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VI. THE JUNTA DOS MATHEMATICOS.

Advisory Committees.

KING JOHN II. is known, on several occasions, to have referred questions of a scientific or technical nature to men of learning who enjoyed his confidence and who he believed would wisely advise him. He did so when Columbus urged him to send an expedition across the Ocean Sea in search of Cypangu and the East Indies.(1) On that occasion the members of this Junta-to employ a designation used not quite logically in connection with such ephemeral committees-were Dr. Diego Ortiz de Vilhegas, a native of Calzadinha in Leon, who had come to Portugal in 1476, as spiritual director of that "most excellent lady," D. Joanna, and stood high in the Royal favour(2); Dr. Rodrigo of Pedras negras, the chief physician of the King, with whom his influence was considerable, as we learn from the `Epistola' of Cataldo de Aquila, printed at Lisbon in 1500; and Master Josepe or José, a Jew, who is undoubtedly identical with José Vizinho, a pupil of the famous astronomer Rabbi Abraham ben Samuel Zacut of Salamanca, Professor of Astronomy and Mathematics in the University of his native town, until 1492, when with thousands of his co-religionists he fled Spain, and found a refuge in Portugal, where King John appointed him Astronomer Royal.(3) This Rabbi Abraham is the author of an `Almanach perpetuum Celestium moduum cujus radix est 1473,' a work originally written in Hebrew, but translated into Latin by José Vizinho `discipulum ejus,' and printed at Leiria in 1496.

A few years afterwards D. Diogo Ortiz, Dr. Rodrigo and a Jew, Moyses, were instructed to prepare a map for the guidance of João Pero de Covilhã and Affonso de Paiva, whom the King was about to dispatch in search of the country of Prester John.(4)

It is, however, another `Junta dos mathematicos' which more especially interests us. This Junta was appointed in 1484 or at latest in 1485. Its task was to lay down simple rules for determining the latitude from meridian altitudes of the sun, for the pole star, which had served for that purpose in the past, was no longer available once the Portuguese navigators had crossed the Equator.

João de Barros and the `Junta.'

We are indebted to the famous historian João de Barros(5) for an account of this Junta. He mentions Behaim as a member of it, and to him alone all later historians - including G. P. Maffei, (6) Petrus Matthaeus (1590), Olfert Dapper,(7) A. Cordeiro, S.J. (1641), and Manoel Telles da Silva (1689)(8) - are indebted for this information, and there is thus no accumulative evidence as suggested by several of Behaim's biographers.

J. de Barros (who wrote in 1539), having informed his readers that when Vasco da Gama reached the Bay of St. Helena he set up his large wooden astrolabe on land, as he had been unable to obtain trustworthy meridian altitudes of the sun on the deck of an unsteady vessel, either with that instrument or with some of the smaller astrolabes of brass with which he had been supplied, and having asserted that the Portuguese mariners were the first to employ these altitudes for the determination of latitude, continues as follows:

"At the time when Prince Henry began the exploration of Guinea the mariners sailed within sight of the coast, being guided by landmarks which they described in sailing directions, such as are still in some way in use at present, and this sufficed for this mode of exploration. But subsequently, when, in the pursuit of their discoveries, they lost sight of the land and penetrated the open sea, they found that owing to currents and other secrets of the sea their estimate of a day's work was frequently erroneous, whilst an observation of the altitude (of the sun) would have shown correctly the distance run. And as necessity is the mistress of all arts, King John II. referred this matter to Master Rodrigo and Master Josepe, a Jew, and both his physicians, and to one Martin of Bohemia, a native of that country, who boasted of being a disciple of John of Monte Regio, famed among the students of the science of astronomy. These discovered this manner of navigating by altitudes of the sun, and made tables of its declination, such as are now in use among navigators, and which are now more exact than in the beginning, when these large wooden astrolabes were in use."

A statement made by so distinguished an author is entitled to respect and deserves careful examination. Still, I may be forgiven for directing attention to the fact that even in the days of Prince Henry the Portuguese were not afraid to venture upon the high sea, for they sailed to the Azores, lying 600 sea miles from the nearest land. Long before them the hardy Northmen, guided solely by the stars and the flight of birds, had found their way across the northern Atlantic, and Columbus would have made his famous landfall equally well had he trusted entirely to his dead reckoning or, like a bird of passage, to his instinct, for his observed latitudes are woefully out.(9) Verily, the Portuguese seamen of that age were better observers than their Spanish rivals!

