FRANCIS MADDISON

MEDIEVAL SCIENTIFIC INSTRUMENTS AND THE DEVELOPMENT OF NAVIGATIONAL INSTRUMENTS IN THE XVfh AND XVIth CENTURIES

COIMBRA-1969

FRANCIS MADDISON

IMPRENSA NACIONAL

MEDIEVAL SCIENTIFIC INSTRUMENTS AND THE DEVELOPMENT OF NAVIGATIONAL INSTRUMENTS IN THE XVfh AND XVIth CENTURIES

COIMBRA-1969 Separata da Revista da Universidade de Coimbra Vol. XXIV MEDIEVAL SCIENTIFIC INSTRUMENTS AND THE DEVELOPMENT OF NAVIGATIONAL INSTRUMENTS IN THE XVth AND XVIth CENTURIES

by

FRANCIS MADDISON

'The history of scientific instruments .. . is one of the best approaches to the understanding of scientific progress, but it is full of difficulties; each instrument is developed gradually; none is created in one time for all time by a single man.' GEORGE SARTON 'CUm vero artis navigatoriae peritia... Mathematicarum scientiarum admini­ culis adhibitis suum apud nos splendorem posse consequi facile perspiceres, Thomas Hariotum iuvenem in illis disciplinis excellentem, honestissimo salario iam diu donatum apud te aluisti, cuius subsidio horis successivis nobilissimas scientias illas addisceres, :usque familiaries duces maritimi, quos habes non paucos, cum praxi theoriam non sine fructu incredibili coniungerent .. . Unam hoc scio, unam & unicam rationem te inire, qua primo Lusitani, deinde Castellani, quod antea toties cum non exigua iactura sunt conati, tandem ex animorum votis perfecerent'. RICHARD HAKLUYT to SIR WALTER RALEGH, 1587 (1).

[Note. This brief survey, as originally read at the I. Reuniiio lnternacional de His­ t6ria da Nautica, was cast in the form of a commentary on lantern slides. In preparing the paper for the press, it has been substantially rewritten and the author has taken the opportunity not only to supply bibliographical references to more detailed treatments of specific topics, but also to refer to other papers which were read at the Reuniiio.] (1) The first quotation is from the essay, 'Ptolemy in his Time', in GEORGE SARTON, Ancient Science and Modern Civilisation, Lincoln (Nebraska), 1954, p. 44. The second quotation is from the dedica~ion of RICHARD HAKLUYT's, De Orbe novo Petri Martyris ... Decades octo, Paris, 1587, printed in E. G. R. Taylor (ed.), The Original Writings & Correspondence of the Two Richard Hakluyts (Hakluyt Society, second series, vol. LXXVII), London 1935, vol. II, p. 360. (Here, and elsewhere in this paper, I have expanded the contraction signs in printed works, putting the added letters in italics). A translation of this passage, by F. C. Francis, is given by TAYLOR, op. cit., pp. 366-367, and in DAVID W. WATERS, The Art of Navigation in England in Elizabethan and Early Stuart Times, London, 1958, appendix n. 0 16, p. 546. On Harriot, see n. 155, below. 4

INTRODUCTION

rn his chronicle of the reign of D. Manuel, Damiao de Go is wrote :

'Neste tempo dom Emanuel nam era casado, nem tinha tornado diuisa, segundo costume dos Prin((ipes, pelo que El REI dom Ioao !he deu per diuisa ha figura da Sphera, perque hos Mathematicos representam ha forma de ha machina do ((eo, & terra, com todo los outros elementos, cousa despantar, & que pare((e que nao care­ ((eo de mysterio prophetico, porque assi quomo estaua ordenado per DEOS que elle houuesse de ser herdeiro del Rei dom Ioao, assi quis que ho mesmo Rei a quem hauia de suc((eder, lhe desse hum a tal diuisa ... ' (2).

This device of an armillary sphere, albeit somewhat distorted by artistic licence, may be seen on a gold coin (known as a meia esfera) minted for Por­ tuguese India during the reign of D. Manuel, and is familiar as a motif of Manueline architecture in Coimbra and Lisbon (3). The device is appropriate, for in the last years of the reign of D. Joao II (ace. 1481) and in the reign of D . Manuel (ace. 1495) navigation developed from what was primarily pure seamanship into a practice which, as Fontenelle put it, 'hath a necessary connection with Astronomy' (4), and which was to rely increasingly on the use of a number of specially devised sci entific instruments. These were instruments which not only could be used satisfactorily on board ship, but which were practical and robust enough for use by seamen and which could be made available in quantity and economically. The history of navigational instruments must specially take account of that elusive interaction between everyday practice of long tradition, scientific theory, and the available tech­ nology and its economic foundations. The nature of the interaction may often elude the historian, but as always science in history is rarely isolated from it. Our knowledge of the practice of navigation in early medieval Europe . is very imperfect. We may deduce from the words of the Roman poet Lucan (c. A.D. 65, that the Pole Star was favoured as an aid to naviga-

(2) DAMIAO DE G61s, Chronica do felicissimo Rei Dom Emanuel, Lisbon, J 566, cap. Y, f. 5v. See LUCIANO PEREIRA DA SILVA , 'A Esfera armilar nas moedas portuguesas', Obras comp/etas, vol. III, pp. 367-371. (3) For details, see PEREIRA DA SILVA, op. cit.. A constant error in these represen­ tations of an armillary sphere is that the ecliptic circle touches the polar circles. (4) Bernard le Bovier de Fontenelle, J 699, quoted from an early English translation (which I have not been able to identify by E. G. R . TAYLOR eM. W. RICHEY, The Geometrical Seaman. A Book of Early Nautical Instruments, London, 1962, p. [ii] . 5 tion (5); we may read in the Northern saga literature of a husanotra, apparently a device used in navigation, but know nothing of its nature or exact function, (6) and speculate about the s6larsteinn owned by St Olaf early in the eleventh century (7); we may suspect the aid derived from observation of the flight of birds, but lack early documentation (8). All we may reasonably

(5) MARCUS ANNAEUS LUCANUS, De bello civi/i(Pharsalia), VIII, 11. 165-168 especially: 'Signifero quaecumque fluunt labentia caelo Numquam stante polo miseros fallentia nautas, Sidera non sequimar; sed, qui non mergitur undis Axis inocciduus gemina clarissimus Arcto, Ille regit puppes.' Cf. also op. cit., III, 11.218-219, where speaking of the Phoenicians, Lucan writes: 'Has ad bella rates non flexo limite ponti Certior haud ullis duxit Cynosura carinis.' For a discussion of the first of the passages cited, see E. G. R. TAYLOR, The Haven­ Finding Art. A History of Navigation from Odysseus to Captain Cook, London, 1956, pp. 46-47. (6) Husanotra is variously translated into Latin as gubernaculum, cornis and scopae, and may in no way be a navigational instrument. See the discussion in FARLEY MoreAT, Westviking. The Ancient Norse in Greenland and North America, London, 1966, pp. 354-355. (7) For a brief discussion of the s6/arsteinn (sunstone) and of the supposed Norse 'bearing dial', see GwYN JoNES, A History of the Vikings, London, 1968, pp. 192-194. On both instruments, in addition to the references given by Jones, see THORKILD RAMSKOU, Solstenen. Primitiv navigation i Norden for kompasset, Copenhagen, 1969, who compares the use of the s6/arsteinn (sols ten in Danish) with that of the modem Kollsman Sky Compass ('twilight compass') in which a Polaroid filter is used to analyse polarized light from the zenith when the sun is near the horizon (between + 30° and - 7°). The so/arstei nn, mentioned in Flateyjarbok and other Icelandic sources, is explained as a piece of cordierite (or other naturally occurring crystal) used in such a way that the direction of the sun may be determined by the polarisation of light transmitted by the crystal. In this connection, it is interesting to recall that Sir Charles Wheatstone (1802-1875) invented a Polar Clock or Dial' incor­ porating a Nicol prism; see Wheatstone, 'On a Means of Determining the Apparent Solar Time by the Diurnal Changes of the Plane of Polarisation at the North Pole of the Sky', Report of the Eighteenth Meeting of the British Association for the Advancement of Science - 1848- Swansea, pp. !Off. A Wheatstone polar clock, made by Darker of Lambeth, is preserved in the Museum of the History of Science, Oxford. The ability of the Norsemen to determine their latitude is discussed by JONES, foe. cit .. and by MowAT op. cit., p. 352. The concept of latitude to be considered in connexion with Norse navigation is, of course, that of 'latitude' relative to any reference point in which the variation of observed altitude of the Pole Star (when visible!) is equated with sailing north or south of the home port, but any form of 'latitude' navigation in early medieval times is of considerable interest in relation to the contact between different cultures. See ROLANDO LAGUARDA TRIAS, 'Interpretacion de los vestigios del uso de un metodo de nave­ gaci6n preastron6mica en el Atlantica' in this publication; also MICHEL MoLLAT, 'Solei! et navigation au temps des Decouvertes', Le Solei! a Ia Renaissance. Science et mythes. Colloque international ... avril 1963 ... (Universite libre de Bruxelles. Travaux de l'Institut pour )'Etude de Ia Renaissance et de l'Humanisme II), Brussels & Paris, 1965, pp. 89-106. (8) The whole question of the influence of the observation of natural phenomena upon the history of navigation deserves much further study. Two interesting late references may be cited here: MARTIN MARTIN in A Late Voyage to St. Kilda, the Remotest of all the Hebrides, or Western Isles of Ecotland. With a History of the Island, Natural, Moral, 6 be sure of is that, by the end of the thirteenth century, the seamen in the Mediterranean could have used a chart, a magnetic compass and sailing directions, possibly also a sand-glass. Sailing, of course, was by dead­ reckoning. Directions were given in the sailing directions, according to the traditional wind directions, as winds, half-or quarter-winds, and the distance sailed was measured merely by estimating the ship's speed and measuring; and in the thirteenth century rudimentary trigonometric tables were applied to navigation. It seems that the Mediterranean sailor was fortunate in comparison with his more northerly contemporaries who had to make do with a floating magnetised needle and the deep-sea lead (which was suitable for use on the continental shelf) (9). In 1377, when Ibn Khaldun (b. Tunis 1332; d. Cairo 1406) prepared his

