G. R . TIBBETTS

THE NAVIGATIONAL THEORY OF THE ARABS IN THE FIFTEENTH AND SIXTEENTH CENTURIES

COIMBRA-1969 !C --o / G . R. TIBBETTS

THE NAVIGATIONAL THEORY OF THE ARABS IN THE FIFTEENTH AND SIXTEENTH CENTURIES

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Separata da Revista da Universidade de Coimbra Vol. XXIV

Composto e impresso na •/mprensa de Coimbra, Limitada• THE NAVIGATIONAL THEORY OF THE ARABS IN THE FIFTEENTH AND SIXTEENTH CENTURIES

by

G. R. TIBBETTS

A. The accounts of Vasco da Gama's first voyage in the Indian Ocean make it clear that when he enquired for an Indian Ocean pilot in Malindi to carry him across the Indian Ocean he was shown a man whose knowledge of navigation appeared quite complex and at the accuracy of whose charts he was surprised. Other European travellers in these regions from Marco Polo onwards had also noted the methods by which their pilots had carried them across the Indian Ocean, and there is considerable evidence that the basic methods used to plot a course by shipping in this area go back to the time of the Periplus and perhaps even centuries beyond. We are lucky therefore in possessing a few manuscripts on Arab navi­ gational science, dating from the 16th century, refering to the navigational practice of the period immediately preceding and originally written from the period 1450 onwards. These works form a group of both theoretical treatises on navigation and pilot-guides similar to European roteiros. The history of these manuscripts and the scholarship expended on them has been mentioned several times by several scholars and it is really only necessary here to mention briefly the authors and the works they wrote. The first navigational work to come to light was the Mu/:z'it of Sidi <;elebi, a Turkish writer and admiral who had been in charge of Sulaiman the Magni­ ficent's Indian Ocean fleet, and who wrote this work in Turkish during his enforced stay in Gujerat after the dispersal of his fleet in 1554. This work turned out to be more or less a direct translation from the Arabic of several_ of the works which I am about to mention and can be virtually ignored fqr the purposes of this paper, although a considerable amount of work was done on trying to explain the navigational procedures mentioned by Sidi <;elebi by James Princep in the J. of the Asiatic Society of Bengal 4 from 1834 onwards (1). It is even doubtful if Sidi <;elebi himself understood the navigational practices he was describing. In 1897 Bittner and Tomaschek produced their «Die topographischen Capite/ des indischen Seepiegels Mohit» (2). This was mainly a full and detailed account of Sidi <;elebi's topography but the place names were compared with those given on the charts of Alberto Cantino of Modena (1502) and Nicolo de Canerio of Lyon (n.d.) which showed a close affinity with the Turkish work. It seems therefore likely that these charts could have used Arab sources and possibly even charts of Arabic origin. It was not until 1912 that M. Gaudefroy-Demombynes revealed that two manuscripts in the Bibliotbeque Nationale (MSS. Arabe 2292 and 2559) contained the Arabic texts of the sources mentioned by Sidi <;elebi (3). In all, these manuscripts contained 26 different works on navigation by the two mu'allims Al:lmad ibn Majid and Sulaiman al-Mahri of which a large proportion were arjuza; that is poems in the rajaz metre. Gaudefroy Demombynes intended to edit these manuscripts but it was really left to Gabriel Ferrand to work on them. When in 1914 he published the second volume of this Relations de voyages et textes geographiques ... relatifs a/'extreme­ orient, he compared these texts with that of Sidi <;elebi including in the foot­ notes parallel passages or words from the Arab texts -but this was mainly in connexion with the topographical content of the texts (4). In 1921 he began a large work to be in four volumes entitled Instructions nautiques et routiers arabes et portugais des xve et XVJe siecles giving the Arab text of these two manuscripts in phototype. It was also to have included a transla­ tion, commentaries on the geographical parts and a glossary of Arabic nautical terms. Finally French translations of contemporary Portuguese roteiros were to have completed the work. The photocopies of both manuscripts were published by 1925 as volumes I and II to this work and finally in 1928 volume III appeared but it did not contain everything that the original plan had intended. There was no translation and no annotations. Ferrand's contribution was an introductory chapter on the profession of navigator (mu'allim) and on the two authors and their works. The volume also included a reprint of the notes by Princep mentioned already and an article by H. Con­ greve on Coromandel navigational practices taken from the Madras Journal of Literature and Science of 1850. But the most important part of the volume was two articles by Leopold de Saussure, the first on the origin of the compass rose and the invention of the compass and the second entiled Commentaire des instructions nautiques ... dealing mainly with the measurement of latitude

(1) «Extracts from the Mohit, that is the Ocean, a Turkish work on navigation in the Indian Seas. Translated by J. Hammer-Purgstaii». J. Asiatic Society of Bengal1834 pp. 545-53; 1836, pp. 441-68; 1837, pp. 805-12; 1838, pp. 767-80; 1839, p. 823-30 (Calcutta, 1834-9). (2) Published in Vienna, 1897. (3) <Star, Ursa Minor and Ursa Major as found in the Arab texts. This last is the work on which practically all that has been written on Arab navigational science to date has been based. No more volumes of Ferrand's work were published and although he produced quite a few articles which used material from the texts he did not publish anything on their navigational content. In addition to these texts a manuscript was found in the library of the Asiatic Museum of the Academy of Sciences in Leningrad (now the Oriental Institute) containing three navigational poems reputed to be by Al:lmad ibn Majid. Although these poems were first noticed in 1819 and were known to Kratchkovsky who informed Ferrand of their existence, nothing was published about them until 1957. Then T.A. Shumovsky published photo­ graphs of the text and a full translation into Russian with many notes and a long introduction. This was translated into Portuguese in 1960 as Tres roteiros desconhecidos (5). Thus until a few years ago Ferrand's work from the 1930's was the most up-to-date research done on this Indian Ocean tradition of navigation. His work was very incomplete and no one had seriously studied the navigational art or science which was the original reason for writing the texts, except for De Saussure's commentary on latitude measurements. Shumovsky in intro­ ducing the poems from Leningrad had only De Saussure to base himself on for the explanation of navigational techniques. His texts were poems and the sense of these poetical works is often difficult to unravel and the whole of Ibn Majid's work is much more involved than that of Sulaiman al-Mahri on which Sidi <;elebi, Princep and finally De Saussure's work was based. The real key to the study of Arab navigation is the long prose work of Ibn Majid entitled the Fawii'id or «the book of useful things» which appears at the beginning of MS. 2292 of the Bib. Nationale. This I have worked on for nearly fifteen years, translating and attempting to understand it and after this time I feel that I am in a position to give an account of my efforts in elucidating the theory behind the texts (6). I also feel that I can add con­ siderably to the efforts of De Saussure and others and can give a fairly adequate account of the methods used by the more scientific or perhaps the more literary of the sea-captains of the Indian Ocean.