The last paragraph in the account given by J. de Barros seems to refer to improved tables of the sun's declination. Dr. Breusing(10) suggests, however, that the author refers to an instrument which superseded the astrolabe for taking a meridian altitude of the sun on ship-board, and that this instrument was the cross-staff. I shall deal fully with this new aid to navigation, and merely observe in this place that the cross-staff was known in Portugal when J. de Barros wrote, in 1539, but that it was not made use of by Vasco da Gama, Magellan or any other seamen of the period with which I deal.

Of the three persons named by J. de Barros as members of the Junta, two, namely Dr. Rodrigo and Josepe or José, have already been referred to, whilst the third, Martin Behaim, shall be dealt with fully a little further on.

The Astronomical Expedition of José Vizinho, 1485.

Josepe or José Vizinho seems to have taken the lead in the work done by this Junta. He was no mere theorist, for we learn from a note inscribed by Christopher Columbus on a margin of the `Historia Papae Pii' (Venice, 1477) that in 1485 he was sent to the Guinea coast for the express purpose of determining a number of latitudes by observing meridian altitudes of the sun. This note reads as follows:(11)

"In the year 1485 the King of Portugal sent Master Jhosepius, his physician and astrologer, to determine the altitudes of the sun throughout Guinea, all of which he performed; and he reported to said most serene king, I being present, that on March 11,(12) he found that the island of idols near Sierra Leone was exactly 5 degrees distant from the Equator, and he attended to this with the utmost diligence. Afterwards said most serene king often sent to Guinea and other places and he always found the results to accord with said Martin Josepius, whereby I have the certainty that the Castle of the Mine is under the Equator."

In another marginal note(13) Columbus states that he himself during various voyages to Guinea had taken altitudes of the sun with the quadrant and other instruments, and that his results agreed with those of Master Yosepius and of others whom the king had sent out. Columbus, in comparing the distances obtained by dead reckoning with those corrected by observations for latitude made by himself and others, concludes that El-Ferghani was right when he gave the earth a circumference of 20,400 miles, and reckoned 56 2/3 miles to a degree of the Equator.

These marginal notes were evidently written long after the events recorded, and Columbus may have made a mistake in recording José's latitudes, just as he made a mistake when he tells us in another marginal note that the latitude of the Cape of Good Hope, as determined by B. Dias, was 45° S. (14) Perhaps the 5 degrees refer to the Castella S. Jorge da Mina, for the Ilhas dos Idolos (Los islands) lie in 9°30' N. That Columbus himself should have made such a mistake is not surprising, for he was a very incompetent observer, but that José, a learned astronomer, should have brought home so erroneous a record is incredible. Still it is well known that latitudes taken on board ship frequently differed to the extent of several degrees from the truth, and on Soligo's Chart of Portuguese Guinea, which I shall deal with fully in the second part of this work, we read off the mouth of the Niger " hic non apar polus," although that locality lies more than six degrees to the north of the Equator.

Summing up, we find that the Junta, and more especially its most active member, José Vizinho, advised that vessels sailing beyond the Equator should observe meridian altitudes of the sun for finding the latitude, that experimental voyages were undertaken to test this method, and Zacut's `Almanach perpetuum' was translated and printed in order to facilitate the calculation of the observations made. These reforms led naturally to the adoption of graduated sailing charts, which had previously been unknown in Portugal.

Behaim as an Astronomer.

