees, and carrying a small magnetic needle to be used as a prismatic compass, or even as a theodolite.
In 1581 Michael Coignet of Antwerp published sea charts, and also a small treatise in French, wherein he exposes the errors of Medina, and was probably the first who said that rhumb lines form spirals round the pole. He published also tables of declination of the sun and observed the gradual decrease in the obliquity of the ecliptic. He described a cross-staff with three transverse pieces, which was then in common use at sea. Coignet died in 1623.
The Dutch published charts made up as atlases as early as 1584, with a treatise on navigation as an introduction.
In 1585 Roderico Zamorano, who was then lecturer at the naval college at Seville, published a concise and clearly-written compendium of navigation; he follows Cortes in the desire to obtain better charts. Andres Garcia de Cespedes, the successor of Zamorano at Seville, published a treatise on navigation at Madrid in 1606. In 1592 Petrus Plancius published his universal map, containing the discoveries in the East and West Indies and towards the north pole. It possessed no particular merit; the degrees of latitude are equal, but the distances between the meridians are varied. He made London appear in 51° 32′ N. and long. 22°, by which his first meridian should have been more than 3° east of St Michael.
For Mercator’s great improvements in charts at about this date see Map; from facsimiles of his early charts in Jomard, Les Monuments de la géographie, the following measurements have been made. A general chart in 1569 of North America, from lat. 25° to lat. 79°, is 2 ft. long north and south, and 20 in. wide. Another of the same date, from the equator to 60° south lat. is 15·8 in. long. The charts agree with each other, a slight allowance being made for remeasuring. As compared with J. Inman’s table of meridional parts, the spaces between the parallels are all too small. Between 0° and 10° the error is 8′; at 20° it is 5′; at 30°, 16′; at 40°, 39′; at 50°, 61′; at 60°, 104′; at 70°, 158′; and at 79°, 182′—that is, over three degrees upon the whole chart. As the measures are always less than the truth it is possible that Mercator was afraid to give the whole. In a chart of Sicily by Romoldus Mercator in 1589, on which two equal degrees of latitude, 56° to 38°, extend 912 in., the degree of longitude is quite correct at one-fourth from the top; the lower part is 1 m. too long. One of the north of Scotland, published in 1595, by Romoldus, measures 1012 in. from 58° 20 to 61°; the divisions are quite equal and the lines parallel; it is correct at the centre only. A map of Norway, 1595, lat. 60° to 70°＝914 in., has the parallels curved and equidistant, the meridians straight converging lines; the spaces between the meridians at 60° and 70° are quite correct.
In 1594 Blundeville published a description of Mercator’s charts and globes; he confesses to not having known upon what rule the meridians were separated by Mercator, unless upon such a table as that given by Wright, whose table of meridional parts is published in the same book, also an excellent table of sines, tangents and secants—the former to seven figures, the latter to eight. These are the tables made originally by Regiomontanus and improved by Clavius.
In 1594 the celebrated navigator John Davis published a pamphlet of eighty pages, in black letter, entitled The Seaman’s Secrets, in which he proposes to give all that is necessary for sailors—not for scholars on shore. He defines three kinds of sailing: horizontal, paradoxical and great circle. His horizontal sailing consists of short voyages which may be delineated upon a plain sheet of paper. The paradoxical or cosmographical, embraces longitude, latitude and distance—the combining many horizontal courses into one “infallible and true,” i.e. what is now called traverse and Mercator’s sailings. His “paradoxical course” he describes correctly as a rhumb line which is straight on the chart and a curve on the globe. He points out the errors of the common or plane chart, and promises if spared to publish a “paradoxall chart.” It is not known whether such appeared or not, but he assisted Wright in producing his chart on what is known as Mercator’s projection a few years later. Great circle sailing on a globe is clearly described by Davis, and to render it more practicable he divides a long distance into several short rhumb lines quite correctly. From the practice of navigators in using globes the principles of such sailing were not unknown at an earlier date; indeed it is said that S. Cabot. projected a voyage across the North Atlantic on the arc of a great circle in 1495.