B. The elucidation of Arab nautical science must begin with an attempt to see how the Arab navigators themselves attempted to distinguish the techni­ ques they used. In their efforts at explaining their science on paper they have given a certain priority to these techniques and attempted to place them

(5) «Tri neizvestnie lotzii Ahmada ibn Miidjida>>. (Moscow, 1957). The Portu­ guese translation was by M. Malkiel-Jirmounsky and published in Lisboa, 1960. (6) A really detailed account of this will be given in my book «Arab navigation in the Indian Ocean before the corning of the Portuguese» accepted for publication by the Royal Asiatic Society. 6 under certain beadings. These headings appear in most of the texts and become as it were branches of navigational science although these are not all of the same importance to us here. These branches were not absolutely fixed and vary according to author and work- different terms are sometimes used for them and extra branches are sometimes given importance. The main divisions of Arab navigational science however seem to be as follows: ishiiriit, the study of landmarks and other visible signs; siyiisiit, the running of the ship and control of the crew- a branch which we would not really regard as part of navigation; mawiisim, the correct estimation of monsoon dates; the science of majra or compass bearings, qiyiisiit, the technique of taking stellar altitudes; masiifiit, longitudinal measurements. All these were techni­ ques necessary for the successful accomplishment by the ship of, a dira or route - a fixed known track between two ports. The route itself was of three sorts according to Ibn Majid -although the last two sorts were combined by Sulaiman al-Mahri- and they were distinguished by the complexity of their navigation and possibily by their precedence in the history of the development of Arab navigation. These were the dirat al-mul or coastal route, the dirat al-matlaq a direct route across the sea between two opposite coasts and the dirat al-iqtidii' (the last word means «imitation» so its use here is very obscure). This last is a route which changes its bearing when out of sight of land. It will be seen therefore that the first route can be accomplished by using a keen sight and having a knowledge of the configuration of the coasts. The technique mentioned above which is required for this is that called ishiiriit, the study of landmarks and visible signs and this is therefore the simplest and perhaps the most ancient form of route. The second type utilises in addition to ishiiriit a knowledge of bearings whether compass bearings or just a knowledge of the points on the horizon where prominent stars set and rise - a fact which may point to the origin of the Arab compass rose. The third type is the most complicated and requires in addition the knowledge of the measure­ ment of stellar altitudes with the aid of the instrument known to most nautical historians as a kamiil- a word which never occurs in the Arabic texts. It may be thought that a knowledge of latitude was essential for all types of route, for instance if one lost sight of land on a route of the first type or became worried about sighting land on a route of the second type, this knowledge would be essential. This was not so however, a knowledge of stellar altitudes seems to have been useful but not essential. A good navigator might use it but the routes given by Sulaiman al-Mahri in detail show that in cases of error one could guess or tell from the compass in which direction land lay. The ship could thus sail straight for it, until the pilot could use his knowledge of the coast to set himself aright. We can dismiss the dirat al-Mul or coastal route quickly although it must be remembered that there was coastal sailing on most of the coasts of the Indian Ocean at the same time as the pilots like Ibn Majid sailed the open sea. Ibn Majid despised the coastal pilot or rubbiin but at the same time ( 7 appreciated the importance of the study of landmarks etc. for every sailor had to approach land at some time if only to make a landfall at the end of his voyage. Convex coasts were always coasted especially the south coast of Arabia and hints about shoals, currents, landmarks and similar things are scattered throughout the texts.

C We must now continue with some account of the techniques developed by the Arabs for use with the other two types of route. The first of these is the taking of bearings. The compass as an instrument is hardly mentioned by the navigational texts; like other instruments of the ship it was meant to be known and understood by the navigators through practical experience. The texts only need to mention it when defects of the instrument or neglect of its use led to errors in one's bearings. The use of the compass must have been considerably earlier than the fifteenth century for its use is so obviously taken for granted by Ibn Majid that the assertations by early European travellers that the Arabs never used the compass for sailing are certainly wrong (7). The earliest Muslim reference to the compass is 1232 A.D. and to its use in navigation about 1282 (8). This use was in the Mediterranean where the practice of the Arabs was approximately that of the Christian sailors and therefore does not shed light on Indian Ocean practices which probably developed independently. We do not know whether Mediterranean usage was adopted from Indian Ocean usage or vice versa. The instrument used by Ibn Majid can only be reconstructed by examining the passages in which it is fleetingly mentioned. There was obviously a magnetic needle for the name for the compass ibra means literally «a needle» and this suggests that a dry form of the compass was used -a form which was used by the 13th century in Europe although the Arab navigational use mentioned above in the Mediterranean was of the «floating fish» type. In addition there was a compass card dii'ira (lit. circle) presumably marked with the thirty-two rhumbs. The whole was arranged in a box /:tuqqa and this was placed in a position convenient for the helmsman to see on a binacle nash al-buqqa. It is possible that the helmsman magnetised the needle by drawing the loadstone across the whole set-up for there is a procedure for using the loadstone «over» the box (tar(ib al-maghhniitts 'ala'l-/:tuqqa). A series of compass defects are mentioned also by Ibn Majid which I have explained in more detail elsewhere (9), but the terminology is so obscure and texts confused and the whole subject is mentioned so fleetingly that it is difficult to determine anything exactly. Needle oscillation is probably

(7) FERRAND, Instructions nautiques, III, pp. 96-7. TAYLOR, E. G. R., The haven­ finding art, pp. 126-7. MAJOR, R. H., India in the fifteenth century, Hakluyt Society, 1867, p. 26. (8) In the Jami' a/-Hikayat by Muh. al-Awfi (1232) and in the work of Bailak al-Qibjaqi written in Egypt about 1282. (9) See my book mentioned in note 6 above. 8 mentioned using a Sanskrit or Indian technical term and perhaps compass variation. The navigators were aware that the needle did not always point due north and put this down to the fact of faulty magnetisation or slovenly work on the part of the helmsman. Other causes like the cold or the needle being badly balanced on its point were used to explain compass errors. There is also another phrase from Sulaiman al-Mahri about the pivoting of the compass which seems to refer to the pivoting of the card itself and this leads one to suppose that the form the Arab compass took was that of a pivoting card. However it must not be overlooked that Sulaiman al-Mahri was writing in the middle of the sixteenth century when Europenas using this type of compass bad been sailing in the Indian Ocean for some time. The Arab Indian Ocean compass card has been described by nearly everyone who bas written on this subject since Princep. Its form is well­ known to most historians of navigation and consists of north and south points with 15 equal divisions between, named after 15 prominent stars which rise and set approximately in the 15 directions; the Arab word mat/a' (rising) and mughi:b (setting) before the name of the star indicating whether the eastern or western horizons are meant- although only when the distinction is necessary. De Saussure pointed out that the use of this rose is much older than the use of the magnetic compass. It must have originated in the Indian Ocean as some stars are not visible further north and some of the southern stars are too high in the sky in more northern latitudes to be used as directional stars on the horizon. Attempts to show the date of the system or its place of origin from the actual choice of stars are all doomed to failure for before the advent of the magnetic compass there was no need for an accurate subdivision of the compass rose. A place could be reached from another by aiming at the setting point of a certain star, and this would be sufficient for practical purposes. It is possible that originally many stars were used as directional stars and the number was finally reduced to the sixteen used on the compass card. Survival of the use of others (e.g. Mirzam and Aldebaran) for 1/2 rhumbs near the east and west points may point to this earlier period. More to the point is which star was used when the term employed refers to a whole constellation and why some terms seem to have changed places in the north-south alignment. The navigators were aware of this and stress the fact that in the 15th century, these were only names of convenience and ignorant sailors should not use the stars literally -a fact which shows that some of them must still have prefered the use of the actual stars to that of the compass. Sulaiman al-Mahri gives a list of actual bearing for these impor­ tat compass rose stars and gives a list of stars which could be used for more accurate determinations of the exact rhumbs.