In what way, it may be asked, could Martin Behaim aid Dr. Rodrigo and José Vizinho in the task they had undertaken? He was no seaman, for at that time he had crossed the sea but once, and that as a passenger, on a voyage from Antwerp to Lisbon. He may have boasted of being a pupil of Regiomontanus, and may have been admitted, as a lad, to the observatory of that great astronomer; but it is quite certain that he profited little or nothing from lessons he may have received on these occasions.(15) In his letters, as far as they have reached us, there is no allusion to his ever having taken an interest in astronomical work; among the articles he dealt with as a merchant there are no astronomical or other scientific instruments. Columbus, in his numerous marginal notes, never once mentions his name. The only contemporary to hint at Martin Behaim's qualifications as a seaman or astronomer is Hieronymus Monetarius in a letter addressed to King John in 1493.(16) In that letter he recommended Behaim as being "well fitted" to accompany an expedition for "disclosing the East to the West." Monetarius, however, is hardly a competent witness on such a question. An examination of the famous globe of Nuremberg enables us to form a more trustworthy estimate of Behaim's capacity. We there find that he placed the mouth of the Congo in lat. 24° S., and the Montenegro in lat. 38° S., the true latitudes of these localities being 6° 4' and 15° 40' S. This proves conclusively that if Behaim accompanied the famous expedition of Cão as cosmographer or astronomer, as is maintained by his biographers, he was absolutely ignorant of the work he had undertaken. On the other hand, if this portion of his globe is merely a compilation, he exhibited a deplorable incapacity as a compiler, for since Dias' return in 1488, the latitudes along the African coast, as far as the Cape, were approximately known.

Moreover, several legends on the globe prove Behaim's ignorance as a "cosmographer." Thus we read, in 78° N., "the longest day here lasts six months," and in the gulf of Guinea, within the tropics, the curious reader is told that it is summer there when we in "Europe have winter," a statement quite appropriate to the southern temperate zone, and possibly taken over from some old map, and put in the wrong place. Another legend proves Behaim's absolute ignorance in matters connected with the art of navigation, for it tells us with reference to the Indian Ocean:

"Here the Stella maris, by us called Polus Arcticus, cannot be seen, and those who navigate this sea must sail (shape their course) with the help of the astrolabe, for the compass does not point (to the north)."

No doubt such nonsense was believed at one time by the ignorant,(17) but no seaman, nay, no observant landsman who had once crossed the Equator, as Behaim claims to have done, could have penned such a sentence.

It is not likely that a man so inexperienced as was Behaim at that time, at all events, could have taught anything to a man of the scientific attainments of Mestre José. He may have boasted at Lisbon of being a pupil of Regiomontanus, and, on the strength of this boast, may have been invited to join a Junta of astronomers; but his want of knowledge would soon have betrayed itself. Yet, in spite of these considerations, some of his more imaginative biographers have credited him with achievements which would entitle him to a foremost position among the scientific men of his age. J. F. von Bielefeld,(18) copying a statement in that untrustworthy `Dictionnaire' of Louis Moréri, suggests that "Behaim was the first to apply the compass (19)to the navigation of the high sea, an achievement, if true, deserving of immortality."

Antonio Ribeiro dos Santos, the author of a `Memoria sobre alguns mathematicos Portuguezas,'(20) actually adopts these wild statements. He says with reference to Behaim: "He was a disciple of the famous mathematician John de Monte Regio, Professor of Astronomy, who devoted himself with much diligence to the study of cosmography and navigation. He entered the service of Portugal and was well received by Kings Affonso V.(21) and John II. on account of the nobility of his person, his attention to his profession and discourses. The lastnamed Prince, on February 18, 1485, appointed him one of his esquires (escudeiros), and the navigation of the Portuguese derived much profit from him. Of him it is said that he was the first to adapt the compass for the general use of navigators, which would suffice to immortalize his name and confer much honour upon Germany, his fatherland."

A. Ziegler,(22) in `Regimontanus ein geistiger Vorläufer des Columbus' (Dresden, 1874, p. 17), speaks of Behaim as "one of the most learned mathematicians and astronomers of his century, a famous navigator and Portuguese cosmographer," and in a paper published in the `Deutsche geographische Blätter' (Bremen, 1878, p. 117), he actually suggests that Behaim was the spiritus familiaris of Ruy Faleiro,(23) to whom he revealed the secrets of cosmography and new methods for determining the longtitude.

Quite as fantastic is the statement put forth by a more recent writer, J. P. de Oliveira Martins (`Les explorations des Portugaises,' Paris, 1893, p. 20), who would have us believe that John II., "when he ascended the throne and founded at Lisbon a school of mathematics, summoned from Nuremberg a pupil of Regiomontanus, Martin Behaim, upon whom devolved the rôle formerly filled at Sagres(24) by Jacomé of Majorca."

