The First Voyage Round the World/Pigafetta's Treatise of Navigation




The armillary sphere, of which the author gives a drawing, serves to explain the system of the world according to Ptolemy, and could also serve as an astrolabe, for one sees at the top of it a kind of handle or ring, by which to hold it suspended, as is seen in the above-mentioned drawing. He begins his treatise by giving us an idea of that system, as have done all those after him, who have written of the elements of the nautical art and of pilotage.

"The earth is round," he says, "and remains suspended and immovable in the midst of all the celestial bodies. The first index fixed on two poles, the arctic and antarctic, which are supposed to correspond with the poles of the earth. It runs from East to West, and transports with itself all the planets and stars. Besides this there is the eighth sphere, the poles of which are at 23 deg. 33 min.,[1] it runs from West to East.

"It is supposed that all the circumference of the earth is divided into 360 degrees; and each degree is of 17 leagues and a half, consequently the circumference of the earth is 6,300 leagues. Land leagues are of three miles and sea leagues of four miles.[2] "The ten circles of the armillary sphere, of which the six major pass through the center of the earth, serve to determine the situation of countries and climates. The Ecliptic determines the movement of the sun and the planets: the two Tropics indicate the point to which the sun declines from the equator towards the North in summer, and towards the South in winter. The Meridian, always variable, because it passes through all points of the equator, cutting it perpendicularly, designates the longitude, and it is on it that the latitudes are marked."

Of Latitude.

After having well explained the armillary sphere with all its parts, and their use according to the system of Ptolemy, the author goes on to teach the method of taking the altitude of the pole, on which the latitude is calculated; fixing the pole at 0° and the equator at 90°.

"The Polar star," he says, "is not precisely on the point corresponding to the axis of the earth; but it turns round it, as do all the other stars. In order to know its true position with regard to the pole, it must be observed where the Guard stars[3] stand. If these are on the western arm,[4] the polar star stands one degree above the pole: if they are on the line[5] the pole star stands 3 deg. 30 min.[6] below the pole: if they are on the eastern arm the pole star is one degree below the pole. When one wishes to take the altitude of the pole star, in whichever of the above-mentioned four places the Guard stars may be, the degrees which the pole star has above the pole will be subtracted from its altitude, or those which it has below the pole will be added to it. I have spoken in the account of the voyage of the stars of the Antarctic Pole.

"The latitude of the place may also be ascertained by the sun's altitude. 1. If you find yourself between the equinoctial and the arctic pole and the shadow falls towards that pole, look how many degrees and minutes meridianal declination the sun has that day; and this you will subtract from the altitude of the sun which you have taken: afterwards, deducting the remaining degrees from 90 deg., you will have in the residue the number of degrees of North latitude, that is your distance from the equator. 2. If the sun has a boreal declination, in such a manner that the shadow falls towards the south, take the sun's declination on that day, and add it to the sun's altitude which you have taken, from that sum subtract 90 degs., and the remaining degrees will indicate your boreal latitude. 3. If the sun is between the equinoctial and the antarctic, and the shadow falls towards the antarctic, observe the sun's declination for that day, subtract it from the altitude taken, according to the first rule, and you will have the degrees of south latitude. 4. If, when you and the sun are between the equinoctial and the antarctic pole, the shadow falls towards the north, you will add the altitude you have taken to the sun's declination that day, and act according to the second rule. 5. When you have an altitude of 90 deg., you will be so many degrees distant from the equator as there are degrees of the sun's declination, and if the sun has no declination you will be under the equator. 6. If you are to the north of the equator, and the sun is in the southern signs you will look what is its declination, you will add these degrees of declination to those of the altitude observed, and as many degrees as are wanting from 90 deg., so many will you be distant from the equinoctial. 7. You will do the same when you find yourself to the south of the equinoctial, whilst the sun is in the northern signs.

"Of Longitude.

"Longitude indicates the degrees from east to west: I have considered many methods or means for ascertaining it, and I have found three methods[7] fitting for that object. The last is the most convenient for those who do not know astrology. At the present time the pilots content themselves with knowing the latitude; and are so proud that they will not hear speak of longitude.