D. The most important of all the techniques used by the Arab sailors was that of measuring their latitude by means of stellar altitudes (qiyas). This process was again examined by De Saussure from information obtained 9 from Sidi <;elebi and (through Ferrand) from Sulaiman al-Mahri, but his comments were limited to the use of the Pole Star and the two Bears. The instrument used for this process was described in detail by Sidi <;elebi and commented on by Princep - little has been added since his time. He mentions «a small parallelogram of horn (or wood)? about two inches by one with a string inserted in the centre. On the string were nine knots». An example of this instrument was presented to him by a navigator from the Maldives and was called a kamiil. This is the name that all historians of navigation have called the instrument since, but the navigators never used this word - as it comes from the Maldives it may not even be Arabic. The references given by Shumovsky to this word are not references to the instrument at all (10). Sidi <;elebi used the word loh (lit. «tablet») and his detailed des­ cription shows that he is not always describing the same instrument as Prin­ ceps Maldivian kamiil. Sidi <;elebi had an instrument consisting of nine tablets each with a string through it or with one string through them all. The nine tablets each had a different width to correspond with different angular latitudes on the horizon. The smallest tablet was divided by grooves, so that the set gave a complete range of division from 1- 12 isba'. The smallest tablet (4 isba') measured the exact distance between a and f3 Aurigae and this was used as a check for the whole system. Sidi <;elebi states that this was the instrument used by the ancients and by his day the system of knots seems to have been established, and he describes a method of calcula­ ting the knots similar to that shown Princep. Sulaiman al-Mahri and Ibn Majid never properly describe the instrument which they use. Like the compass, it was to be seen by the apprentice navi­ gator on his ship and its description was not necessary. Only by studying Sidi <;elebi's description can we understand their use of the instrument. Theirs seemed to have graduations of isba' and was referred to as a khashaba (lit. a piece of wood). However variant forms f:zataba and khiitjaba suggest that we have here a foreign word, the spelling of which was not properly known to the writers. We must therefore understand a wooden tablet measuring an angular distance between the eye and the horizon, having graduations, but whether the graduations were on the wood or knots on a string we cannot say, no string is ever mentioned by the Arabs. There were several kinds of khashaba; one of 12 isba', one of four and one of two isba'. Presumably the first had a maximum measurement of 12 isba', the last a minimum of 2 isba'. The 4 isba' khashaba was more complicated for there were several sorts, large, medium and small. The technique for using each was not the same, presumably because error was more prevalent in one than in another, although nowhere do the texts make it clear what the exact technique was. Whether the difference in technique and error was due to the distance from

(10) Shumovsky produces two examples of the use of the word, as kama/ (83r 1.15 and 86r. 1.4). Neither of these contexts applies to the instrument inquestion. 10 the eye at which the instrument was used or due to the thickness of the wood or whether the construction of these various types different, is not clear. The unit of measurement used by the navigators, the isba' has also been described many times. The word literally means a finger and was considered to be the angle subtended by a finger held at arms length against the horizon. Four fingers was a dhubbiin, a word of unknown origin, which was the dis­ tance between a and fJ Aurigae. The isba' was divided into eight units known as ziim (lit. «watch» of three hours) so that the navigator theoretically reckoned the rise of the pole one isba' above the horizon as equivalent to one daj's sail due north. Attempts have been made to equate the isba' with an exact angular measurement in order to see just how accurate the Arab measurements of of latitude were, but the measurements always break down somewhere. By the time of Ibn Majid the isba' had become standardised although it was originally dependant on the width of the navigator's finger and the length of his arm. However variations existed for Ibn Majid gives different readings for certain places often depending on the nationality of the navigator. Ibn Majid says there are 224 isba' in a circle, which is a convenient figure for that makes 7 to each compass rhumb and 8 to each lunar mansion. Sulaiman al-Mahri, working from the Polar distance of the Pole Star, states that there must be 210 to the circle but for all practicable purposes he reverts to 224 ; the traditional figure.

