The first voyage round the world, by Magellan

by Antonio Pigafetta

“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:⁠[426] 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.”

“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;⁠[427] 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.⁠[428] 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,⁠[429] as soon as it goes out of the true meridian; but take an observation of the south⁠[430] 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.⁠[431]”

“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 are 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.⁠[432]”

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.”