and Topographical..., London, 1698, described how, after setting out from Scotland at 6 p.m. on 29 May 1967: 'Our Crew became extremely fatigued and discouraged without sight of Land for Sixteen Hours; at length one of our Number discovered several Tribes of the Fowls of St. Kilda flying, holding their Course Southerly of us, which (to some of our Crew) was a demonstration we had lost our Course, by the Violence of the Flood and Wind both concurring to carry us Northerly, though we steer'd by our Compass right West. The Inhabitants of St. Kilda take their Measures from the Flight of those Fowls, when the Heavens are not clear, as from a sure Compass, Experience showing that every Tribe of Fowls bends their Course to their respective Quarters, though out of sight of the Isle; this appeared clearly in our gradual Advances; and their Motion being compar'd, did exactly quadrate with our Compass. The Inhabitants rely so much upon this Observation, that they prefer it to the surest Compass; but we begg'd their Pardon to differ from them, though at the same time we could not deny but their Rule was as certain as our Compass.' ALEXANDER 0. EXQUEMELIN in De Americaenische Zee-Roovers, Amsterdam, 1678, speaking of turtles in the Cayman Islands, wrote: 'It is incomprehensible how these creatures manage to find the islands, having quitted other regions to get there; they come from the Gulf of Honduras, some 150 leagues away. Sometimes, ships, which have missed their landfall through adverse currents and have been unable to find their latitude have finally set course by the noise of turtles blowing, and so reached the islands.' (The original Dutch edition not being available to me, I have used the translation by Alexis Brown, published at Harmondsworth, 1969, p. 74). Whatever instruments of other artificial aids may have been available to the navi­ gator at any particular time, the role of observations such as these and of sheer experience must not be underestimated; cf. G. R. TIBBETS, 'The Navigational Theory of the Arabs in the Fifteenth and Sixteenth Centuries', and ERNST CRONE, 'How did the Navigator determine the Speed of his Ship and the Distance run?', both in this publication; MoLLET, op. cit.; and D. W. WATERS, 'Science and the Techniques of Navigation' Art, Science, and History in the Renaissance (ed. by Charles S. Singleton), Baltimore, 1968, pp. 189-237, esp. pp. 190-191. (9) TAYLOR, op. cit., passim, and G. BEAUJOUAN, 'La Science dans !'Occident medieval chretien', Histoire generate des sciences, vol. I, Paris, 1957, ch. VII, esp. pp. 272 ff. The first reference to the log is late- 1574; see CRONE, op. cit .. 7

Muqaddima, the prolegomena to his universal history, he wrote this about the problems of navigation:

'Navigation on the sea depends on the winds. It depends on know­ ledge of the directions the winds blow from and where they lead, and on following a straight course from the places that lie along the path of a particular wind ... The countries situated on the two shores of the Mediterranean are noted on a chart... which indicates the true facts regarding them and gives their positions along the coast in the proper order. The various winds and their paths are likewise put down on the chart... It is on this ... that (sailors) rely on their voyages. Nothing of the sort exists for the Surrounding Sea. Therefore, ships do not enter it, because, were they to lose sight of shore, they would hardly be able to find their way back to it .. .' (10).

This passage begs the whole question of the successful voyages of the northern peoples, that is, the problems of high-latitude navigation, and ignores the use of traditional, oral, rutters by Ibn Khaldiln's co-religionists in the Indian Ocean. The latter used astronomical techniques (such as measuring altitudes by finger breadths') which could be instrumentalised (11). Never­ theless, it is a fair statement of the state of navigation in the Mediterranean in medieval times, before economic, cultural and political forces required a marked improvement. To improve navigation, it was necessary to be able to determine, reasonably accurately, position on the open sea, in fact, to find latitude and longitude. Inevitably, this meant adopting astronomical techni­ ques, inaddition to the improvement of the magnetic compass and of the marine chart, both of which were already available in rudimentary form to the mariner. These changes in technique began in the late 15th century, so we shall first consider briefly the scientific instruments available during the late medieval period. Medieval scientific instruments (specially those which survive or about which we have any detailed information) are not instruments for astro­ nomical observation in any strict sense of the term (12). It follows that these instruments, apart from any special difficulties that might arise

(10) IBN KHALDiiN, The Muqaddimah. An Introduction to History (translated by Franz Rosenthal), 3 vols., London, 1958, vol. 1, p. 117. (11) TmBEITS, op. cit., and references there given; see also T. A. SHUMOYSKII, Araby i more, po stranitsam rukopise'i i knig, Moscow, 1964, and SULAYMAN NAovi, The Arab Navigation (translated from the Urdu by ~abal) ad-din 'Abd ar-Rahmlin), Lahore, 1966. (12) A comprehensive bibliography of publications on medieval and later scientific instruments will be found in FRANCIS MADDISON, 'Early Astronomical and Mathematical Instruments. A Brief Survey of Sources and Modern Studies', History of Science, vol. 2 (1963), pp. 17-50; a supplement for publication in the same journal is in preparation. In the footnotes that follow, references to publications on particular instruments are mostly 8 from their use on board ship, could serve little or no purpose in navigation. Medieval astronomical instruments were used for teaching, for calculation, and for certain simple observations such as telling the time. However, it must be recognised that the existence of medieval instruments provided a tradition of theoretical observational devices, of geometrical and calculating devices, of simple machinery even, all of which is part of the background against which navigational instruments developed. Medieval instruments exhibit in their cast and worked brass, in the engraving of the scales, and in the manufacture of gears, techniques of a high order.

MEDIEVAL SCIENTIFIC INSTRUMENTS

An illustration in a manuscript of c. 1450 of Heinrich Suso's Hor/oge de Sapience (13) (fig. 1) depicts a range of time-telling devices so as to sym­ bolise the title of Suso's work. There is a large mechanical clock (weight­ -driven and controlled by a verge and foliot escapement) a small table clock (spring-driven), three sundials, a horary quadrant, a planispheric astrolabe, and a bell-ringing device. With the exception of the latter, all these instruments were utimately to influence the progress of navigation, though at the time this illustration was drawn not one of these instruments, nor others which the artist did not include in his picture, had any practical use in