I must leave it to the sound judgment of my readers in how far extravagant claims, such as these, can be reconciled with what we know of Behaim and of the history of Portugal in the time of John II.

The Astrolabe.

Far less fanciful are those authors who merely credit the Junta with having "invented" the astrolabe or "adapted" it to the use of navigators. One of the earliest among the former is Manuel Pimentel (`Arte de Navigar,' Lisbon, 1682), whose lead was followed by Admiral Ignacio da Costa Quintella (`Annaes da Marinha Portugueza,' Lisbon, 1839, I., 190). Thus the Junta might merely have simplified the planispheric astrolabe of the astrologers, so as to adapt it to the use of seamen. This planispheric astrolabe, of which numerous examples may be seen at the British Museum,(25) had a shallow well -the mater astrolabii-within which was placed an engraved chart of the heavens as seen in a given latitude, on a stereographic projection. An ingeniously devised Reta or Arenea (Spider's Web) moved concentrically above this chart, and by means of it certain astronomical problems could be solved graphically. The improvement by Regiomontanus merely consisted in a device which rendered the instrument more useful to astrologers desirous of finding the "initia coelestium domiciliorum," a device of no interest whatever to the seaman.(26)

THE ASTROLABE OF REGIOMONTANUS,1468

The seaman's astrolabe,(27) as shown in the illustration, was a much more simple instrument. A disc or a ring of wood or metal, 3 to 15 inches in diameter, was crossed by lines representing the horizon and zenith. The rim between the horizon and zenith was divided into 90 degrees. A movable rule or alidade, with sights, turned round a point or pin in the centre of the circle. The observer sat with his back to the main mast, held the astrolabe in suspension on a finger of his left hand, whilst he moved the rule up and down with his right until the sun was on with both sights. Supposing the astrolabe had been suspended vertically, this yielded a correct, though somewhat rough, altitude of the sun. Of course, on deck a rolling vessel, the results obtained even by a skilled observer were frequently far from satisfactory, and Master John, one of the pilots of Cabral's fleet, tells us that errors of four or five degrees in the resulting latitude were almost unavoidable.(28) Hence, when it was desired to obtain trustworthy results, the observer landed and set up an astrolabe of larger dimensions upon a tripod stand. This was done by Vasco da Gama when he arrived at the Bay of St. Helena.

THE SEAMAN'S ASTROLABE

Murr(29) was the first to connect Behaim with the introduction or adaptation of the astrolabe for the service of the Portuguese marine, and his view was accepted by Francisco de Borja Garção-Stockler,(30) Humboldt, (31)Rudolf Wolf,(32) and others. It is, however, stated by Manuel Telles da Silva, Marques de Alegrete,(33) that the astrolabe was made use of for the first time by Diogo d'Azambuja in 1481, that is, several years before Behaim arrived in Portugal.(34)

The Meteoroscope.

Sebastião Francisco de Mendo Trigozo (35)suggests that Behaim merely made known in Portugal certain instruments made in Nuremberg, and the `Ephemerides' of Regiomontanus. Among the instruments he mentions the meteoroscope of Regiomontanus, an adaptation of a similar instrument devised by Ptolemy, and described in a letter to the learned Greek Cardinal Bessarion.(36) Martin Cortes,(37) the son of the famous conqueror of Mexico, explains how this instrument enables an observer to determine the latitude and time by extra-meridian altitudes of the sun. The "hemisphère nautique" invented in 1581 by Michal Cognet of Antwerp, and described by G. Fournier, (38)is in reality nothing more than the upper half of the meteoroscope. Fournier, a very good judge, looks upon this instrument as being absolutely useless on board ship, as its orientation depended upon a knowledge of the variation of the needle when making an observation.

THE METEOROSCOPE.

The Cross-Staff.