"i. From the latitude of the moon the longitude is calculated of the place in which the observation is made. The distance of the moon from the ecliptic is called its latitude: the ecliptic is the path of the sun. The moon, in its movement, always increases its distance until it reaches the furthest point of its distance: and thence it returns back, to diminish, so to say, its latitude, until it is with the head or tail of the dragon[8] there it cuts the ecliptic. And since the moon, whilst it lengthens its distance from the ecliptic, has more degrees towards the west than towards the east, it must necessarily have more latitude on one side (of the globe) than on the other: and when the latitude is known, by measuring the degrees and minutes with the astrolabe, it will be known whether it is found, and how far it is found towards the east or the west. But in order to ascertain the longitude, you must know in what latitude the moon ought to be at that same moment in the place from which you sailed, for instance, in Seville. By knowing the latitude and longitude of the moon at Seville in degrees and minutes, and seeing also the latitude and longitude which it has in the place where you are, you will know how many hours and minutes you are distant from Seville; and afterwards you will calculate the distance in east or west longitude.

"ii. The moon furnishes another method for ascertaining the longitude, but that is when I knew the precise hour in which the moon observed at Seville ought to be in conjunction with a given star or planet, or ought to be in a certain opposition to the sun, of which the degrees are determined: and this I can know by means of an almanack. And since that happens in the east before it happens in the west, as many as may be the hours and minutes that may elapse from the time when the conjunction took place at Seville, till the time in which I observe it to take place, so much will be my longitude west of Seville. But if I should see the conjunction take place before the hour in which it ought to happen with respect to Seville, then my distance in longitude will be east. For each hour, fifteen degrees of longitude are calculated.

"To understand this does not require any great genius. It should be borne in mind that the moon has a motion opposed to the general motion of the heavens; that is, it goes from west to east, and in every two hours it progresses a degree and a few minutes; and since it is in the first heaven, and the stars are in the eighth, it certainly never enters in conjunction with them; but sometimes it interposes itself before the rays which come from them to our eye: but this does not happen at the same time to those who are at Seville, and to those who are at Valencia. The annexed figure will give an idea of this, from which it is seen that the ray of the star d is intercepted by the moon c for those who are at a and not for those who are at b for whom it was intercepted when the moon was at e.

First Voyage Round The World Conjunction.png

"iii. The compass can also supply a method, still easier, for finding the longitude of the place in which you are. It is known that the compass, or the magnetised needle which is in it, directs itself to a given point, because of the tendency which the loadstone has towards the pole. The reason of this tendency is because the loadstone does not find in the heavens any other spot in repose except the pole, and on that account directs itself towards it. This is an explanation of the phenomenon which I propose; and I believe it to be true, so long as experience does not inform us of some better explanation.

"In order to know, by means of the needle, the degrees of longitude, form a large circle, in which place the compass, and divide it into 360 deg.: and having placed the needle at 360 deg., where it indicates the arctic pole; when the needle is in repose, draw a thread, which should pass from the arctic pole, pointed out by the needle to the antarctic pole, and let this thread be longer than the diameter. After that take the south, which you will know by the greatest altitude of the sun. Turn the compass, until the thread which traverses it coincides with the direction of the meridian shade; then, from the antarctic pole of the needle, with the thread which remained over, draw another thread to the arctic pole, that is, to the flower;[9] and you will thus find how many degrees the needle of the compass is distant from the meridian line, that is, from the true pole. So many will be the degrees of longitude, which you will have from the place where the compass begins to set itself in motion.[10] Therefore, with the more accuracy you take the true meridian so much the more exactly will you be able to ascertain the degrees of longitude. And from this it may be seen that the meridian should never be taken with the compass, because it north-easts or north-wests,[11] as soon as it goes out of the true meridian; but take an observation of the south[12] with the astrolabe, and judge that it is midday when the sun is at its greatest height.

