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 altitudes at sea. It was one of the few instruments possessed by Columbus and Vasco da Gama. The old cross-staff, called by the Spaniards “ballestilla,” consisted of two light battens. The part we may call the staff was about 1 in. square and 36 in. long. The cross was made to fit closely and to slide upon the staff at right angles; its length was a little over 26 in., so as to allow the “pinules” or sights to be placed exactly 26 in. apart. A sight was also fixed on the end of the staff for the eye to look through so as to see both those on the cross and the objects whose distance apart was to be measured. It was made by describing the angles on a table, and laying the staff upon it (fig. 1). The scale of degrees was marked on the upper face. Afterwards shorter crosses were introduced, so that smaller angles could be taken by the same instrument. These angles were marked on the sides of the staff.

To observe with this instrument a meridian altitude of the sun the bearing was taken by compass, to ascertain when it was near the meridian; then the end of the long staff was placed close to the observer’s eye, and the transversary, or cross, moved until one end exactly touched the horizon, and the other the sun’s centre. This was continued until the sun dipped, when the meridian altitude was obtained. Another primitive instrument in common use at the beginning of the 16th century was the (q.v.), which was more convenient than the cross-staff for taking altitudes. Fig. 2 represents an astrolabe as described by Martin Cortes. It was made of copper or tin, about in. in thickness and 6 or 7 in. in diameter, and was circular except at one place, where a projection was provided for a hole by which it was suspended. Weight was considered desirable in order to keep it steady when in use. The face of the metal having been well polished, a plumb line from the point of suspension marked the vertical line, from which were derived the horizontal line and centre. The upper left quadrant was divided into degrees. The second part was a pointer pt of the same metal and thickness as the circular plate, about 1 in. wide, and in length equal to the diameter of the circle. The centre was bored, and a line was drawn across it the full length, which was called the line of confidence. On the ends of that line were fixed plates, s, s, having each a small hole, both exactly over the line of confidence, as sights for the sun or stars. The pointer moved upon a centre the size of a goose quill. When the instrument was suspended the pointer was directed by hand to the object, and the angle read on the one quadrant only. Some years later the opposite quadrant was also graduated, to give the benefit of a second reading. The astrolabe was used by Vasco da Gama on his first voyage round the Cape of Good Hope in 1497; but the movement of a ship rendered accuracy impossible, and the liability to error was increased by the necessity for three observers. One held the instrument by a ring passed over the thumb, the second measured the altitude, and the third read off.

For finding latitude at night by altitude of the pole star taken by cross-staff or astrolabe, use was made of an auxiliary instrument called the “nocturnal.” From the relative positions of the two stars in the constellation of the “Little Bear” farthest from the pole (known as the Fore and Hind guards) the position of the pole star with regard to the pole could be inferred, and tables were drawn up termed the “Regiment of the Pole Star,” showing for eight positions of the guards how much should be added or subtracted from the altitude of the pole star; thus, “when the guards are in the N.W. bearing from each other north and south add half a degree,” &c. The bearings of the guards, and also roughly the hour of the night, were found by the nocturnal, first described by M. Coignet in 1581.

The nocturnal (fig. 3) consisted of two concentric circular plates, the outer being about 3 in. in diameter, and divided into twelve equal parts corresponding to the twelve months, each being again subdivided into groups of five days. The inner circle was graduated into twenty-four equal parts, corresponding to the hours of the day, and again subdivided into quarters; the handle was fixed to the outer circle in such a way that the middle of it corresponded with the day of the month on which the guards had the same right ascension as the sun—or, in other words, crossed the meridian at noon. From the common centre of the two circles extended a long index bar, which, together with the inner circle, turned freely and independently about this centre, which was pierced with a round hole. To use the instrument, the projection at twelve hours on the inner plate was turned until it coincided with the day of the month of observation, and the instrument held with its plane roughly parallel to the equinoctial or celestial equator, the observer looking at the pole star through the hole in the centre, and turning the long central index bar until the guards were seen just touching its edge; the hour in line with this edge read off on the inner plate was, roughly, the time. Occasionally the nocturnal was constructed so as to find the time by observations of the pointers in the Great Bear.

The rough charts used by a few of the more expert navigators at the time we refer to will be more fully described later (see also and ). Nautical maps or charts first appeared in Italy at the end of the 13th century, but it is said that the first seen in England was brought by Bartholomew Columbus in 1489.

Among the earliest authors who touched upon navigation was John Werner of Nuremberg, who in 1514, in his notes upon Ptolemy’s geography, describes the cross-staff as a very ancient instrument, but says that it was only then beginning to be generally introduced among seamen. He recommends measuring the distance between the moon and a star as a means of ascertaining the longitude; but this (though developed many years after into the method technically known as “lunars”) was at this time of no practical use owing to the then imperfect knowledge of the true positions of the moon and stars and the nonexistence of instrumental means by which such distances could be measured with the necessary accuracy. Thirty-eight years after the discovery of America, when long voyages had become comparatively common, R. Gemma Frisius wrote upon astronomy and cosmogony, with the use of the globes. His book comprised much valuable information to mariners of that day, and was translated into French fifty years later (1582) by Claude de Bossiere. The astronomical system adopted is that of Ptolemy. The following are some of the points of interest relating to navigation. There is a good description of the sphere and its circles; the obliquity of the ecliptic is given as 23° 30′. The distance between the meridians is to be measured on the equator, allowing 15° to an hour of time; longitude is to be found by eclipses of the moon and conjunctions, and reckoned from the Fortunate Islands (Azores). Latitude should be measured from the equator, not from the ecliptic, “as Clarean says.” The use of globes is very thoroughly and correctly explained. The scale for measuring distances was placed on the equator, and 15 German leagues, or 60 Italian leagues, were to be considered equal to one degree. The Italian league was 8 stadia, or 1000 paces, therefore the degree is taken much too small. We are told that, on plane charts, mariners drew lines from various centres (i.e. compass courses), which were very useful since the virtue of the lodestone had become recognized; it must be remembered that parallel rulers were unknown, being invented by Mordente in 1584. Such a confusion of lines has been continued upon sea charts till comparatively recently. Gemma gives rules for finding the course and distance correctly, except that he treats difference of longitude as departure. For instance, if the difference of latitude and difference of longitude are equal, the course prescribed is between the two principal winds—that is, 45°). He points out that the courses thus followed are not straight lines, but curves, because they do not follow the great circle, and that distances could be more correctly measured on the globe than on charts. The tide is said to rise with the moon, high water being when it is on the meridian and 12 hours later. From a table of latitudes and longitudes a few examples are here selected, by which it appears that even latitude was much in error. The figures in brackets