Dr. A. Breusing,(39) director of the "Seefahrtschule" of Bremen, was the first to suggest that the instrument made known to the Portuguese by Behaim, was the cross-staff, and Dr. S. Günther(40) agrees with him. The earliest description of this instrument is by Levi ben Gerson, a learned Jew of Bañolas in Catalonia, and was dedicated to Pope Clemens VI. in 1342.(41) Levi calls his instrument "baculus Jacob," George Purbach,(42) "virga visoria," and Regiomontanus, "radius astronomicus." The last has frequently been credited with its invention, but J. Petz has shown that he was acquainted with Levi's description of it.(43) Pedro Nunes,(44) the famous Portuguese astronomer, quotes Regiomontanus when describing the baculus or radius astronomicus. Among Portuguese and Spanish seamen it became known as balestilha, among Frenchmen as arbalète, in England as cross-staff.(45) It is a very simple contrivance for observing stellar distances and the altitudes of heavenly bodies. Our illustration sufficiently shows its appearance and the manner of its use. It merely consisted of a staff along which a "transom" could be shifted at right angles. Divisions of equal length were marked along staff and transom. An observer desirous of obtaining the altitude of a star, placed one end of the staff against his right eye and then shifted the transom until its lower end touched the horizon and the upper end hit the star. Nunes, however, points out that owing to the indefiniteness of the horizon at sea, the results could not be trusted. The instrument was useless for taking the altitude of the sun, unless the eye was protected by a coloured glass or the sun was visible only dimly behind a screen of vapour. It became practically available only after John Davis had converted it into a back-staff,(46) which enabled the seaman to take his observations with his back turned to the sun.

THE CROSS-STAFF.

When Nunes' essay was published, in 1537, the crossstaff had been placed in the hands of mariners, but in Behaim's days it was unknown to them. Columbus, Vasco da Gama, Cabral, Duarte Pacheco Pereira made use of the astrolabe and quadrant, but never mention a cross-staff. A. Vespucci, when appointed Piloto mayor in 1508,(47) was instructed to examine the pilots in the use of the two instruments named. Under these circumstances we are bound to disbelieve that Behaim made known the cross-staff to the Portuguese seamen.

A BACK-STAFF.

The Quadrant.

There are, of course, a few other instruments which a merchant coming from Nuremberg might have introduced to the notice of Portuguese astronomers, such as metal quadrants, and sundials.

The quadrant had been in use among Portuguese seamen long before the arrival of Behaim among them, for Diogo Gomez tells us that in 1456 he made use of it in observing the altitude of the Pole Star.(48) Our illustration shows how it is used, and needs no further explanation. In at least one respect this simple instrument was superior to the astrolabe, for it enabled the observer to determine the altitude of the sun when seen looming through fog or thin clouds, which could be only done with the astrolabe when the luminary shone brightly.

A QUADRNT.

The Nocturnal.

The nocturnal or horometer, an instrument for ascertaining the hours of the night by observing the Pole Star and its so-called guardians, was already known to P. Apianus. P. Nunes thought little of this instrument, and it does not seem that it was ever used on board ship.(49)

Sundials.

In the letter which Dr. Monetarius wrote to King John of Portugal in 1494 he mentions the "quadrant, cylinder and astrolabe" as instruments likely to guide Behaim and other mariners in a proposed voyage across the western ocean. I have dealt already with the quadrant and the astrolabe. As to the "cylinder," it is nothing but one of those portable sundials for the manufacture of which Nuremberg and other German cities were famous in the fifteenth and sixteenth centuries. The "cylinder," of which Sebastian Münster(50) gives an illustrated description, resembled a miniature post-office pillar-box about 70 mm. in height, from the top of which a gnomon or "index" extended horizontally. There were other kinds of "horologii viatorum" or travellers' dials, vulgarly known as "compasses." They were combinations of a horizontal string sundial with a compass. One of the most ancient of these instruments may be seen in the museum at Innsbruck. It is dated 1451, bears upon its shield-shaped lid the German eagle, and was probably made for the Emperor Frederick III.(51) A similar dial, dated 1453, from the Spitzer Collection, is now in the British Museum. The arms of Habsburg are engraved upon its shield, and with the exception of the style of ornamentation both instruments are alike. The dial-plane measures 78 by 59 mm. and holds a compass. On lifting the shield-shaped lid, a string, serving as gnomon, is drawn up. Usually, however, these string dials were made in the shape of a square box, as described in the `Cosmographicus Liber' of P. Apianus (Landshut, 1528).

