must be observed: if they fhould be on the western arm †, the polar ftar is 1° above the pole; if on the rule or line, the polar ftar is 3° 30' beneath the pole §; if on the eastern arm the polar ftar is 1° below the pole. When defirous of taking the height of the pole, after obferving in what pofition the guards are, and after afcertaining the height of the polar ftar from the horizon, the degrees that this ftar is above the pole, or below, must be subtracted, or added. I have spoken of the antarctic pole in the narrative of my voyage.

"II. The latitude of a place may likewife be found by the height of the fun: ift. When between the equator and the arctic the fhade at noon falls towards that pole, the number of degrees and minutes of the fun's declination on that day must be fought for in the almanack, and be deducted from the degrees and minutes of its elevation, taken by obfervation; fubtracting afterwards the remaining degrees from 90°; the refult will be the boreal latitude. 2d. When, being in the northern hemisphere, the fun has a northern declination, and the fhadow falls towards the fouth, the declination of the fun on that day being found, it must be added to its elevation above the horizon, and the fum of the two be deducted from 90°; the remainder is the lati tude north. 3d. When the fun is between the equator and the antarctic pole, and the fhadow falls at noon towards the fouth, the amount of the declination of the fun must be deducted from its elevation, as in the first rule, and the remainder be fubtracted from 90°, which will give the latitude fouth. 4th. When, as well as the fun, the obferver is between the equator and the antarctic pole, and the fhadow at noon falls towards the north, the sum of the declination of the fun must be added to its elevation, as in rule the second, and the amount be deducted from 90°; the remainder gives the latitude fouth. 5th. When the height of the fun is 90°, the distance of the obferver from the equator will be equal to the declination of the fun; and if the fun has no declination on that day he will be on the equator. 6th. If the obferver be north of the equator, and the fun be in the fouthern figns, the amount of its declination on that day must be added to its elevation, and the fum be deducted from 90°; the residue is the diftance north from the equator. 7th. By a fimilar operation, when the obferver is south of the equator, and the fun in the northern figns, the latitude fouth may be found.”

Of the Longitude.

"Longitude indicates the degrees from east to west. I have ftudied different methods of ascertaining it, and selected three, which appear to me the best ¶. The laft is the most convenient for thofe unacquainted with aftrology. Pilots now a days are fatisfied with knowing the latitude, and are so presumptuous they refuse to hear mention of longitude.

See the preface to this Extract, page 384.

By this the arm of the inftrument ufed is to be understood; this inftrument was probably the me teorofcope of Regiomontanus, which had a crofs in the middle, or perhaps the common astrolabe, with the dioptre, or medeclino as Pigafetta calls it, on the equator.

Pigafetta means the meridional line from the pole to the equator.

I have previously remarked that, although the radius of the circle defcribed by the polar ftar mea. fures at this time no more than a degree and a half, in the time of Pigafetta it measured 3° 17′ 37′′; con fequently when our author fays 3° 30' he is not very wide of the truth; and when the imperfection of the different inftruments used by him is confidered, there can remain no caufe for furprize at an error of such little magnitude.

As occurs when the obferver is between the place of the fun in the ecliptic and the equator. Thefe three methods are probably thofe which, according to Caftagneda were taught Magellan by the aftrologer Faleiro. tt ift.

3D 2

"ift. By the latitude of the moon one may form a judgment of the longitude of the spot where the obfervation is made. By the latitude of the moon is understood its distance from the ecliptic. The ecliptic is the line of route or orbit of the fun. The moon in her rotation conftantly gets further from this line until at her greatest distance from it; afterwards fhe approaches it again until in conjunction with the dragon's head or dragon's tail*, when the cuts the ecliptic. Now, as the moon, on receding from the ecliptic, at the fame time paffes to the weft, fhe muft neceffarily have a greater latitude on one part of the globe than the other; and when her latitude is known, which is afcertained in degrees and minutes by the astrolabe, her position east or weft is found, and the number of degrees and minutes fhe diverges to either quarter. But the longitude of the fpot of obfervation cannot be determined without knowing exactly in what latitude and longitude the moon ought to be at the fame inftant at the place of departure, at Seville for example: when the latitude and longitude of the moon at Seville in degrees and minutes are known, by comparing them with the latitude and longitude of the spot, the difference will fhew how many hours and minutes the meridian in which the obferver may be, is diftant from that of Seville; and thus the longitude from that city may be afcertained.