"If it is not possible to take the sun's altitude at midday, that can be determined with an hour-glass of sand, taking the hours of the night from sunset till the moment of its rising. Having learned the hours of the night, you will know how many are wanting of the twenty-four, and these you will divide into two equal parts. When half of this has elapsed, be sure that it is midday, and that the shadow indicates to you the true meridian. But since the sand clock may often be inexact, it will be better to take the sun's altitude with the astrolabe by means of its mediclino.[13]

"The true meridian may also be ascertained, or rather the equinoctial line, which cuts the meridian at right angles, by observing the points where the sun rises and sets, and by observing how much they are distant from the equinoctial either to the north or to the south. For this purpose an astrolabe is formed with the globe; that is, a circle is made representing the earth's circumference, divided into 360 deg. At sunrise fix two pins in the circumference, in such a manner that a line drawn from one to the other should pass through the centre, and place the pins so that both should be in a line opposite the sun's center. Place two other pins in the same way in the circumference when the sun sets. You will thus see how much the sun declines from the equinoctial line, either to the north or to the south. And as many degrees as the pins are distant from the equinoctial, so many degrees the the sun's declination. Having found the sun's rising and setting, you will also find the medium distance; that is, the meridian line, and afterwards you will see how much the compass or magnetic needle north-easts or north-wests. You will infer from this how far you are from the Fortunate islands; that is, from Tenerife towards the east or the west. This method has been tried by experience.[14]

"Direction of the Ship.

"If you wish to navigate to any place, you must first know its position; that is, its latitude and longitude. Then, by means of the compass you will point directly to that place. And since the compass varies to east and west, you must, by the methods above described, ascertain its variation, and subtract or add that which is necessary, so that the ship's head, regulated by the compass, may have the required direction.

"Should the compass be lost, or if its variation east or west is not known, you may regulate yourself by the sun at midday. When you have fixed the meridian in such a manner that it cuts the ship in its width, it will be easy to direct the prow wherever you wish. Here is an example: suppose you wish to go from north-east to south-west, place the chart in such manner that the ship should have her head to west and the poop to the east; then on the circle of the winds, divided into 360, or in four times 90, fix two pins, one at 45 degrees between east and north, the other at 45 degrees between west and south; bring the two pins on the line of the meridian by turning the ship's head for that purpose, and the prow will be directed to the place to which you are going. If the pins do not come in a line with the meridian, it is a sign that you are navigating in a false direction, and you must rectify the course. When you reach land, you will see that what I have said is true.

"With an astrolabe made with plates,[15] observations may be taken of the meridian line, the poles, and the equinoctial line, at any hour of the day or night, looking at the moon or any star; and for these, place in the middle of the astrolabe instead of the verghezita or sight,[16] two straight bars between which you will observe the star."

Thus the method being known by which the required direction is given to the ship, the author teaches the method for determining the point or degree on the chart of the winds,[17] to which the ship on leaving a place to go to a given country should be directed. For clearness, he gives some examples of this. "Do you wish," he says, "to go from south to north, or vice versâ, on the same longitude? always proceed on the same meridian. Do you wish to go from east to west, or vice versâ, in the same latitude? always proceed on the same parallel. Do you wish to go from one place to another as many degrees distant in longitude as it is different in latitude? Then take the course of 45 degrees either to the south-west or south-east, or north-west or north-east. If the latitude is greater than the longitude, then add to the 45 degrees as many degrees towards the nearest pole, as the number of degrees by which the latitude exceeds the longitude. For instance, if I wish to go from Cape St. Vincent to Cape Bojador, I reckon the degrees of longitude and those of latitude to know the difference between these two capes. I find that the degrees of longitude are five and a half, and those of latitude are eleven, from which I subtract the degrees of longitude and there remain 5 deg. 30 min. Then, instead of going in the direction of from north-east to south-west (as I should do if the longitude were equal to the latitude], I go from 5 deg. 30 min. above north-east towards north, to 5 deg. 30 min. below south-west towards south. If the longitude is greater than the latitude, the lesser number is still subtracted from the greater: and the direction will be 45 deg. after deducting the residue. For instance, do you want to go from the island of Ferro to Guadeloupe; you know that the first is in 27 deg. latitude and the second in 15 deg.; then take their difference, which is 12 deg.: look at the map for their longitude, and you see that Ferro is in 1 deg. and Guadeloupe in 45 deg., whence their difference is 44 deg.: subtract from these the 12 deg. residue of latitude, and there remain 32 deg. Then you must subtract these 32 deg. from 45 deg., and there will remain 13 deg. Therefore your course will be from north-east 13 deg. north to south-west 13 deg. south.