restricted to basic general works and to publications not included in the bibliography mentioned above. On medieval instruments in general, see DEREK J. PRICE, 'Precision Instruments to 1500', A History of Technology (ed. by Charles Singer, E. J. Holmayard, A. R. Hall & Trevor I. Williams), vol. III, Oxford, 1957, pp. 582-619; ERNST ZINNER, 'Wissenschaftliche Instru­ mente', Kaysers Kunst- und Alltiquitiitenbuch, vol. II, Heidelberg, 1959, pp. 39-88; MARCEL DESTOMBES, 'La Diffusion des instruments scientifiques du haut moyen age au xv• siecle', Cahiers d'histoire mondiale, vol. X, n. 0 1 (1966), pp. 31-51; EMMANUEL PoULLE, 'Les Instru­ ments astronomiques du moyen age', Le Ruban rouge, n. 0 32 (mars 1967), pp. 18-29, reprin­ ted 1969 as Museum of the History of Science, Oxford, Selected Off-print n. 0 7; and ERNST ZINNER, Deutsche und niederliindische astronomischen Instrumente des 11.-18. Jahrhunderts, 2nd ed., Munich, 1967. A number of medieval instruments are illustrated in HENRI MICHEL, Scientific Instruments in Art and History (translated by R. E. W. & Francis R . Maddison), London, 1967; and for the general technological background see VA.cLA v HusA, JosEF PETRAN and ALENA SuBRTOVA, Hommes et metiers dans !'art: du XII• au XVII• siecle en Europe centrale, Paris, 1967. (13) See ELEANOR P. SPENCER, 'L'Horloge de Sapience. Bruxelles, Bibliotheque royale, MS.IV.III.', Scriptorium, vol. 17 (1963), pp. 277-299; HENRI MICHEL, 'L'Hor/oge de Sapience et l'histoire de l'hortologerie', Physis. Revista di storia della scienza, anno II (1960), fasc. 4, pp. 291-298; and C. B. DROVER, 'The Brussels Miniature. An Early Fusee and a Monastic Alarm', Antiquarian Horology, vol. 3, n. 0 12 (September, 1962), pp. 357-361. The Hor/oge is an account of Suso's mystical experiences and is primarily a dialogue between Sapientia and her Disciple (the author). FIG. I - An illustration in a manuscript, c. 1450, of Heinrich Suso's Horloge de sapience, in the Bibliotheque royale, Brussels (MS. IV. J J I. f. 13v). The author is seated at the left, listening to Sapientia. A representative selection of time-telling devices has been depicted by the artist. On the left is a mechanical clock, with a twenty-four (I-XII, twice) dial and a single hand (cf. fig . 15); from the clock a rope operates a bell-hammer through a mechanical linkage. The bell and linkage are omitted from this reproduction. Hanging from the front of the clock is a planispheric astrolabe (cf. fig. 5). On Sapientia's left, there is another mechanical device, obviously some form of bell-ringing mechanism, perhaps a carrillon operated by a crank, or an alarm. On the table are (from left to right) : a hori­ zontal (?compass) dial (cf. fig. 8); a spring-driven table clock movement including a fusee; and a universal equinoctial dial (cf. fig. JO). Hanging from the table are a pillar dial (cf. fig. JO). Hanging from the table are a pillar dial (chilindre) and a horary quadrant (cf. fig . 6). Bibliotheque royale, Brussels Flo. 2- An armillary sphere representing the Ptolemaic system; ? c. 1425, of brassand gilt brass, overall height: 290 mm; diam. of base: 135 mm. Within the rings, representing the equator (divided into the 24 hours, with sub-divisions down to 4 minute intervals), the tropics, the polar circles, and the ecliptic (divided into the 12 zodiacal signs, each sub­ divided into 30°), there is a plain wooden globe on the polar axis. The sphere can be placed in the horizon circle of the stand to represent the heavens as seen form any latitude; the presence of a notch in the meridian ring, 45° from the Pole, and of two diametrically opposite slots in the horizon ring, suggets that a semi-circular hand may have been used to lock the sphere in a position suitable for use in latitude 45°. On the base of the stand engraved an eccentric zodiac/calendar scale (0° Aries = 11 March) with a rotatable index; inset in the base is a small compass, showing only the four cardinal points, with a south­ pointing needle (see Taylor, 'The South-Poiting Needle', cited in n. 44). The vertical support, linking the edge of the base to the horizon ring is provided with the means of suspending and aligning a plumb-line and bob. The positions of five named stars (the names of Cornu ari[etis] and Aldebaran can be seen on the photograph) are carefully marked on the zodiac band of the sphere, and the longitudes assigned to these stars conform closely with those of star catalogues of the fourteenth and the beginning of the fifteenth centuries. There is no doubt that the maker was attempting an accuracy of better than half a degree; and, therefore, if we were to assume that he was using tables not more than a quarter of a century out of-date, and admit a possible error of measurement of a third of a degree (equivalent to a precessional movement of around 25 years), we should arrive at a probable date of the first quarter of the fifteenth century. This date, however, is somewhat earlier than that suggested by the position of the vernal point in the zodiac I calendar scale, but is not inconsistent with the style of the instrument, which is one of the earliest surviving armillary spheres. A groove cut centrally in the zodiac band may have held a rotatable collar bearing and index (or 'sight') adjustable to the position of one of the named stars or to the solar declination. This would have enabled the sphere to have been used for - simple observational purposes (e.g. time-telling), but like most European armillary spheres its prime use was certainly demonstrational.

Museum of the History of Science, Oxford

'• .

..f.,;• 9 navigation (14). The most important medieval scientific instruments, known m the fifteenth century are:

a) The armillary sphere (15).

This is the instrument used by D. Manuel as his device (16). The Ptole­ maic geocentric system is shown by a small globe- the Earth - in the centre of the celestial sphere which is delineated by rings representing the polar circles, the tropics, the equator and the ecliptic. The example shown (17) in fig. 2 is of engraved brass with a globe of wood; it is probably of the fifteenth century, and one of the oldest surviving armillary spheres. Deriving from Ptolemy's astrolabon, the armillary sphere in Islam appears mainly to have been, like Ptolemy's instrument, an observational instrument, and to be effective, had to be large (18). In the European tradition, the armillary sphere is not primarily an observational instrument (19); with few

(14) Cf. GuY BEAUJOUAN and EMMANUEL PouLLE, 'Les Origines de Ia navigation astronomique aux xrv• et xv• siecles', Le Navire et l'economie maritime du XV• au XVIII• siecle. Travaux du Colloque d'Histoire maritime tenu le 17 mai 1956, a l'Academie de Marine (Biblio­ theque generale de !'Ecole pratique des Hautes Etudes, Paris, VI• section, 1967); and EMMANUEL PouLLE, 'Les Conditions de Ia navigation astronomique au xv• siecle', in this publication. (15) There is no comprehensive history of the armillary sphere, but see FRIEDRICH NOLTE, Die Armillarsphiire (Abhandlungen zur Geschichte der Naturwissenschaften und der Medezin, II), Erlangen, 1922; and DEREK J. PRICE, 'A Collection of Armillary Spheres and Other Antique Scientific Instruments', Annals of Science, vol. X, n. 0 2 (June 1954), pp. 172-187. (16) · See above. (17) Museum of the History of Science, Oxford, n.0 55-64. I wish to thank Dr. J. D. North for dating this instrument on the basis of the stellar longitudes marked on the ecliptic circle and for writing a note which has been incorporated in the caption to the illustration. (18) The scales of small instruments could not be accurately engraved down to small divisions of arc, but large instruments were difficult to make rigid. The armi/lae of Tycho Brahe are examples of large observational armillary spheres; see Hans Rreder, Elis Stromgren and Bengt Stromgren (trans. & eds.) Tycho Brahe's Description of his Instruments and Scientific Work as given in Astronomiae instauratae mechanica ( Wandesburgi, 1598), Copenhagen, 1946, esp. pp. 52-67. (19) Only a survey of the manuscript material describing the armillary sphere, the spherical .astrolabe, and the celestial globe will elucidate the obscure history of these three related instruments in medieval Europe. On the evidence of the few surviving medieval armillary spheres, these were small instruments, with no ali dade or other aid to observational use, often attached to a 'handle' rather than to a self-supporting stand. The Libras del saber de astronomia of Alfonso el sabio, c. 1276, do, however, describe an armillary sphere for observational use, but the influence of these treatises, written not in Latin but a ver­ nacular, appears to have been slight. The spherical astrolabe (of which no European examples are known to survive) passed from Islam to Europe as the sphera so/ida ('Sphera solida que et astrolabium sphericurn appellatur .. .' wrote Prosdocimo de' Beldomandi, c. 1400; see ANTONIO FAVARO, 'Intorno ad un trattato anonimo sull'astrolabio riconosciuto lO exceptions (20), the European armillary sphere is solely intended for demonstra­ tional or didactic purposes. A more elaborate sphere than that shown in figure 2, with star pointers attached to the rings, could show the apparent rotation of the stars about the pole and serve also for the solution of simple problems in spherical trigonometry. Although the non-observational character of these types of armillary spheres is apparent an instrument derived in the sixteenth century from the armillary sphere became a useful nautical instrument (21). In the study of the development of scientific instruments, a chronological typology of form is often as important as the pratical use, or even the theoretical concept underlying the form, associated with a given instrument at any particular time (22).

b) The equatorium (23).