E. The articles of De Saussure and Princep leave the impression that the Arab measured their latitude entirely by the altitude of the Pole Star, and when this was invisible by the Farqadan ({Jy Ursae Minoris), again when when this was invisible, by the use of the stars of Ursa Major. This was not so. The whole art of Arab navigation by stellar altitude (i.e. qiyiis) was that as long as a bright star was shining in the heavens they were never at a loss for their latitude. In many cases the measurements taken on other stars were converted to Pole Star altitudes but they were quite often left as they were. Quite a few of the poems copied in the Bibliotheque Nationale mss. are in fact versified tables of place-names giving their latitude according to a particular star or combination of stars. In Sulaiman's description of the Red Sea, latitudes are given in terms of Pole Star altitudes and in altitudes of al-murabba' the southern cross, because it was easier to measure with with the latter for one stood with ones back to the prevailing wind and more accurate readings could be taken this way. The works of Sulaiman show that six or seven different methods of using stars for latitude determination were considered important or necessary under normal conditions. Ibn Majid however excelled himself by mentioning almost seventy different ways of measuring using nearly every bright star in the sky. These stars and the methods of using them fall into certain fixed classes, some of which are given technical names by the navigators. The first is the culmination of a star i.e. when the star could be used for any latitude north or south. In order to gauge the culmination accurately positions 11 of neighbouring stars were sometimes used, but the easiest method for fixing any position of the heavens was to state which lunar mansion was culminating at the same time. Thus, they talk of measuring the Pole Star at the culmi­ nation of al-Sarfa ((J Leonis) i.e. at the inferior culmination of Polaris. Achernar (Sulbar) was measured at its culrllination at the culmination of Batn al-I;Iut and Sharatan ((J Andromedae and a Arietis). The second class of measurement from the point of view of accuracy was the abdiil measurement. This consisted in taking the altitude of two stars when they were in a position of equal altitude. This measurement was only abdiil when the stars were of equal declination and thus formed with the Pole an isosceles triangle having a horizontal base. The height of the Pole could then be ascertained and the figure converted to Pole Star altitude if required. Examples were the use of Canopus with a Crucis at the culmination of al-Jabha (a Leonis), and the use of Vega and Capella at the culmination of Batn al-lfut ((J Andromedae). It will be seen that abdiil relationships weree ssentially of the meridional type as the meridian bisected the line joining the two stars. Thus the only inaccuracy could come from the fact that the two stars chosen did not always have exactly the same declination, and as it was often difficult to find two suitable stars: most of the abdiil relationships suffered from this inaccuracy. The navigators compensated for this by stating that certain measurements were only accurate over certain ranges of latitude although Vega and Capella were regarded as very accurate in all latitudes. An extension of the abdiil form of measurement is the use of the position of equal altitude of any two bright stars. The errors here can be considerable and are greater the further the stars are from the meridian. Measurements of this sort have to be produced from actual measurements taken at the latitude concerned and «tables» learnt by heart. Their latitude range is extremely lirllited and some can only be used satisfactorily at one latitude. These however could be useful for a pilot sailing due E or W who could then con­ tinually check his latitude throughout the night by using this sort of measure­ ment as it occurred. Favourite examples of this sort of measurement ase the use of Castor and Achernar or Canopus and Vega, but by far the most common of equal altitude measurements are those where the two stars are close together at the same time. Examples of this are a(J Centauri (Jy Ursae Minoris and (Jb Crucis. Another far less common type of measurement was the vertical position of two stars, but often this was no more than a device to check the meridional position of one of the stars. The exact position of verticality was difficult to deterrlline and often a third star was needed to help produce the correct position for measurement. Ibn Majid gives several groups of three stars that can be measured together and even one where four bright stars have equal altitude in four corners of the heavens. But this is not the end of the complications of stellar measurement. All the above methods depend on the establishment of a certain position 12 of the heavens and then the measurement of the altitude of one or more of the stars in question in order to find ones position. As I have mentioned just now, some of these combinations of stars had an extr0mely limited appli­ cation. In order to lengthen this application another system of measurement was produced in which the relationship of one star to the horizon was fixed and the variations of the second star due to latitude position was measured. This system was known as qaid or as I prefer to translate it «fettering» of one star to the horizon. This comprised the measuring of one star's altitude whenever another star appeared at a known height above the horizon. An example is that of l; Ursae Majoris and a Arietis which were both 8 isba' above the horizon when the Pole Star was 8 isba'. Now they (according to Ibn Majid) decrease 1/2 isba' as the Pole Star decreases 1 isba' (i.e. with the normal equal altitude measurement) until the Pole Star is at 5 isba' and they are at 6 1/2. This is probably the limit of their application. By using the qaid method and keeping l; Ursae Majoris («fettered») at 8 isba', a Arietis would rise and fall 1 1/2 isba' to an isba' rise and fall of Polaris. a Arietis could also be «fettered». Thus there were three different methods of using these two stars, six if you include the fact that they can be used with either l; Ursae Majoris or a Arietis rising (and the other star setting). Practically however the use of the «fettering» system was more limited than one might think. This system tended to exaggerate the errors or variation found over a range of latitude when the two stars were not equidistant from the meridian. The navigators were aware of this. Also it must be understood that these qaid measurements cannot be taken continually over a period of time as the heavens revolve. Only one measurement can be taken on one night for the particular star fettered can only be at the correct fettering altitude for a moment each night. This applies to all stellar measurements; the navigator kept his position not by observing one group of stars (unless it were the Guards) but by checking from each available measurement as the correct position for its observation passed by in rotation. It was extremely useful to have different stars in different parts of the heavens for checking ones position if the Pole Star or the Guards were obscured by cloud. The six main methods of star measurement given by Sulaiman al-Mahri, seven if we include the use of Polaris itself, must now be noted. These are 1. the use of Polaris at its lowest culmination and at the culmination of {J Leonis, together with I a. the horizontal position of the Guards at the culmination of {J Leonis used when Polaris is invisible and lb. the horizontal position of the three stars t5 s l; Ursae Majoris used when the Guards are no longer visible. The last occurs slightly later than the two previous positions. These are all dealt with in detail by De Saussure in vol. III of Ferrand's Instructions nautiques.

2. The use of a Crucis on the meridian at the culmination of y Virginis. 3. {315 Crucis in their horizontal position at the culmination of Spica. 13

4. The horizontal position of a{J Centauri at the culmination of a{J Librae. 5. The use of Achernar on the meridian. 6. Canopus and Achernar at equal altitude at the culmination of the Pleiades. 7. The use of Sahm ai-Awwal at the culmination of a Capricorni. Sahm al-Awwal is a difficult star to identify but it is most likely a Pavon is which is on the meridian at this time. It will be noticed that Sulaiman finds the use of Polaris and the Bears sufficient for the northern horizon but finds several groups useful on the southern horizon. Ibn Majid emphasises several other groups of northern stars like the abdiil relationships previously mentioned and also other positions of the Guards. Other groups like s Ursae Majoris with a Andromedae, or a Canum Venaticorum with fJ Andro­ medae are quite common. In the Sofaliya poem from the Leningrad ms., many star groups are used for different parts of the African coast, but the most common are the two Bears; Arcturus with either Spica, Canopus or a Centauri; a Crucis with a or fJ Centauri; Capella with the stars of Orion.