A HORIZONTAL STRING SUNDIAL, 1451.

But whilst horizontal dials or "compasses" served only in the latitude for which they were made, an equinoctial dial, that is, one whose dial-plane is parallel to the equinoctial plane with a stylus or gnomon rising perpendicularly from its centre, could easily be converted into a universal dial, adjustable to any latitude. The manner in which this was done is shown in our illustration. Such an instrument might have proved of real service to the mariner, especially as it would have enabled him likewise to determine the variation of the compass-needle, and even the latitude (by measuring the length of the shadow cast by the gnomon), but I am not aware of its ever having been introduced on ship-board in Behaim's day. Magellan, many years afterwards, was content to carry hour-glasses, similar to those which still survive in many kitchens, where they regulate the time for boiling an egg.(52)

A UNIVERSAL EQUINOCTIAL SUNDIAL

Of course, it is quite possible that Martin Behaim imported into Portugal portable sundials, small metal astrolabes and other instruments for which his native town was famous, just as his brother Wolf, about ten years afterwards, imported "Nuremberg eggs" or portable wheel watches, which had only recently been invented.(53)

The Ephemerides.

Martin Behaim has been credited not only with having introduced into Portugal certain astronomical instruments, but also with having made known there the `Ephemerides' of Johann Müller of Königsberg, known as Regiomontanus. These famous `Ephemerides ab anno 1475 ad annua 1506' were published at Nuremberg ten years before Behaim came to Portugal, and were reprinted at Venice in 1483. Is it likely that King John, who took such a lively interest in scientific pursuits, and his advisers, should have remained ignorant of the existence of a work of such importance? But even supposing that these `Ephemerides' had first become known in Portugal through the agency of Behaim, they would not have attracted any special attention. José Vizinho, the most active scientific adviser of King John and of his successor King Manuel, knew, as a matter of course, that the `Almanach' of Zacuto, his former teacher, contained tables which would enable an observer to compute readily his latitudes from an observation of the meridian altitude of the sun, which was not possible as long as only the `Tables' of King Alfonso(54) of Castile were available. This `Almanach perpetuum celestium motuum,' having been translated by José Vizinho from Hebrew into Latin, was first printed at Leiria in 1496, but there is no doubt that MS. copies, especially of the few tables of special interest to mariners, existed long before that time.(55) The `Almanach' contains four "tabulae solis" for a cycle of four years (1473-6), including three ordinary and one leapyear, and a "Tabula declinationis solis ab equinoctiali." The former give the sun's geocentric longitude for each of the twelve signs of the Zodiac and for each day of each year, whilst the latter gives the sun's declination corresponding to these longitudes. This declination table differs but slightly from a similar table included in the work of King Alfonso. With the help of Zacuto's tables a latitude would be computed as follows:

It is credibly reported that Zacuto instructed the pilots who sailed in his time on voyages of discovery,(56) and there can be no doubt that his `Almanach' was in use in the Fleets of Vasco da Gama, Cabral, João de Nova and Albuquerque.(57) Of course, they may have been supplied as well with the `Ephemerides' of Regiomontanus, and we know that Columbus and Vespucci made use of the work of the great German astronomer. Andres de San Martin, one of the pilots in Magellan's fleet, who was killed in Sebu in 1521, had both the `Almanach' of Zacuto and the `Ephemerides,' and found both woefully in error when attempting to calculate a longitude from a conjunction of Jupiter and the moon, which he had observed on December 17, 1519.(58)

Francisco Albo, another pilot of Magellan's expedition, who was fortunate enough to return to Spain, to judge from the log-book as published by Navarrete (IV., 1837, p. 209), evidently had tables of declination of our modern type. (59)These tables are entered with the date, and furnish the sun's declination at a glance, without the computer being obliged to have recourse to a "Tabula Solis" giving the sun's geocentric longitude. Eugen Gelcich(60) surmises that "tables were prepared in this form at the suggestion of Behaim and of his colleagues of the Junta, in order to meet the requirements of mariners." José Vizinho might, of course, have prepared such tables, and so might any ordinary pilot, for their computation called for little skill and no knowledge of astronomy. But I demur even to the suggestion that Behaim, whose ignorance of nautical matters I believe to have been proved, had a share in this humble work.