A complicated instrument to which much ingenuity was devoted and of which only a few survive, the equatorium is a geometrical calculating instrument used to determine the positions of the planets according to the Ptolemaic mathematical theory. Numerous equatoria were devised, perhaps

opera di Prosdocimo de 'Beldomandi', Bibliotheca Mathematica, n. s., vol. 4 (1890), pp. 81-90, esp. p. 83), and appears to have been used occasionally as an instrument for serious observ­ ations, witness the rubric to a set of star coordinates added to Richard of Wallingford's treatise on the Albion (a form of equatorium), written in a late fourteenth century hand in a Corpus Christi College (Oxford) manuscript deposited in the Bodleian Library, Oxford, MS. C.C.C. D.l44, f. 76v: 'Tabula stellarum diligenter extractum per plura exemplaria et per plura instrumenta videlicet per speram soli dam .. .' (I am indebted to Dr. J. D. North for this reference). On the Alfonsine armillary sphere, see Manuel Rico y Sinobas (ed.), Libras del saber de astronomia del rey D. Alfonso X de Castilla, 4 vols., Madrid, 1863-1866, vol. II, pp. i-viii, 1-79. ZINNER, op. cit., plate 4, n. 0 3, illustrates an armillary sphere with handle, c. 1500, now in the Germanisches Nationales Museum, Nuremberg. See also FRANCIS MADDISON, 'A 15th Century Islamic Spherical Astrolabe', Physis, anno IV (1962), pp. 101-109; ZOFIA AMEISENOWA, The Globe of Martin Bylila of 0/kusz and Celestial Maps in the East and in the West (Polska Akademia Nauk. Komitet Historii Nauki. Mono­ grafie z dziej6w nauki i techniki, vol. XI). Wrocaw, Cracow & Warsaw, 1959 [Bylila's globe was made c. 1490 by Hans Dorn of Vienna]; and the illustration on plate 60 of MICHEL, Scientific Instruments ... of the celestial globe made in 1493 by Johann St6ffler and now in the Germanisches Nationalmuseum, Nuremberg. (20) E.g. those of Tycho (see n. 18 above), and some of the armillary spheres made by the Arsenius workshop at Louvain, of which there is an unsigned example, c. 1565, in the Museum of the History of Science, Oxford, n. 0 57-84/23a (fig. 39). (21) See below. (22) Another example may be drawn from the history of the sector (see below); see the section on Galileo's compasso geometrico e militare in FRANCIS MADDISON, 'Galileo and the History of Scientific Instruments', Saggi su Galileo Galilei, Pisa (forthcoming). (23) See EMMANUEL PouLLE, Astronomie theorique et astronomie pratique au moyen age. Conference donnee au Palais de Ia Dtkouverte, le 3 juin 1967, Paris, 1967, and references there given. FIG . 3 - A Ptolemaic equatorium, c. 1500, of brass, diam. 194 mm, perhaps made by Fran<;ois Fine. This equatorium is similar to that described by Franciscus Sarzosius, of Cella in Aragon, in his .. .In aequatorem planetarum libri duo : prior fabricam aequatoris complectitur, posterior usum atque utilitatem hoc est veros motus ac passiones in zodiaci decursu contigentes aequatoris ministerip investigare docet, Paris, J 526. Over a plate of equants, there can be rotated a deferent carrying three epicyclic discs which can be adjusted (by sliding) over diagrams of the equation of the centre for the Sun, Venus, Mercury, the Moon, Mars, Jupiter and Saturn. By this means, the mathematical constructions of Ptole­ maic theory are simulated and problems related to planetary motion solved. On the other side of this instrument is a planispheric astrolabe.

Museum of the History of Science, Oxford FIG . 4- A torquetum illustrated in Petrus Apianus, Astronomicum Caesareum, lngolstadt, 1540, sig. omv. An alidade, to which is fixed a semicircular scale (90° -0° -90°) equipped with a plumb-line and bob, moves over a scale (90° -0° -90° -0° -90°) in the vertical plane. The latter scale is supported by a second alidade which moves over a scale (divided according to the signs of the zodiac) in the plane of the ecliptic. Fixed below the ecliptic scale is a scale (divided into 24 hours) in the plane of the Equator. Observations of both altitude and azimuth are possible and the conversion from ecliptic to equatorial co-ordinates (and vice versa) are facilitated . 11 the earliest in Muslim Spain in the eleventh century (24). The illustration (fig. 3) shows an equatorium (on the back of an astrolabe) c. 1500 (25), of a type described in 1526 by Franciscus Sarsozius of Aragon (26).

c) The torquetum (27).

This is an instrument devised at the end of the thirteenth century, a fertile period in the history of astronomical instruments, either by Franco of Polonia who described it in 1284, or by Bernard of Verdun. Ostensibly an observational instrument giving direct readings in equatorial or ecliptic co-ordinates, it is very doubtful if it was often so used; rather it is another instrument for didactic purposes. The illustration (fig. 4) is from Peter Apian's magnificently produced Astronomicum Caesareum, published at lnglolstadt in 1540 (28).

d) The planispheric astrolabe (29).

The planispheric astrolabe (30), the best known and one of the oldest of medieval scientific instruments, was not primarily an instrument for observation in the sense of determining accurately the position of a celestial body. However, it was used observationally for timetelling by day or night,

(24) Equatoria, devised by Ibn as-Sam]) and by az-Zarqellu in Toledo in the eleventh century, are described in the Libros del saber; see RICO Y SINOBAS, op. cit., vol. 3, pp. 239-284. On the development of astronomy in Muslim Spain, see the works of J. M. Milh'ls y Valli­ crosa (listed in MADDISON, 'Early Astronomical and Mathematical Instruments .. .', p. 42) and SA'ID AL-ANDALUsi, Kitab tabakat al-umam (Livre des categories des nations) (trans. & ed. by Regis Blachere) (Publications de l'Institut des Hautes Etudes Marocaines, vol. XXVIII), Paris, 1935 (one of the earliest histories of science and philosophy). (25) Museum of the History of Science, Oxford, n.0 57-84/176. (26) EMMANUEL PouLLE and FRANCIS MADDISON, 'Un Equatoire de Franciscus Sarzosius', Physis, anno III (1961), fasc. 3, pp. 223-251. (27) See PouLLE, 'Les Instruments astronomiques .. .', pp. 27-28. Very few torqueta survive; one which belonged to Nicholas de Cusa (1401-1464) is now in the hospice at Kues, another made by Hans Dorn (see AMEISMOVA, op. cit.) is in the Collegium Maius, Cracow, and one made c. 1590 by Erasmus Habermel of Prague is in the Hessisches Landesmuseum, Kassel (see MICHEL, Scientific Instruments ... , pl. 51 & pp. 124-25). (28) Sig. 0 IIIIv. A superb facsimile of Apian's book was published at Leipzig in 1967, together with a commentary by DIEDRICH WATTENBERG, Peter Apianus und sein Astronomicum Caesareum (in German and English). (29) See PouLLE, 'Les Instruments astronomiques .. .', pp. 18-23 ; HENRI MICHEL, Traite de /'astrolabe, Paris, 1947; WILLY HARTNER, 'The Principale and Use of the Astro­ labe', and 'AsturH'lb', reprinted in Hartner, Oriens-Occidens, Hildesheim, 1968, pp. 287-318. See also MADDISON, 'Early Astronomical and Mathematical Instruments .. .', passim, and FRANCIS MADDISON, Hugo Heft and the Rojas Astrolabe Projection (Agrupamento de Estudos de Cartografia Antiga, serie separatas n.0 XII), Coimbra, 1966, both of which include a large number of bibliographical references. (30) The phrase 'planispheric astrolabe' is useful to avoid confusion with either the spherical astrolabe (see n. 19, above), or the mariner's or sea-astrolabe (see below). 12 and in surveying (e.g. for determining the height of a building). In modern terms, it is an analogue computer, serving to solve astronomical problems by simulating the apparent rotation of the stars about the pole. It may be considered as an armillary sphere which, by means of stereographic projection, has been reduced toa planisphere; the use of stereo graphic projection, in this case from the south pole on to the plane of the equator, results in angular measurements from the centre remaining undistorted. From Ptolemy's planisphaerium, through Eastern Islam and Mulism Spain, the history of the planispheric astrolabe may be traced to the first knowledge of the instrument in medieval Christian Europe in the tenth century, the knowledge becoming practical in the twelfth century. This type of astrolabe (31) had a wide diffusion in medieval Europe, and its prime use as an instrument for teaching ensured its inclusion in university courses, where it was important in making familiar astronomical concepts. The illustration (fig. 5) shows a small late Gothic astrolabe, made by Jean Fusoris (c. 1365-1436) (32). The back of this instrument is fairly typical: within the outer circle of degrees are (in the upper half) a diagram of unequal hours for use as a sundial with the alidade, and (in the lower half) a 'shadow-square' giving umbra versa (tangents of the arc) and umbra recta (cotangents) (33). The shadow-square was introduced on European astrolabes in the twelfth century; attention is here drawn to it because of the nature of the earliest known illustration of a mariner's astrolabe (34). Whether or not planispheric astrolabes were ever carried on board ship or used for serious observations in connection with voyages in medieval times (35), they coul never be true nautical instruments. A very