F. It might be useful now to add a few details to De Saussure's notes on the use of the Pole Star and the Bears and also to say something of the use of the Southern Cross. The use of Pole Star altitudes to determine one's latitude is one of the mo~:>t important techniques of Arab Indian Ocean navigation and was the equivalent to the Mediterranean and Atlantic method of measuring the noon altitude of the Sun. The use of the Pole Star instead of the Sun was probably due to the fact that in tropical latitudes the sun's altitude was always high and this with its brightness made it difficult to measure by direct observation whereas the Pole Star was always conveniently placed close to the horizon. Thus the Pole Star was the most convenient for measurement with a kama/ and the Indian Ocean navigators never thought of using the shadow length for navigational measurements. The Sun's noon time altitude also varied from day to day throughout the year and tables were needed to give one the precise height for the particular day. On the other hand the North Pole remained at the same height for any given latitude and the Pole Star made a small circle round the Pole which was probably ignored at first, although later, when finer readings were possible, it could easily be taken into account by noticing the position of the rest of the heavens. This difference in Pole Star height was known as the biishl: and was named after the lunar mansion which was culminating at the time. Thus when the biishi: of Aldebaran is described as 3 isba', this means that when Aldebaran culminated the Pole Star registered 3 isba' more in any particular place than it did at its minimum altitude which was the usual value remembered or noted by the navigators: the standard measurement of Pole Star altitude was known as al-qiyiis al-asli: «the basic measurement» and to convert Pole Star readings to this it was neces­ sary to subtract the biishi: of the culminating mansion. Ibn Majid in his treatise the Fawii'id gives a great deal of space to describing the position 14 of the heavens as each mansion culminates, for if the mansion was obscured by clouds, other stars could be used to check the biish'i. One of the most obvious checks was the use of the Guards, but it must not be supposed, as Ferrand and De Saussure did, that the Guards were the real and only check on the position of the Pole Star nor was this the only use of the Guards. The most usual check on the position of the Pole Star was the lunar mansion and the Guards were used primarily as measuring stars in their own right. The Regiment of the North seems to me to be originally a Mediterranean or Atlantic usage and not of Indian Ocean origin. The actual distance of the Pole Star from the Pole is given by the navi­ gators as 2 isba', thus the maximum biish'i was 4 isba'. This was the diameter of the circle made by the Pole Star round the Pole and the Pole Star registered this maximum height which was at the culmination of a Pegasi at its upper culmination. The fact that the phenomenon of precession caused the Pole Star's polar distance to vary over the ages was known to the navigators but was ignored in actual practice. The ancients had recorded a maximum biishi of six isba' and while Ibn Majid regards this as an error, Sulaiman regards it as a historical curiosity. Another variation due to precession was the change in position of the Pole star's lower culmination with regard to the culminating mansion. The usual culminating lunar mansion was according to the navigators al-Sarfa ((3 Leonis), but they had their doubts about the accuracy of this and several positions between f3 Leonis and e Virginis were suggested at various times. The fact that it was extremely difficult to measure the change in height when the Pole Star was at the upper and lower extremes of its course made the exact position difficult to ascertain. However the navi­ gators realised that the mean biishl positions were easier to measure and that they were situated exactly 7 mansions away from the lowest position of the Pole Star. As I have just mentioned the Guards were not primarily used as indicators of the biishi values by the navigators. Their importance to the Arabs lay in the fact that after the Pole Star had disappeared beneath the horizon they were the most prominent stars near the northern end of the meridian. The navigators therefore used them in their horizontal position to express latitudes which were too low to express in terms of Pole Star alti­ tudes. This position also occured at the culmination of f3 Leonis, i.e. at the same time as the Pole Star's lower culmination so that the difference between the two systems could be estimated easily. This difference was reckoned as 7 isba' so that an altitude of one isba' of the Pole Star was equivalent to an 8 isba' altitude of the Guards. This was continued southwards until the Guards were 1 isba' high, when the stars of the Great Bear came to be used. The stars of the Great Bear used for this measurement according to the Arab texts were the three which form the handle of the Plough i.e. de b e ~ Ursae Majoris. These were horizontal in southern latitudes almost at the same time as the horizontal position of the Guards. In actual fact they were sightly later, but again extremely convenient for the conversion 15

- the difference being this time 12 isba', 1 isba' of the Guards being 13 isba' of the Great Bear. Of the other uses of the Guards, the upper positions i.e. the culmina­ tion of fJ Ursae Minoris and the vertical position of (Jy, could be used when the Pole Star was invisible but they are not given the importance one would expect by the Arab navigators. The lower vertical position of (Jy and the due east and west positions were given more prominence by Ibn Majid but the lower culmination and the lower horizontal position were not mentioned frequently. Another curious measurement was the use of fJ Ursae Minoris when a(J Crucis were horizontal. This was mentioned twice by Ibn Majid. Before we leave the question of stellar altitude mesurement I must mention the use to which the Arabs placed the Southern Cross. The name of the constellation in the Arab texts is murabba' «the quadrilateral» and the star used for measurement was the lower one i.e. a Crucis at its culmination which was when y Virginis culminated. The Cross was visible everywhere in the Indian Ocean and in the Red Sea was still visible in the latitude of Jedda. Being in the Soutern hemisphere it was often visible when the stars of the northern part of the sky were covered with cloud and it was specially useful in the Red Sea where the almost continuous north wind made the taking of measurements in a northerly direction quite inaccurate. Both Sulaiman and Ibn Majid give complete lists of a Crucis altitudes in the Red Sea. It was a meridional measurement and was acc'Urate at all latitudes and rose as the Pole Star fell and vice versa by the same amount. This places murabba' automatically in the southern hemisphere, a fact which has never been noticed by any European scholar who has studied the texts. The standard value of a Crucis is that it is 4 isba' at Ras al-Hadd although the texts give various equivalents in Pole star altitudes, i.e. when the Pole Star is 10 isba' high it can 1 be anything from 4 / 4-5 isba'. In fact in the Arabian Sea it is described as falling from over 8 to 2 when the Pole Star rises from 6 to 13. It is possible that in less accurate days, a Crucis was measured when (Jb Crucis were horizontal. Ibn Majid and Sulaiman recognised the error in this, but Ibn Majid uses it as a rough and ready method. They then used the horizontal position of (Jb Crucis as a separate measurement at the culmi­ nation of Spica. These two stars usually appeared 2 isba' higher than the measurement of a Crucis at the same place- thus at Ras al-Hadd they meas­ urement of a Crucis at the same place- thus at Ras al-Hadd they measured 1 6 isba'. y Crucis was also used and was 7 / 2 isba' at Ras al-Hadd. Other measurements used with the Cross were the vertical position of ay Crucis, near the meridian but difficult to fix the position, and the horizontal position of a(J Crucis which was some distance from the meridian. Altogether, says Ibn Majid, there are sixteen methods of using the Cross. a(J Centauri were also used frequently by the Arabs for altitude measurements. G. Having now described the basic techniques used by the Arabs I must in as short a time as possible, describe some of the ways in which these techniques were developed. 16

One of the most obvious lacunae m the Arabs' theory of navigation was the measurement of some form of longitude or distance parallel to the equator. Without a prime meridian and some accurate form of time measure, the measurement of absolute longitude was impossible, but there is considerable evidence in the texts to suppose that the Arabs felt a need for some standard set of east-west measurements resembling longitudes. Before the time of Ibn Majid it seems to have been thought possible to measure longitude from the rise and fall of two stars - one due east and the other due west- although how this was thought to have been achieved is impossible to say. This practice was known as Maraqq wa-maghzar «rising and falling» and the writers of navigational treatises ridicule it whenever they mention it. The stars used seem to have been Altair with Castor or Castor with Vega. Sulaiman states that this method was used by the ancients but only an ignorant navigator would attempt to use it, explaining that any movement apparent in a star east or west was due to the movement of the heavens and not due to that of the ship. The navigators did however take east-west measurements and both Ibn Majid and Sulaiman al-Mahri give lists of these in the form of distances between points at the same latitude on opposite coasts. These distances were known as masiifiit (sing. masiifa) a word which means just «distances» and these were measured in ziim or «watches>> which represented a sailing of three hours duration. Masiifiit could be measured by actually sailing the longitudinal distances and measuring ones way, but the actual method of measuring the way is never mentioned by the texts. The errors of this method were listed by Sulaiman al-Mahri, and they were due to the different wind and water resistance of individual ships and the strength and direction of the wind and currents when the journey was made. The fact that some ships are said to be faster than others and hence covered a greater distance in a given time may indicate that the distance was measured in hours sailing rather than as a distance covered on the surface of the water. There was a more scientific way of measuring masiifiit and this was by adopting the system of tirfa measurement. The tirfa was a method of measuring departures and was in fact equivalent to the European method of «raising the Pole». The tirfa was the distance travelled by a ship on a fixed bearing in order to raise the Pole star altitude by one isba'. Tirfa measurement seems to be older than the European system of «raising the Pole» and it is possible that the European method is derived from the Indian Ocean process. However tirfa measurement cannot be older than equidistant rhumb division which may have originated in the Orient with the navigational use of the compass and cannot have been very ancient, although when Ibn Majid wrote his earliest works in the 1460's, it was a well established process. Tirfa measurement also required a fixed unit of distance and for this the ziim (watch of three hours sailing) was used and equated to the distance sailed due north to raise the Pole Star's altitude 1/8 isba', thus we are given the equation 8 ziim equals 1 isba'. 17