The earliest printed tables of this kind I found in Martin Fernandez de Enciso's `Suma de Geographia' (Seville, 1519). These tables, like all those of a subsequent date, are calculated for a cycle of three ordinary and one leap year, as in Zacuto's `Almanach.' Two sets of similar tables are found in a MS. Codex now in the library of the Duke of Palmella, and published at his expense.(61) This codex contains a treatise on the mariner's compass by João de Lisboa,(62) dated 1514, besides a number of other papers and documents by unknown authors dating from the end of the fifteenth to the middle of the sixteenth century. Among these are two sets of declination tables, the one of the usual type, the other peculiar, inasmuch as the point of reference for what its author called "declination" is the North Pole. Thus decl. 23° S. is expressed by 90°+23°=113°, whilst decl. 23° N. is given as 90°-23°=67°. Neither date nor author of these two sets of tables is given. The last set of tables which need be mentioned are printed in Pedro de Medina's `Arte de Navigar' (Valladolid, 1545).

The fact that these various tables were computed independently is made manifest by the following table, which gives the southern declination for the first of January of each of the four years of a cycle.

Breusing, Günther and Ruge on Behaim's services on the Junta.

It is now time to ask what, in the opinion of competent critics, had Behaim done to entitle him to a position on a scientific committee which J. de Barros assigns to him, or the appointment as cosmographer and astronomer of the important expedition which left Portugal in 1485 under the leadership of Diogo Cão?

Dr. A. Breusing,(63) Director of the School of Navigation at Bremen, who lays stress upon the importance of improved instruments of observation, contents himself with suggesting that Behaim made known in Portugal the cross-staff and a metal astrolabe of handier size than those which he supposes to have been in use up to his time.

Dr. S. Günther(64) suggests that Behaim paid a visit to Lisbon in 1482 or 1483, that he there heard of the efforts which were being made to improve the art of pilotage, whereupon he let it be known in the course of conversation, that he, as a pupil of the great astronomer Regiomontanus, had acquired knowledge likely to prove of great service to mariners. The King, when he learnt this, invited the young stranger to join the Junta dos mathematicos, which had recently been appointed. Behaim, as a matter of course, accepted this invitation, and thus secured a position in Portugal. He then returned to Germany, to wind up his affairs, went back to Portugal in 1484, and was at once appointed to accompany an expedition for the exploration of South Africa. Günther then maintains that the introduction of the cross-staff and of the `Ephemerides' most amply justified the Portuguese mathematicians in inviting this youthful stranger to join in their deliberations.

Dr. Sophus Ruge, in a review of Günther's excellent biography,(65) accepts the view that Behaim paid a flying visit to Lisbon in 1482, where he boasted of having studied astronomy under Regiomontanus, and was commissioned in consequence to procure certain astronomical instruments, including a cross-staff, for which his native Nuremberg was famous. With that object he visited Nuremberg in 1483, was taught there the use of these instruments, and although never appointed a member of the Junta, his technical advice proved of such value that it secured him the appointment as astronomer of Cão's expedition.

All this is most ingenious, no doubt, but it is mere conjecture. He might have paid a visit to Lisbon in 1482, for nothing is known of his movements between June 9, 1479, when he was at Antwerp, and February, 1483, when he was summoned before the magistrates at Nuremberg for having danced at a Jew's wedding. Instead of returning immediately to Lisbon with his instruments, he attended the Easter fair at Frankfurt, and the fair at Bergen in October or November, where he bought cloth and borrowed money, and was only ready on May 4,1484, to leave Antwerp for "foreign parts."(66) The documents still available mention cloth, galls, and a few other articles as the merchandise he dealt in, but refer in no single instance to "instruments." Had he been commissioned to buy instruments at Nuremberg, as conjectured by Dr. Ruge, he would no doubt have returned immediately to his mandatories. At the same time it is curious that a supposed pupil of Regiomontanus should have been obliged to visit Nuremberg in order to make himself acquainted with the use of instruments invented or manufactured by his master. Still, it is just possible that Behaim did import instruments into Portugal, but there is absolutely no proof extant that he ever did so.

Footnotes

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