(31) We consider here only the ordinary planispheric astrolabe which has a series plates (tympana) for use in different latitudes. Various universal (i.e. usable in any latitude) astrolabes were devised, of which the two best known are the saphea arzachelis (revised as the astrolabum catholicum of Gemma Frisius), using a stereographic projection, and that known as the Rojas astrolabe, using an orthographic projection. On both, see MADDISON, Hugo Heft .. . , passim. (32) Museum of the History of Science, Oxford, n.0 IC 192. On Fusoris, see EMMANUELE POULLE, Un Constructeur d'instruments astronomiques au XV• siec/e, Jean Fusoris (Bibliotheque de !'Ecole des Hautes Etudes, IV• section - sciences historiques et philologiq ues, fasc. 318), Paris, 1962. (33) See MICHEL, Traite .. . , pp. 39-40, 73, 91. (34) See below. (35) Observations made on land at points of call during a voyage must, of course, be distinguished from observations made at sea. The astrolabe, possessed by a priest who, with seven other people, returned in 1364 to Norway from a voyage to the 'northern islands', was not likely to have been used at sea (seeR. A. SKELTON, THOMAS E. MARSTON and GEORGE D. PAINTER, The Vinland Map and the Tartar Relation, New Haven (Conn.) & London, 1965, p. 180). On the possible nautical use in medieval times of the planispheric astrolabe, it is worth-while recalling the following remarks of Emmanuel Poulle (BEAU­ JOUAN & POULLE, op. cit., p. 113): 'J'ai pu consulter a peu pres tous les traites medievaux d'astrolabe accessibles en France; il n'y est nulle part fait allusion a une quelconque utilisation nautique. Je precise que les emplois geographiques y sont frequents : determination de Ia diffe- fiG. 5 - The front (a) and the back (b) of a planispheric astrolabe, not signed but certainly by Jean Fusoris, c. 1430, of brass ; diam.: I 00 mm. a) The front has a rete (showing the ecliptic, part of the equatorial circle, and 22 fixed stars indicated by pointers, the whole bounded by the Tropic of Capricorn) which can be rotated about the Pole to move over a plate for a particular latitude (engraved with the horizon, circles of altitude, the zenith, and lines of unequal hours - in this case for latitude 53°; 4 other plates are stored below, in the mater). The rete and the plates are in stereographic projection from the South Pole of the celestial sphere on to the plane of the equator. The rotation of the rete simu­ lates the apparent rotation of the stars about the Pole and permits the solving of many problems related to this phenomenon ; positioned in relation to the altitude circles on the plate by means of an observation of the altitude of one of the stars marked on the rete, or of the Sun, the time may be readily ascertained. The limb, surrounding the plates and the rete is divided in degrees of arc, and there is a rotatable index (rule) . b) The back is engraved with scales of degrees of arc for measuring altitudes with the aid of the aliadde. The upper half is engraved with a diagram of unequal hours for use as a sundial with the alidade. In the lower half is a shadow square, used with the alidade for the determination of the heights of objects and buildings by simple trigonometry. Museum of the History of Science, Oxford FIG. 6 - A horary quadrant, of the type known as quadrans vetus, c. 1300, of brass; radius : 158 mm. A plumb-line, carrying a sliding bead, and its bob are now missing, as is part of the cursor which sl ides along the scale of 90° on the circumference. In use, the mid­ point of the cursor was adjusted to the latitude according to the scale of degrees; the plumb­ line was held taut across the appropriate date on the solar declination scale on the cursor and the bead moved till it lay on the 6 o'clock (midday) hour-line in the unequal hour diagram engraved above; the plumb-line was then allowed to hang freely and the quadrant directed towards the sun so that the shadow of the fore-sight fell squarely on the back-sight. The position of the bead would then indicate the time (in unequal hours). Superimposed on the unequal hour diagram is a form of shadow square. On the back is a zodiac/calendar scale (0° Aries = 14 March) from wh ich a central (? lunar) volvelle is mi ss ing. This is, apparently, the only surviving quadrans vetus.

Museum of the History of Science, Oxford 13 small astrolabe would have been useless, and the wind resistance offered by the fairly light solid metal plate of a larger instrument would itself have made it useless on board ship; besides, an astrolabe was an expensive and complicated instrument which the available technology could hardly have produced in quantity.

e) The quadrant (36).

The illustration (fig. 6) shows the earliest surviv.ing European quadrant; it dates from about 1300 and is of the type known as quadrans vetus (37), a type of quadrant that dates back to the 12th century. It is a horary quadrant, that is, a quadrant primarily for use as a sundial. A plumb-line, with a sliding bead and weighted with a bob, hung from the apex. In use, the centre mark of the sliding zodiac/calendar scale was adjusted to the number of degrees of the latitude on the scale along the arc. The plumb-line was then held taut across the the date and the bead moved along the line until it coincided with the 6 o'clock hourline. Finally, the quadrant was directed towards the sun until the shadow of the forward sight fell squarely upon the back-sight. The

renee de longitude entre deux viiJes par le moyen de !'observation d'une eclipse luna ire, difference de latitude, etc.. Or, une chose assez amusante caracterise tous les traites medievaux; c'est ce qu'on pourrait appeler le sens commercial de leur diffusion; on y est frappe par le souci constant de se montrer, a mesure qu'on avance dans le temps, de plus en plus complet, par Ia preoccupation de reunir, comme en un corpus, toutes les utilisations eventueiJes, meme les plus invraisemblables. J'en suis amene a conclure que, si les marins avaient un tant soit peu utilise cet instrument, il en aurait bien transpire quelque chose, d'une maniere ou d'une autre, dans Ia litterature astrolabique.' Although the astrolabe, throughout its history, must be considered as an instrument primarily used for teaching or simple practical ends, serious observations were sometimes attempted with its aid. As late as 1638, the Savilian Professor of Astronomy at Oxford, John Greaves, used a planispheric astrolabe to determine the latitude of Rhodes: 'By observations under the walls of the city of Rhodes, with a fair brass astrolabe of Gemma Frisius, containing 14 inches in the diameter [probably the astrolabe by Thomas Gemini, 1559, now in the Museum of the History of Science, Oxford,], I found the Latitude to be 37° and 50'. A larger instrument I durst not adventure to carry on shore in a place of so much jealousy'. (Thomas Birch (ed.), Miscellaneous Works of Mr. John Greaves ... , 2 vols., London, 1737, vol. II, p. 371; see also FRANCIS MADDISON, 'John Greaves (1602-1652) and his Journey to the Levant (1637-1640)', forthcoming). (36) See PETER ScHMALZL, Zur Geschichte der Quadranten bei den Arabern, Munich, 1929; J. M. MILLAS VALLICROSA , 'La Introducci6n del cuadrante con cursor en Europa', Isis, vol. XVIII (1932), pp. 218-58, reprinted in MILLAS, Estudios sobre historia de Ia ciencia espanola (Consejo superior de Investigaciones cientificas. Instituto «Luis Vives» de Fila­ sofia. Secci6n de Historia de Ia Filosofia espanola. Estudios, vol. II), Barcelona, 1960, pp. 61-78; MICHEL, Traite ... , ch. II, S 8, pp. 22-24 & ch. XVI, pp. 123-126 [on the Pro­ phatius astrolabe-quadrant]; EMMANUEL PouLLE, 'Le Quadrant nouveau medieval', 2 parts, Journal des savants, avril-juin 1964, pp. 148-167 & juiiJet-septembre 1964, pp. 182-214 ; and PoULLE, 'Les Instruments astronomiques .. .', pp. 18, 23-27. (37) Museum of the History of Science, Oxford, n.° F. 10. 14 bead on the plumb-line, now allowed to hang freely, indicated the time. Some quadrants had a shadow-square and could be used for practical geometry. on the plumb-line, now allowed to hang freely, indicated the time. Some quadrants had a shadow-square and could be used for practical geometry. An earlier, simpler, type of quadrant was the quadrans vetustissimus; the later astrolabe-quadrant devised by Prophatius Judaeus of Montpellier in the 13th century is known as the quadrans novus. None of these quadrants had any advantage over the astrolabe, but their use was taught in the universities. However, the quadrant became, in its simplest form (i.e. a graduated arc of 90°) a navigational instrument and influenced the design of later instruments (38).