In addition to the distance travelled along the rhumb, the departure was also measured i.e. the longitudinal distance reached, but the Arabs always measured the departure in terms of the distances between two neighbouring rhumbs and not as departures from due north. A table given here of the values of Sulaiman al-Mahfi shows that the Arab measurements theoretically were fairly accurate when the departures were small but varied considerably when the rhumbs were close to the east­ -west points (11 ).

Rhumb Distance along rhumb Departures Actual fig. Sulaimiin Actual fig. Sulaimiin al-Jah (N) 8 8 al-Farqadan (N by W) 8 .2 9 1.6 2 al-Na'sh (NNW) 8 .75 10 3.33 4 al-Naqa (NW by N) 9.5 11 5 .33 6 al-' Aiyuq (NW) 11 .25 12 8 8 al-Waqi' (NW by W) 14.5 15 12 12 al-Simak (WNW) 21 20 19 .33 18 al-Thuriiyya (W by N) 41 35 40 .2 34 al-Debaran (WtN) 81 .75 66 or 76 81 .33 66 al-Ta'ir (W) 00 00 00 00

These figures are those of Sulaiman himself. Ibn Majid and presumably most other pilots used a simpler and less accurate set of figures which Sulaiman also gives (departures of 2, 4, 6, 8, 12, 17, 22, 32). However how these accurate values of Sulaiman were arrived at is rather difficult to imagine as the attempts of both Ibn Majid and Sulaiman to give theoretical examples are made unin­ telligible by illogical arguments. Sulaiman makes the same mistakes as Ibn Majid and only this fact enables us to understand Ibn Majid's work by com­ paring it with that of Sulaiman. The basic mistake is to assume that the two shorter sides of a right angled triangle equal the longer. Thus a ship sailing due north to raise I isba' of Pole star altitide sails 8 zam, one sailing N by W raising 1 isba' will have a departure of 2 zam and the tirfa- the distance sailed along the rhumb will be 8 + 2 i.e. 10 zam. A ship sailing NNW to raise 1 isba' will also have a departure (from N by W) of 2 zam, therefore it will have sailed 10 + 2 i.e. 12 zam, or its total departure from due north now being 2 + 2 i. 4 zam, the distance sailed will be 8 + 4 zam i.e. 12 zam and so on- simple mathematics. (Fig. 1, following page). This was obviously an original rule of thumb method which the literary navigators tried to dress up in a scientific guise. However the larger the departure from due north the larger the error and the rhumbs near the east-

(11) The departure figures are given from due north in the European fashion for convenience; I have stated in the text that the Arabs refer always to the distances between consecutive rhumbs.

2 18 west points fooled the navigators completely. Ibn Majid states that pilots had attempted to work out a system of latitudinal departures from east point and he shows how their efforts are erroneous and gives, in very obscure lan­ guage, a correction established by himself. Even his correction can hardly have made sailing simpler on these rhumbs. However the simplified mathe­ matics which I have just mentioned is one of the basic features in Arab theore­ tical route finding. It will also be seen that using these departure figures it is possible to measure theoretically the longitudinal distances between two ports on the same latitude i.e. masafa. Thus if one sails from one port until one has raised or lowered the Pole-Star's altitude a known number of isba' and then sails back to the second port on a new bearing by adding (or in some cases subtracting) the departures from due north one can find the longitudinal distance in zam. Sulaiman al-Mahri goes one step further and produces a route with three different bearing which requires the sum of their departures for the complete masafa. However he states that the greater the number of bearings used the greater the error. Using the Arab values for departures this would certainly be so; only a two bearing route using 45° bearings from the cardinal points could possibly be accurate.

H. It is now necessary to work out what practical effect those methods of navigating had on the art of navigation as practised in the Indian Ocean by the Arabs and presumably the other nations whose vessels crossed the same seas. Using the compass it was possible to sail in 32 definite directions from any given port until one reached a latitude equivalent to a certain altitude of the Pole Star above or even below the horizon. If the port desired was at this point all was well. But on the other hand this point could be the place for changing bearing and then sailing on a new bearing until the right latitude and the desired destination were reached. If one therefore set out with a knowledge of the bearings and Pole Star altitudes required one could, theoretically, reach ones destination. What the Arab lacked was a second coordinate based outside his ship which he could use to check his exact position so that he could pinpoint his position on a chart and compare it to the configuration of the invisible coasts. Sailing along a rhumb line was useful as long as the wind or current, the helmsman, or magnetic deviation did not interfere and change the actual bearing when one was not prepared. The Arabs must have used tirfa departures to show far out they were when they reached their desired latitude for the problem of two ships sailing up neighbouring rhumbs and their distance apart after a certain time is the most frequent problem discussed by the navigators in their works. However all they could possibly state was that they were some zam further along a latitude line than they ought to be and this figure was based on the time taken (in watches) to do the previous leg of journey, or perhaps, if they measured their «way» by the distance covered to reach that latitude. They had no practical method of correcting their position relative to their destination from this information. 19