"2d. The moon furnishes me with another method of determining the longitude of any fpot; but for this purpose must be known the precife inftant when at Seville the moon is in conjunction with a certain ftar or planet, or when fhe is in oppofition to the fun, or forms an exactly ascertained angle with that planet, which I gather from an almanack. Now, as either phenomenon occurs in the east before it does in the weft, I discover my longitude weft by the time that has elapfed between its occurrence at Seville and the inftant at which it is obferved by me. But if the phenomenon takes place at the point of obfervation before it happens at Seville, the difference of time points out the longitude eastward. For each hour fifteen degrees of longitude must be reckoned. "No great genius is required to comprehend what I have mentioned. It fhould be known that the moon has a peculiar movement, oppofite to the general one of the heavens, seeing her courfe is from weft to east, and every two hours fhe paffes over a degree and fome minutes. And as the moon is placed in the first heaven and the ftars in the eighth, fhe occafionally eclipfes certain ftars, by paffing between them and us, or intercepts their rays from our obfervance, an event which cannot take place at the fame time to be feen at Seville and at Valentia, which the figure beneath will explaint."

D
*

C

B

*That is to fay, the nodes or orbit of the moon cut the ecliptic

This figure was wanting in the manufcript, but was eafily fupplied from the text.

By

By this figure is feen that the rays of the ftar D are intercepted by the moon at C from the obfervance of thofe at A, but not from that of thofe at B; although when the moon proceeds to E, the fame star will in like manner be concealed from the gazer

at B.

"III. The compass may likewife furnish a much more ready means of discovering the longitude. It is well known that the compafs, or the magnetic needle which it contains, conftantly points to one fixed fpot, on account of the tendency of the magnet towards the pole. The caufe of this tendency is the magnet finding no point at reft in the heavens except the pole, to which confequently it ever directs itself. This, at leaft, is the explanation I propose of this phenomenon, and that which I fhall deem a good one, until experience produce a better.

"To know, by means of the magnet, the longitude of a place, form a great circle, in which the compafs may be placed, and divide this circle into three hundred and fixty degrees: turn the compafs until the magnetic needle points to 360°, where the arctic pole is indicated. When the needle is at reft draw a thread from the arctic to the antarctic pole, which may cut the centre, and let this thread be of greater length than the diameter of the compass. After this take the line of noon, which is to be determined by the greatest elevation of the fun: turn then the compass until the thread which traverfes it is on the line of the true meridian, that is to fay, on the fhadow caft by the dial at noon; then, with the remainder of the thread, draw a line from the antarctic pole of the needle which paffing through the centre may cut the fleur-delis which points out the north, and observe how many degrees the needle is distant from the meridional line, that is from the true pole; the number of degrees diftant will indicate the number of degrees of longitude from the fpot where the compafs points true confequently, the more exact the obfervation of the true meridian, the more exactly will the degree of longitude be determined. By what I have faid will be feen that the meridian must never be determined by the compafs, because it north-eafts or north-wests immediately after a departure from the true meridian, but with the aftrolabe at noon; and the noon must be found by afcertainment of the inftant of the greatest elevation of the fun.

"When the height of the fun at noon cannot be taken, it may be determined by a fand-glafs, by reckoning the hours of the night, from the inftant the fun fets to that of its rifing. When the length of the night is thus known, that of the day is gathered by fubtracting it from twenty-four; by dividing this by two the fum is the time from fun-rife till noon, at which inftant the gnomen will indicate the meridian. But the fand-glafs being oftentimes incorrect, it is far better to take the height of the pole, by means of the astrolabe and its mediclino f.

"The true meridian may also be found, or rather the equinoctial line which cuts the meridian at right angles, by observing the points at which the fun rises and sets, and measuring its deviation north or fouth from the equinox. To effect this, an astrolabe is made of the earth; that is to fay, a circle is formed representing the circumference of the earth divided into three hundred and fixty degrees. Fix two pins

*That is to fay, when the magnetic needle coincides with the meridian. + Meaning it declines towards the caftor the west from the north.

I cannot find that any aftronomer or aftrologer in the days of Pigafetta, for example Regiomontanus, Apianus, Gimma Frifius, Danti, Clavius, &c. make any mention whatever of the mediclino; but by what our author here fays, as well as in other places, it seems the mediclino is the moveable rule fixed on the centre of the aftrolabe, which is fometimes denominated allidade, at others dioptre, and in Italian traguardo.

in this circle in fuch manner that a line from one to the other may cut the centre, and at fun-rise turn this circle in fuch manner that the pins may be in a line with the centre of the fun; at the inftant the fun fets repeat the fame operation. By this means you will find the declination of the fun from the equinoctial line, whether northward or fouthward. When you have determined the angle at which the fun rifes and fets from the equinoctial line, you obtain the mean distance, which is the meridional line; and you will thus fee how much the needle north-eafts or north-wests: by the degrees of deviation of the needle you will know your longitude from the For tunate islands, that is to fay, from Teneriffe, whether eastward or weftward. This method has the fanction of experience *."