f) Other types of sundial (39)

i) Navicula (40). A nautically inspired, somewhat whimsical, medieval instrument which derives from the quadrant is the so-called navicula de venetiis. Figure 7 shows the only known medieval navicula, probably of about 1450 (41). The back, which is not illustrated, bears a shadow-square. ii) Horizontal dial. Figure 8 shows parts of small portable horizontal dials, probably earlier than 1500 (42); the compass box contained an early example of a compass needle on a pivot. Dials of this type could only be used in a particular latitude. iii) Universal equinoctial dial. The origins of the universal equinoctial dial, which can be adjusted for use in any latitude are still obscure. The illustrations show three early examples. Figure 9 is of a dial which may be attributed to Hans Dorn of Vienna, c. 1480 (43). The small compass has a variation line marked on the plate under the needle (44). Figure 10

(38) See below. (39) On sundials in general, see PRICE, 'Precision Instruments .. .', pp. 594-601; KATH­ LEEN HIGGINS, 'The Classification of Sundials', Annals of Science, vol. IX, n. 0 4 (Dec. 1953), pp. 342-348; HENRI MICHEL, Les Cadrans so/aires de Max Elskamp, Liege (Musee de Ia Vie wallone), 1966; RENE R. J. ROHR, Les Cadrans so/aires. Traite de gnomonique theori­ que et appliquee, Paris, 1965; and MADDISON, 'Early Astronomical and Mathematical Instruments ... ', passim (for further references). (40) See DEREK J. DE SOLLA PRICE, 'The Little Ship of Venice- a Middle English Instrument Tract', Journal of the History of Medicine and Allied Sciences, voJ. XV, n. 0 4 (Oct. 1960), pp. 399-407. (41) Museum of the HistorY. of Science, Oxford, n.0 G. 73. (42) Museum of the History of Science, Oxford, n.os 130 & 131. (43) Museum of the History of Science, Oxford, n.0 G. 425. On Dorn, see AMEISE­ NOWA, op. cit., and ZINNER, Deutsche und niederliindische astronomischen lnstrumente .. . , pp. 292-297. (44) On the variation as marked on the compasses of sundials, see HANS GUNTHER KoRBER, 'On the History of Compass Sundials and their Makers' Knowledge of Magnetic Declination', Actes du XI• Congres international d'Histoire des Sciences. Varsovie-Cracovie, 24-31 aout 1965, 6 vols., Wroclaw, Warsaw & Cracow, 1968, vol. III, pp. 89-94, and the •

FIG. 7- A navicula venetiis, neither signed nor dated, c. 1450, of brass; overall height (excluding replacement hook): 94 mm.; width: 81.5 mm. The navicula is, in principle, similar to the later so-called Regiomontanus dial, but its form is different. The ··mast' of the 'ship' bears the latitude-scale on which is adjusted the cursor from which the plumb­ line hangs. The 'mast' is tilted until the projecting end, below the 'keel' of the 'ship', lies against the appropriate part of the zodiac scale. The thread of the plumb-line is then held against the same relative position on the second zodiac scale, on the right-hand side of the instrument ,and a sliding bead (now missing) on the thread moved to that position. The sights (in the castellated 'poop' and 'forecastle') are directed towards the sun; if the plumb-line be now allowed to hang freely, the bead will indicate the time on the hour-lines on the 'hull' of the ship. On the back of the 'hull', are a shadow-square, and an unequal hour diagram. Museum of the History of Science, Oxford FIG . 8 - a) a compass box,? c. 1500, of brass; overall diam.: 34 mm ., bearing the letter 'm' [ = meridies] on the base plate; probably the lower part of a compass dial with a lift-off cover. b) The hour-plate and gnomon of a compass-dial, ? c. 1500, of brass; diam.: 33 mm.; the southern point is marked by an arrow. Both parts were found in England.

Museum of the History of Science, Oxford FIG. 9- A German astronomical compendium, probably by Hans Dorn of Vienna, dated 1481, gilt brass; 67 x 72 mm. overall. The compendium is shown open, revealing the universal equinoctial dial (of which the gnomon is now missing). Within the hour-scale, for equal hours (numbered 1-12, twice), there is a ratable 24-hour scale, for Babylonian and Italian hours, which is adjusted according to the solar declination scale, engraved at the southern edge of the equal hour scale. The hour-plate can be adjusted, for use in the range of latitudes 20°=60°, by means of the hinged support which engages in the scale engraved on the plate surrounding the compass. On the outside of the hinged lid, there is a lunar volvelle and aspectarium; inside the lid , and surrounding the compass, the latitudes of various towns and countries are engraved. Under the base, there is an unfinished horary quadrant, the sights for which are on the side of the case opposite the hinge.

Museum of the History of Science, Oxford FIG. 10- a) A very small universal equinoctial dial, not signed,? 15th century, brass; diam.: 33 mm. The compass-needle is missing, as is any means of adjustment for latitude. On the lid is a primitive form of nocturnal (see fig. 23). b) A universal equinoctial dial, not signed,? 15th century, brass; diam.: 51 mm. The compass-needle appears to be original and is north-pointing. A top-plate over the compass, providing a scale for latitude adjust­ ment, is missing. On the lid is a simple form of nocturnal (see fig. 24). A smal crescent moon, punched on the compass-plate, midway between west and north, may be a maker's mark. c) A universal equinoctial dial, not signed, ? c. 1500, gilt brass; max. diam.: 64 mm. The compass-needle is missing (see fig. 11). On the lid is a nocturnal (see fig. 25). On the bottom, there is engraved the coat of arms of an unidentified abbot or bishop. In use, the hour-ring of this type of dial is set to the co-latitude of the place where it is to be used , the gnomon is set at right angles to the hour-ring, and the dial oriented by means of the compass. Museum of the History of Science, Oxford FIG. II - The compass-rose engraved on the bottom of the compass-box of the equinoctial dial shown in fig . JOe. Museum of the History of Science, Oxford

15 shows three somewhat different types of equinoctial dial, probably about 1500 (45). In each case the compass is larger in proportion to the instrument as a whole, and the lid of each dial bears an early form of nocturnal (46). Figure 11 shows the compass of sixteen points of the dial in figure lOc; here, there is no variation line. The small size of instruments such as these precludes the any accuracy in measurement of time.

g) The magnetic compass (47).

The early European history of the magnetic compass is still obscure. The use of magnetic compasses in portable sundials may be a case of an astronomical, or, strictly speaking, a gnomonic instrument, borrowing from the mariners. The first European written reference to the use at sea of the compass (probably a floating needle) is that of Alexander Neckham in his De naturis rerum, which was well-known by the end of the twelfth century. Between 1203 and 1208 Guyot de Provins wrote in his Bible:

' ... Par la vertu de la magnette U ne pierre !aide et brunette Oil li fers volontiers se joint Ainsi regardent le droict poinct; Puis, qu'une aiguille l'ait touchie Et en un festu l'ont fichie En l'eaue la mettent sans plus Et le festus Ia tient desus. Puis se tourne Ia pointe toute Contre l'estoile, si sans doute Que ja por rien ne faussera Et mariniers nul dotera ... (48). references there given; also, on early knowledge of variation, see E. G. R. TAYWR, The South-Pointing Needle', Imago Mundi, vol. VIII (1951), pp. 1-7, and Joseph Needham, Wang Ling and Kenneth Girdwood Robinson, Science and Civilisation in China, vol. 4 'Physics and Physical Technology', part I, Cambridge, 1962, pp. 293-314. It seems clear that variation was marked on the compasses of portable sundials before the first recorded observations of changing variation at sea (Columbus, 13-17 September 1492). (45) Museum of the History of Science, Oxford, n.os 190 S. 5, & F. 60. (46) See below. (47) See NEEDHAM eta/., op. cit., vol. 4, part I, pp. 229 ff.; A. Schiick, Der Compass, Hamburg, 1911-1918; and HEINZ BALMER, Beitriige zur Geschichte der Erkenntnis des Erdmagnetismus (Veroffentlichungen des Schweizerischen Gesellschaft fiir Geschichte der Medezin und der Naturwissenschaften, vol. XX), Aarau, 1956; WATERS, The Art of Navigation ... , pp. 20ff.; A. C. CROMBIE, Augustine to Galileo, 2nd ed., 2 vo1s., London, 1959, vol. 1, pp. 120 ff. and references in bibliography, pp. 261-262;and LYNN WHITE, JR., Medieval Technology and Social Change, London, 1962, pp. 132-133. (48) WHITE, op. cit., p. 132. It seems improbable that a piece of loadstone, however thin, floated on water was ever used as a practical compass, despite the description given by Petrus Peregrinus (1269) of a graduated compass (with an index arm) wherein there 16