"Direction of the Winds.

"The rose of the winds, divided into 360 deg., will give a clearer idea of what has been here said; it being well understood that the pilot must place the center of the winds on the point from which he starts, or from which he takes the course, and he must fix the pole to the true pole observed from the sun, and not trusting to the compass, which north-easts or north-wests.

"Then, to ascertain whence comes the wind, place a little stick with a little sail[18] in the centre of your rose or circle of winds, divided into 360 deg., and placed in such a manner that north and south stand on the true Solar meridian. The direction of the vane moved by the wind will indicate exactly which wind blows: on the equinoctial is east and west; at 45 deg. there is north-east, south-west, north-west, and south-east; at 22½ deg. towards north you have north-north-east, and so on with the others."

  1. Now the declination of the ecliptic, which answers to the poles of the eighth sphere of Pigafetta, is 23 deg. 28 min. 30 sec. Note, Milan edition.
  2. Supposing that the surface of the globe under the equator were half land and half sea, and then giving to each league three and a half miles, we should have 22,050 miles for the circumference of the earth: a measure very little differing from that which results from giving to each degree at the equator sixty Italian miles, by which the circumference is 21,600 miles. Note, Milan edition.
  3. The guard stars are 6 and 7 of Ursa Minor, which form a triangle with the pole and pole star; now 7 at the belt of Cassiopeia is used. Note, Milan edition.
  4. This means the arm of the instrument used; it might be the meteoroscope of Regiomontano, which had a cross in the middle: or an astrolabe like it; or the common astrolabe with a dioptron, or mediclino, as Pigafetta calls it, placed on the equator. Note, Milan edition.
  5. That is the meridian line from the pole to the equator. Note, Milan edition.
  6. Though the radius of the circle which the pole star goes round is now little more than a degree and a half, in the time of Pigafetta it was 3 deg. 17 min. 37 sec, so that if he reckoned it at 3 deg. 30 min. it is wonderful that he should have made so small an error, notwithstanding the imperfection of his instruments. Note, Milan edition.
  7. These three methods are probably those which, according to Castañeda, Faleiro taught to Magellan. Note, Milan edition.
  8. That is to say, the knot where the orbit of the moon cuts the ecliptic. Note, Milan edition.
  9. The fleur-de-lys placed at the north.
  10. That is, where it coincides with the meridian and begins to deviate or vary. Note, Milan edition.
  11. That is, varies east or west.
  12. Or of midday.
  13. I do not find any mention of the mediclino in any writer of the times near that of Pigafetta who have treated of the astrolabe, such as Regiomontanus, Appianus, Gimma, Frisius, Danti, Clavius, etc.; but from what our author says here and elsewhere, it appears that the mediclino is that movable rule, fixed on the centre of the astrolabe, which turns round it, and is named sometimes albidade, or dioptron, or traguado, or linea di fiducia. Note, Milan edition.
  14. Amoretti, in his introduction to this Treatise of Navigation, in the Milan edition, observes that Pigafetta was misled by a false theory when he supposes that there is in the heavens a point in repose to which the magnetic needle tends, but that the exact direction of the magnetic needle coincided, or at least approximated to the meridian of the isle of Ferro, which is not now the case; and that in some other places the variation of the compass had been observed to correspond with that of the longitude. By the table of variations of the compass published by Lambert in the Ephemerides of Berlin (Astronomische Jahrbuch) for the year 1779, it is seen by an easy calculation that at the beginning of the sixteenth century the magnetic equator or zero of deviation was very near the isle of Tenerife. Now it is further off, and the distance increases. M. de Bouganville found there the deviation to the west to be 14 deg. 41 min.; and Staunton, the companion of Lord Macartney, found it to be 17 deg. 35 min.
  15. We have two astrolabes in our museum constructed with several plates: one is of brass, and another of card, for more easy manipulation. Note, Milan edition.
  16. "Traguardo," level or traverser.
  17. "Rosa dei venti."
  18. Or flag, as appears from the drawing.