On Steering the Ship.

"Would you navigate to any country, it is first requifite you should know its geographical position, that is to fay its latitude and longitude. After which, by the help of the compass you will fteer directly towards it. And as the needle north-easts or northwefts, its deviation must be found by the means I have prefcribed; then fubtract or add what is neceffary to the compafs in order that the prow of the fhip, regulated by the compass, may conftantly point in the direction required.

"If unfortunately the compafs fhould be loft, or if its real deviation from the meridional line fhould be unknown, the pilot must regulate himself by the fun at noon. When the meridian is fo fixed that it cuts directly across the veffel its prow may be directed any way at pleasure. For example; fuppofing the pilot would fteer from north-east to south-weft, turn the compafs in fuch manner that the veffel may have its prow towards the west and its poop towards the east; then on the circle of the winds, divided into three hundred and fixty degrees, or four times ninety, fix two pins, one at forty-five degrees from the east and the north, the other at equal distance from the west and south; turn then the helm so that the two pins may be on the meridian, and the prow will point whither the veffel is to fteer: provided the pins should not be on the true meridional line, the course will be a false one, and must be rectified. When the veffel makes the land the truth of what I fay will appear.

By means of an astrolabe composed of plates †, the meridional line may readily be found, as well as the poles and the equinoctial line by obfervation of the fun by day, and at night of the moon and ftars. For these laft, instead of the verghezita, two small sticks must be placed in the middle of the astrolabe, through which the star may be obferved."

After thus defcribing the method of giving the direction wifhed for to the veffel, Pigafetta proceeds to teach the means of determining the point of the compass to which the veffel in failing from one part to another should steer. In order to make himself the better understood he adduces feveral examples. "Are you defirous,' fays he, " of going from fouth to north, or from north to fouth, under the fame lon gitude, keep constantly on the fame meridional line. Would you fail from east to

* I have already obferved that in the time of Pigafetta the needle at the Canaries was nearly on the magnetic equator; and it muft further be obferved that chance has carried navigators into certain parts where the degrees of declination corresponded with the degrees of longitude from the island of Teneriffe.

+We have aftrolabes made of different kinds of plates, the largeft for fake of lightnefs being of paste. board; the others are of brass or copper.

This probably is the fame thing with the mediclino. See Note, page 389. 8

weft,

weft, or the contrary, keep always under the fame parallel. If inclined to proceed from one spot to another which is distant as many degrees of longitude as of latitude, you must steer 45° towards the north-west or north-eaft, or towards the fouth-west or fouth-eaft. If the difference of the latitude is greater than that of the longitude, add to 45° the number of degrees which the latitude has more than the longitude to the pole to which you are fteering. For example; fuppofe I wifhed to go from Cape St. Vincent to Cape Bojador, I compute the degrees of longitude and latitude to know the difference between the two capes; I find the difference of longitude to be 5° 30′, of latitude 11° I therefore deduct 5° 30' from 11°, and find the remainder 5° 30' more than north-eaft towards the north, and less than fouth-weft towards the fouth. If the longitude is greater than the latitude, the inferior number of degrees is in.like manner deducted from the greater; and the course to steer will be the remainder of 45°, after fubtracting the quotient. For example; fuppose I wish to go from the island Ferro to Guadaloupe, I find the former lies in latitude 27°, the other in 15° north; I thus afcertain the difference to be 12° of latitude. I next obferve on the chart their longitudes; as that of Ferro is feen to be 1°, and that of Guadaloupe 45°, the difference is 44°; from this I fubtract the 12° of latitude, and have for a remainder 32°; this refidue I deduct from 45°, and have 13° for the difference. The courfe to, steer must therefore be from north-east 13° north, to fouth-west 13° south *.”

Direction of the Winds..

"The compafs, on which the rhumbs are marked, divided into 360°, will give a better idea of what I have juft now remarked, it being firft understood that the pilot muft reckon his point of departure from the centre of the compafs; he must at the fame time take care to determine precisely the true pole by the elevation of the fun, and not from the needle, prone to deviate from the north towards the east and west. In order to learn whence the wind blows, fix a small stick with a vane in the middle of the compafs, fo placed as that the north and fouth may be upon the true meridional line. The direction of the vane acted upon by the wind will fhow whither it blows. On the equinoctial line of the compafs are the eaft and weft; at 45° you find the north-eaft, north-weft, fouth-eaft and fouth-weft; at 22° north-north-eaft and northnorth-west, and fo with the reft."

*This laft is an error. Where the longitude is greater than the latitude, the furplus fhould be added. to the longitudinal direction, whether east or weft. Thus, inftead of steering fouth-west 13° fouth, in the inftance of this problem, the veffel fhould be fteered fouth-west 13° welt. ENG,TR.