Before about 1218, Jacques de Vitry had written that the compass was 'valde necessarius ... navigantibus in mari', and by about 1225 the navigational use of the compass was apparently a commonplace in Ice­ land (49). Petrus Peregrinus de Maricourt, in his famous Epistola de magnete of 1269, described a pivotted compass. There were two pivots, above and below a vertical arbor carrying the compass needle; at right angles to the needle was a transverse index of brass or silver which pointed east-west when the needle pointed north-south. The compass was provided with a transparent cover and with an alidade (sighting rule); the limb of the compass box was graduated in degrees of arc (four quadrants of 90° each). The influence of the astrolabe may, perhaps, be detected in some aspects of this design. Petrus Peregrinus clearly envisaged an astronomical navigation:

'Per hoc instrumentum diriges gressus tuos ad civitates et insulas et loca mundi quecumque, ubicumque feuris in terra vel in mari, dummodo longitudines et latitudines ipsorum sint tibi notae' (50).

was, apparently, a floating loadstone (on Petrus see below, n. 50). The magnetic compass, therefore, probably dates from the first use of a magnetised steel needle floated in a straw (cf. the passage from Guyot) or otherwise. See Henri Michel's account of the difficulties he encountered in the course of practical experiments in 'Notes sur l'histoire de Ia bous­ sole', Communications de l'Academie de Marine de Belgique, vol. V (1950), pp. 5-6 of the off-print. The quotation from Guyot is given in MICHEL, op. cit., and NEEDHAM, op. cit., vol. 4, part I, pp. 246-247. (49) WHITE, ibid., but cf. WATERS, The Art of Navigation ... , p. 25, n. 2, where a fifteenth centttry traveller in the Baltic is quoted: 'per questo mare non se navega cum carte ni bossola rna cum scandaso'. (50) GUY BEAUJOUAN, £'Interdependence entre Ia science scholastique et les techniques uti/itaires (XII•, XIII• et XIV• siec/es), Paris, 1957; G. HELLMANN, Rara magnetica (Neudrucke von Schriften und Karlen tiber Meteorologie und Erdmagnetismus, n. 0 10), Berlin, 1898, p. 11; the passage quoted will be found on sig. E[i)r-v of the editio princeps of Petrus' letter - Achilles P. Gasser (ed.), Petri Peregrini Maricurtensis De magnete, seu Rota perpetui motus, libel/us ... , Augsburg, 1558. The Leyden manuscript of Petrus' letter amplifies this passage, but the additional lines are considered spurious; see SILVANUS P. THOMPSON, 'Petrus Peregrinus de Maricourt and his Epistola de Magnete', Proceedings of the British Academy, vol. II (1907), pp. 377-408, esp. p. 396. Thompson gives a summary of the contents of the Epistola and a list of manuscripts and editions; he also discusses the plagiarism of the Epistola by JEAN TAISNIER, Opusculum perpetua memoria dignissimum, de natura magnetis, et eius effectibus ... , Cologne, 1562 (Thompson, pp. 404-405), of which an English translation appeared in ? 1579. The use of a simile as in the following passage from one of the Alfonsine Siete Partidas (13th cent.) suggests that navigational use of the magnetic compass was by then commonly known: 'Et bien asi como los marineros se guian en Ia noche oscura por el aguja que le es medianera entre Ia estrella et Ia piedra, et les muestra por do vayan tambien en los malos tiempos como en los buenos, otro si los que han de ayudar et de aconsejar al Rey se deben siempre guiar por Ia justicia ... ' (quoted by Juuo REv PASTOR, La FIG. 12 - Two armed loadstones, not signed, ? c. 1700; a) a cooper mounting retains the roughly shaped loadstone and its steel pole-pieces; approx. 98 x 92 mm overall ; b) a chased silver mounting retains a carefully shaped loadstone and its well-fitted steel pole-pieces; approx. 55 x 47 mm overall, excluding suspension ring.

Museum of the History of Science, Oxford FIG. 13 - Theodore Haak (1605-J 690), F.R.S., by John Richardson. On the table is an armed loadstone, similar to that illustrated in fig . 12b. The Royal Society of London 17

Pieces of loadstone were necessary for magnetizing a compass needle either by rubbing it before floating or mounting it, or by induction afterwards (51). The dating of most loadstones is uncertain, and no loadstones of probable medieval origin appear to have been recorded; those loadstones which do survive are 'armed' or 'capped' with pole pieces, and his arming is a product of the experimental magnetism of the sixteenth century. Armed loadstones (52) are shown in figures 12 and 13. Concerning the medieval history of the loadstone, there is a curious specific statement by the seventeenth century historian Rodrigo Mendez Silva, who wrote that in the year 1403, 'se perficiono el vso de la piedra himan, vtilissima a la nauegacion' (53). It would be interesting to know to what event he thought he was referring. Little is known of the design of medieval compasses. Those in portable sundials are of the simplest, with perhaps a meridian line and four c.ardinal points engraved on the brass base of the compass-box (54). An illustration (fig. 14) drawn in the margin of a cosmographical poem by Gregorio Dati (1363-1436) or Leonardo Dati shows a compass of which the fly (or possibly the lid) bears the Stella Maris, which become traditional decoration of the compass-rose. Crude illustrations of mariner's compasses drawn on fifteenth century maps show a round box and a pivotted fly similar to those of later marine compasses (55).

h) The mechanical clock (56) The mechanical clock may fittingly end this brief survey of medieval scientific devices which ultimately affected the development of navigation.

Ciencia y Ia tecnica en el Descubrinzento de America, 2nd ed., Buenos Aires, 1945, p. 159). (51) See WATERS, The Art of Navigation ... , pp. 22-23, 27-28. (52) See WILLIAM GtLBERT De Magnete [London, 1600] (trans!. & ed. by P. FLEURY MOTTELAY, London, 1893, repr., New York 1958, pp. 137-141; WILLIAM BARLOW, Magnet­ ica/ Aduertisements: or Diuers Pertinent obseruations, and approved experiments concerning the nature and properties of the Loadstone ... , London, 1666, pp. 28-37; and MADDISON, 'Galileo .. .'. The loadstones illustrated in fig. 12 are in the Museum of the History of Science, Oxford: a) n.0 2415, b) n.0 2412. (53) RODRIGO MENDEZ SILVA, Cata/ogo real, y genealogico de Espana ... , Madrid, 1656, p. 120. (54) See above, & figs. 9 and 11 . (55) WATERS, The Art of Navigation ... , pp. 26-27; TAYLOR, The Haven-Finding Art ... , pp. 98-100 and pl. VII; and the numerous illustrations in SCHUCK, op. cit., and in A. FoN­ TOURA DA COSTA, A Marinharia dos Descobrimentos, Lisbon, 1933, & later eds. (56) On the early history of the mechanical clock, see the relevant sections in J. DRUM­ MOND ROBERSTON, The Evolution of Clockwork, with a Special Section on the Clocks of Japan... together with a Comprehensive Bibliography of Horology, London, 1931; R. W. SYMONDS, A History of English Clocks, London & New York, 1947; DEREK J. DE SOLLA PRICE, 'On the Origin of Clockwork, Perpetual Motion Devices and the Compass', United States National Museum (Smithsonian Institution). Bulletin 218: Contributions from the Museum of History and Technology, Washington, 1959, pp. 81-112; WHITE, op. cit.; SILVIO

2 18

The mechanical clock, that is, a clock controlled by a mechanical escapement, is an invention of the late thirteenth century, not earlier than 1271 if we accept Lynn Thorndike's interpretation of a passage in Robertus Anglicus' commentary on the Sphere of Sacrobosco (57). It was then that there was first developed the verge and foliot escapement - by whom, where, and on the basis of what technological models, are questions the answers to which

Fro. 14 - Compass-box and rose from manuscript, written in the first half of the fifteenth century, of La Sfera by Gregorio Dati (1363-1436) or Leonardo Dati. Reproduced from A. E. Nordenskiold, Periplus. An Essay on the Early History of Charts and Sailing- Direc­ tions (transl. by Francis A. Bather), Stockholm, 1897, p. 45; the manuscript (ex coli. Count Manzoni) was in the author's possession.

remain unknown. There seems little doubt that the first mechanical clocks were not only large public clocks which sounded the hours, but often also elaborate astronomical clocks, showing the motions of the sun and moon and other celestial bodies. They were, in fact, mechanised astrolabes or equatoria, operated by an elaboration of the weight-driven mechanism required to sound the bells at the appropriate intervals, and controlled by the newly invented escapement. The latter is the key to the subsequent history of clockwork, for mechanisms including the weight drive had long been used in alarm-bell ringing devices controlled by some form of clepsydra; mechanisms for carillons and the moving figures or 'jacks' that often struck