Thus when one inspects the routes given by the navigators for journeys (especially long distance ones) across the ocean, one discovers at once how the problem was solved practically. The port of destination was in nearly every case arrived at by sailing along the parallel of latitude. The average Arab journey consisted in aiming in an adequate direction froll?- home or from a known point of entering the open ocean until the latitude of the port of destination was reached and then heading for this port along the parallel, using stellar altitude to keep one accurately on the parallel. Even the methods of measuring stellar altitude seem geared to this procedure. The early Portuguese voyagers have left us accounts that the Arabs had excellent charts ruled closely with parallels of latitude and longitude. The Arab texts never mention charts, unless the word rahmiini: could stand for the chart. The rahmiini: was the only written document the Arab navi­ gators possessed, and as the only written documents that have survived are the texts in the form of navigational tratises and mnemonic poems corresponding to European roteiros, it is assumed that this is what is meant by the term rahmiini:. As the Arabs never possessed a standard meridian it is impossible to see how they could have produced charts having parallels of longitude, although latitudinal parallels of Pole Star altitudes could be constructed. Using the parallels of Pole Star altitudes and bearings given by the navigators as coordinates for making a chart, I have constructed charts of considerable accuracy (12). The Arabs could have done the same, although this does not tally with the description given by the Portuguese navigators. They could have used the masiifa values but would have needed a base line from which to begin either by producing an imaginary one or by re-con­ structing the African and Arabian coasts from bearings and working from these. The real snag then is the width of Peninsular India. It may be thought that Cantino when producing his map of the Indian Ocean in 1502 obstained his -at that time- unusual coastline from oriental sources, especially since he gives the equivalent of isba' values for many places. That he obtained them from a native Indian Ocean chart seems unlikely. I have not compared Cantino's longitudinal widths of the Ocean with the Arab masiifiit, but hope to do this in the near future with what results I cannot say. Cantino's coastline compares most unfavourably with the charts produced using Arab bearings and stellar altitudes, also his stellar altitudes are placed irregularly down the coast. I am inclined to think that Cantino used oriental toponomy only and added the isba' values as extra information to the legends.

I. Two further refinements of Arab navigation must be mentioned. The first is the process of takkiya which both authors cover in some detail

(12) These charts were seen at the meeting in Coimbra (Oct. 23-26, 1968). 20

but also with some confusion (13). Takkiya seems to represent a change of bearing due to the strength of the wind. This was a particularly useful thing when sailing north in the Red Sea for at some unknown point one would meet the prevailing north wind, the maximum latitude south and the strength of which depended on the season but was never predictable. On meeting the north wind the Arab sailors made for the islands off the shores of the Red Sea, the new bearing varying with the strength of the wind. This was takkiya and a considerable amount of space has been devoted to this in the navigational texts. Tables of takkiya positions are given by Sulaiman al-Mahri at intervals of 1/2 isba' up the Red Sea, in each case giving the islands sighted on reaching the coast from the position given. Alternative islands are given for a weak or a strong north wind. Takkiyat positions are said to be due to variations in strength of the north wind. When the north wind is strong the bearing taken towards the Arab coast is E by N or due east and to the Sudanese coast, WSW or SW by W. When the north wind is weak the directions are NE or NE by N to the Arab coast and due west towards the Sudan. It is not clear whether these directions are forced on the pilot by the wind and no alternatives were possible, or whether the pilot chooses them as the most acceptable in the circumstances. A note at the end of the tables says that takkiya.t are conditioned «by the north wind's striking you while you are halfway between the two coasts and you cannot reach land except in the places mentioned». This would indicate that the pilot had no alternative, but it seems odd that he sould be incapable of steering his ship into the wind and at the same time making allowances for its strength. The whole operation seems to indicate that ships sailed north in the Red Sea with a favourable south-east wind until they met the prevailing north wind of the Red Sea. Knowing their latitude, they would then know where they would strike the coastal islands and what bearing would be suitable. Once in the neighbourhood of the coastal islands, they could shelter, or battle their way north taking advantage of changes in wind strength and direction. On the other hand the takkiya.t tables could show them at which latitude they must leave the open sea if they wished to reach the coast at certain places. The latitude would vary with the strength of the north wind at the time. Ibn Majid uses the word takkiya in a wider sense than this. It often means little more than change bearing, although the underlying sense of battling with a head wind is always there. Therefore the term seems as if it might stand for nothing more than «to tack» or «wear», although the Arab terminology vsually has an ansther word for this operation. One final point is the phrase used by the navigators of «snipping the compass card» or bisecting the angle beteveen the rhumbs. It might be thought that having a card of thirty-two rhumbs the Arabs could sail in any

(13) I originally wrote about takkiya in my article on «Arab navigation in the Red Sea». Geog. Journal CXXVII, pt. 3, pp. 322-34 (London, 1961). 21 direction of the compass. It is therefore surprising - to me at least - to find that they seem capable of only sailing on one of these thirty-two rhumbs, theoretically that is. The normal way to reach a destination which had a bearing of half a point or a fraction of a point was to sail down the nearest thumb until the correct latitude was reached and then run along the parallel to reach the port. If running along the parallel was impossible, the port could be approached from the original course by another whole bearing preferably a 45° one. Ibn Majid shows that it was possible to sail on half a point to reach a port and still use the calculations for tirfas and similar operations. His tone however indicates that he was advocating an innovation and that this was not normally attempted.

K. This then is a brief summary of the main points of Arab naviga­ tional theory. How much of this was used by the average pilot on Indian Ocean vessels is doubtful. Arab vessels in this present century have sailed to most of the ports of the Indian Ocean with little more than a second hand European compass. Nevertheless navigational texts appear in Arabic in the 19th century and again in the 20th century, so some pilots must have found a use for them. What is obvious from all later Arab works is that the stellar altitude method of navigation and much of the other material has been replaced by European methods. The method of shooting the sun was probably taken over almost as soon as the Europeans arrived and longitudes and latitudes measured in degrees appear in the later Arab works with values which agree with European contemporary values. There was no question of attempting to adapt Arab academic geographical results to practical navigation. The original pilot of the fifteenth century may have used his compass - some vessels may not have had this - and measured his Pole Star or Southern cross altitudes but most of his navigational theory was in his head. The most important parts of Arab navigational theory are those parts which I have not mentioned here - a knowledge of landmarks and visible signs, like the appearance of certain fish, birds and weed which always appears off certain coasts or in certain waters. Sea snakes of the west coast of India were vital and depths of the sea at places where they were found and the distance off the coast are recorded in several places, there is even a poem by Ibn Majid especially on this subject. Finally every pilot must have known the dates of the monsoons. The Arab word mawiisim (sing. mawsim) means strictly «the season for sailing» and the texts not only give complicated lists of dates for leaving the main ports in each monson, but give a series of dates for small operations like the times to sail from the Arabian coast to Soqotra and the winds and currents one was likely to meet at those times. This however is another long subject and cannot be dealt with here. I have however dealt with all of this as well as dealing with what I have described in this paper in much more detail in the section on navigational theory in my forthcoming book on Arab navigation in the Indian Ocean before the coming of the Portuguese. 22

DISCUSSAO

TEIXEIRA DA MoTA- No col6quio internacional da hist6ria maritima realizado em 1962 em Louren9o Marques, ao salientar a importanda hist6rica dos velhos metodos de navega9iiO dos arabes no Indico, fiz urn apelo para que OS orientalistas publicassem boas e completas tradu9oes em linguas europeias dos antigos textos nauticos arabes. E por isso motivo de profunda satisfa9iio verificar que G. R. Tibbetts se vern dedicando desde ha bastantes anos ao estudo desses textos, e promete para breve a edi9iio de uma obra baseada neles, da qual nos oferece agora esta excelente sintese, que tantas novidades contem se nos reportarmos aos trabalhos classicos de G. Ferrand e L. Saussure. Entre o muito que haveria a comentar, apenas algumas breves notas. Em primeiro Iugar, a grande variedade na utiliza9iio de estrelas, para alem do que os trabalhos anteriores permitiam saber. Mas utiliza9iio que nao tinha em vista a deterrnina9iio de latitudes, e por isso parece mais correcto falar apenas de navega9iio por alturas estelares. E signi­ ficativo que o autor nao tenha conseguido encontrar qualquer referenda concreta, nos textos que estudou, a utiliza9iio de cartas nauticas. Algumas antigas fontes portuguesas falam de cartas dos arabes, mas em termos que revelam que nao deviam ser verdadeiras cartas miuticas para marcar o ponto e sol tar rumos. E pena que nao se conh~a nenhuma daquelas antigas cartas, para devida eludda9iio de tao obscuro ponto. Outro aspecto que tambem se afigura pouco claro e o da utiliza9iio da agulha magnetica, ja que a rosa de tal agulha nao poderia na maior parte dos casos coinddir com a tradidonal rosa sideral. Nao sera a interpreta9iio de E. G. R. Taylor - utiliza9iio apenas ocasional da agulha magnetica ­ a mais correcta? Finalmente, ha a apontar, nos exemplos que da acerca da natureza dos roteiros arabes, grandes afinidades com os primitivos roteiros portugueses do fndico, denotando uma muito possivel influenda daqueles nestes. Alias as cr6nicas e outras fontes lusitanas referem a larga utiliza9ii0 pelos portugueses de pilotos arabes, denominados genericamente de «robooes», o que pode explicar a fadlidade e rapidez com que os seus roteiros foram conhe­ cidos pelos europeus.

TIBBETTS. -A. In my perusal of the Arab texts it is apparent that the Arabs used the compass considerably more than stellar altitudes. All of the routes given in the text need compass bearings and a considerable number of routes use no stellar altitudes. There was a tendency for navigators, whenever the coast approached allowed this, to use the bearing until the coast could be identified and then to find the port of des­ tination by coastal sailing, neglecting the use of stellar altitudes, but not neglecting the use of the compass. B. I must emphasise the facts that there is no mention of charts in the Arab texts - as far as I am aware - nor do they show any use of the Sun's altitude for measuring their latitude.

CusT6DIO DE MoRAIS. - Depois de cumprimentar o autor, apresenta-lhe varias duvidas: 1) como construiu Tomashek no Mohit as suas cartas, (questao que o autor escla­ receu com as suas cartas presentes); 2) Na comunica9iio indicam-se varios metodos de medir a altura das estrelas, dos quais e mencionado s6 das alturas iguais, das Farkad, no dito roteiro; 3) Usavam os pilotos a agulha? Ibn Madjid no seu roteiro nunca fala nela, contudo os portugueses de Vasco da Gama viram-na em Mo9ambique (mas o autor esclarece que Ibn Madjid faz referenda a agulha).

TIBBETTS. -The arab texts mention the equator many times but never use it for practical purposes of navigation. 23

MARCEL DESTOMBES. - La communication de M. Tibbetts nous apporte des elements nouveaux desquels il me parait qu'on peut tirer immediatement des conclusions en ce qui concerne les instruments. En premier lieu, bien qu'il soit question des cartes et aucune carte arabe n'est connue en fait. Mais il est notoire que les arabes n'utilisaient pas les cartes en parchemin. Les cartes signalees par Miller (al Bakri, al-Istakhri, etc.) etaient en papier, matiere perissable. II y a un temoin de Ia graduation en isbas, c'est Ia carte "Cantino" de 1502. II est aussi question du compas et des relevements, probablement done, ceux-ci etaient pourvu d'une alidade? Le loh (ou Kamal) etait construit pour les latitudes basses mais comment mesurer des hauteurs d'etoiles brillantes superieures a 30°, par exemple, sinon avec un quadrant de cuivre ou de bois, instrument bien connu des arabes?

TIBBETTS. -The maximum star altitude measurable by the «Kamal» according to the Arab texts was twelve isba'; and this was adequate for all purposes in the Indian ocean for the Pole star altitudes of Karachi and Chittagong were twelve and eleven isba' res­ pectively. This- Mowing the value of the isba' to be to be approximately 1° 40'- was 20° at the most. The majority of Arab star measurements were in the neighbourhood of 6-8 isba' which was only just over half of the maximum. Thus the Arabs had no real need to measure altitudes of more than 20° and the Kamal was sufficient for their purposes.

LAGUARDA TRIAS. - Senal6 que la comunicaci6n presentada contiene Ia explicaci6n del origen del Kamal, palabra no arabe, usada en las islas Maldivas que conjuntamente con Ia graduaci6n en codos astron6micos griegos publicada por James Prinsep, confirman Ia procedencia ocidental del instrumento y sa vinculaci6n, por Ia escala com Ia dispertra de Hiparco y el Kap,ar; de Piteas. AI mismo tiempo indic6 que existiria conveniencia en averiguar si el hombre del polo, convenci6n usada en Ocidente desde Ia alta Edad Media para determinar por Ia posi­ ci6n de las guardas de Ia Polar ({3 e y Ursae Minoris) Ia hora de Ia noche, y que aparece mencionada en el Kitab al-Fawa'id de Ibn a!-Majid, reflega tambien procedencia occidental (en este caso portuguesa) o si, pelo contrario, acusa origen oriental. Es seguro, dada Ia versacion del Professor Tibbetts, Ia possibilidade de esclarecer el punto.

TIBBETTS. -Arab nautical science was based on simple practical measurements which were in all probability indigenous to the Indian Ocean. The Arab navigators had no real knowledge of Arab classical mathematical and astronomical sciences which were ultimately derived from the Greek. Ibn Majid however prided himself on his education and quotes the names of several classical authors and their works (e.g. Battani, Ulug Beg and Nasir al-Din Tusi) but he emphasises the fact that he has read them as part of his general education and that the navigators methods has had no basis in classical scientific tradition.

TIBBETTS

In answer to Comdr. Waters

I have attempted to compare the map of Cantino with the information given by the Arab texts. The obvious differences between them is that Cantino prolongs the coast of Malaya south of the equator whereas the Arabs show the end of the Malayan Peninsula to be slightly north of the equator. Cantino also makes the west coast of India due north­ -south and similarly the eastern side of the bay of Bengal. The Arab texts give bearings for these coasts which were much nearer reality than those of Cantino. Finally Cantino's use of polegadas are not evenly distributed from north to south, although he does put at the same latitude on opposite sides of the Bay of Bengal, those place names which have equal polegadas values.