A. BEDINI and FRANCIS R . MADDISON, Mechanical Universe. The Astrarium of Giovani de' Dondi (Transactions of the American Philosophical Society, new series, vol. 56, part 5), Philadelphia, 1966; and CARLO M. OPOLlA, Clocks and Culture 1300-1700, Lon­ don, 1967. (57) LYNN THORNDIKE, 'Invention of the Mechanical Clock about 1271 A.D.', Speculum, vol. XVI (1941), pp. 243-251. FIG. J 5 - The movement of the clock, c. J 390, of Salisbury Cathedral, as now restored and installed in the West aisle of the nave. A typical medieval iron-framed turret clock: the striking-train, with its ' fly' serving as an air-brake, can be seen on the on the left of the photograph; on the right is the going-train. Above this train is visible the foliot with its two adjustable weights; from the foliot decends the verge which engages with the crown­ -wheel by means of two pallets. Salisbury Cathedral

19 the bells were also no novelty at this period (58). The earliest public clock of which we possess any detailed information is that designed c. 1330 by the astronomer, Richard of Wallingford, for the Abbey of St. Albans of which he was Abott; his clock had an elaborate astronomical dial (59). The astrarium, a large library clock, completed in 1364 by Giovanni de'Dondi of Padua, inspired by the Theorica planetarum of Campanus of Novara (13th cent.), was a geared equatorium with seven dials showing the planetary motions, and a calendar of festivals; again, details of this clock are known from the treatise written by the constructor (60). From early in the fourteenth century scanty records survive of public clocks, specially in Italy, whence the knowledge of the mechanical clock appears to have diffused. In 1356 Pere III, King of Aragon, had a public clock and bell installed in the Castell at Perpignan; the designer was Antoni Bovell of Avignon,plomberius to Pope Innocent VI (61). In 1400, according to Mendez, 'se vio en Espana el primer relox, puesto en Ia Torre Giralda de Sevilla ... ' (62). The illustrations show: the basic mechanism- going and striking trains and verge and foliot escapement­ of an early public clock, the Salisbury Cathedral clock, c. 1390 (63) (fig. 15); one type of astrolabe dial found on a medieval public astronomical clock, the clock on the Staromestska radnice (Old Town Hall) in Prague, constructed in 1410 by Mikulas z Kadane (Nicolaus von Kaaden), a professional clock­ maker, probably with the collaboration of Jan Sindel, an astronomer at

(58) See A. UNGERER, Les Hor!oges astronomiques et monumentales les plus remar­ quables de l'antiquite jusqu'd nos jours, Strasbourg, 1931; THEODOR WAHLIN, The Medieval Astronomical Clock in Lund Cathedral, with a Survey of Some Similar Clocks on the Continent and in England, Lund, 1930; ZDENEK HoRSKY, 'Astronomy and the Art of Clockmaking in the Fourteenth, Fifteenth and Sixteenth Centuries', Vistas in Astronomy (ed. by Arthur Beer), vol. 9, London & New York, 1968, pp. 25-33; FRANCIS MADDISON, BRYAN Scorr and ALAN KENT, 'An Early Medieval Water-clock', Antiquarian Horology, vol. III, n. 0 12 (Sept. 1962), pp. 348-353; PRICE, 'On the Origin ... ', passim; MERRIAM SHERWOOD, 'Magic and Mechanics in Medieval Fiction', Studies in Philology, vol. XLIV, n. 0 4 (Oct. 1947), pp. 567-592; and SILVIO A. BEDINJ, 'The Role of Automata in the History of Technology', and DEREK J. DE SOLLA PRICE, 'Automata and the Origins of Mechanism and Mechanistic Philosophy', Technology and Culture, vol. 5, n. 0 1 (Winter ,1964), pp. 9-42. (59) See BEDINI & MADDISON, op. cit., pp. 5-10. Dr. J. D. North of Oxford is preparing an edition of the works of Richard of Wallingford, which will include Richard's description of his clock. (60) BEDINJ & MADDISON, op. cit.. One of the finely illustrated surviving manu­ scripts of Dondi's treatise has been published in facsimile: GIOVANNI DONDI DALL'OROLOGIO, Tractatus astrarii. Biblioteca capitolare di Padova, Cod. D. 39 (ed. by Antonio Barzon, Enrico Morpurgo, Armando Petrucci and Giuseppe Francescato) (Codices ex ecclesiasticis Italiae bibliothecis selecti, vol. IX), Vatican City, 1960. (61) L. CAM6s I CABRUJA, 'Dietari de l'obra del rellotge i Ia campana dell Castell de Perpinya !'any 1356', Homenatge a Antoni Rubio i Lluch. Miscel-llinia d'estudis literaris, histories e linguistics, vol. III, Barcelona, J 936, pp. 423-446. A detailed study of the manu­ script accounts sununarised by Cam6s is in preparation by Dr. C. F. C. Beeson of Adder­ bury (Oxon). (62) MENDEZ, foe. cit .. (63) Now restored and placed in the North aisle of the Cathedral. 20 the Universitas Carolina, Prague (64) (fig. 16); and a modern reconstruction of Giovanni de Dondi's astrarium (65) (fig. 17). Even had their size (66) permitted easy transportation, the nature of the mechanism of such clocks, including as it did a weight drive and a verge and foliot escapement, would have prevented proper functioning whilst in motion. The first step towards a clock that would work on board a ship at sea was taken with the invention of the driving spring. The Horloge de Sapience illustration o( c. 1450 (fig. I) includes a spring-driven table clock. With the exception of the magnetic compass and perhaps the mechanical clock, none of the medieval instruments discussed above was of much use to any practical profession, except that of teaching astronomy. However, these instruments (again with the exception of the magnetic compass and the mechanical clock) are the practical application of a considerable body of astronomical knowledge, a geometrico-mechanical tradition going back in time from medieval Christian Europe, through Muslim Spain and Islam generally, to Hellenistic times (67). A parallel, linked, tradition which has been much neglected is that of what are sometimes called schemata, that is, tables and aide-memoires in the form of diagrams, often circular, with movable volvelles (68). The mnemonic diagrams for mariners of the positions of the 'guards' of the Great Bear or Lesser Bear may be considered in this category (69). There is, however, another, equally important, tradition to be considered, that of the technology involved in the construction of the instruments and in particular of the clocks. The casting or beating of brass and iron to provide suitable plates for the instruments or frames and wheels for the clocks,

(64) See ZDENEK HoRSKY and EMANUEL PROCHAZKA, 'Prazsky orloj', Sbornik pro dejiny prirodnich wJd a techniky / Acta historiae rerum naturalium nee non technicarum, vol. 9 (1964), pp. 83-146; also HoRSKY and PROCHAZKA, 'Prague's Astronomical Horloge', Technical Digest (Prague), vol. 6, n. 0 11, (1964), pp. 21-36. (65) Now in the Museum of History and Technology, Washington, D.C. (66) Although most of the earliest clocks about which we have information were large public clocks, often with astronomical dials, a number of small early clocks are recorded. In 1379, Pere III of Aragon sent his daughter a small astronomical alarm clock (with an astrolabe dial) (ANTONI Rum6 r LLUCH, Documents per l'historia de Ia cultura catalana mig-eva/, 2 vols., Barcelona, 1921-1928, vol. I, p. 265) ; Charles V of France had an or/age portative in 1377 (RoBERTSON, op. cit., p. 44); and there is the controversial spring-driven chamber-clock supposed to have been made c. 1430 for Philip, Duke of Burgundy (WHITE, op. cit., pp. 127, 175). (67) See PRICE, 'On the Origin .. . ', passim, and DEREK J. DE SOLLA PRICE, Science since Babylon, New Haven (Conn.), 1961, ch. 2 'Celestial Clockwork in Greece and China', pp. 23-44. (68) 'I have long felt that the history of the use of diagrams should be included in a history of scientific instruments and this has been an overlooked field .. . Eventually the diagrams became instruments through their movable volvelles.' - Private communication, 19 March 1964, from Dr. Harriet Pratt Lattin of Tiburon (Calif.) to the author. (69) See below. FIG. 16 - The astronomical clock on the Staromestska radnice (Old Town Hall) in Prague, originally constructed in 1410 by Mikulas z Kadane (Nikolaus von Kaaden), a professional clock-maker, probably with the collaboration of Jan Sindel, an astronomer at the Universitas Carolina, Prague; the carbings around the astronomical dial are from the stonemason's workshop headed by Peter Parler. When the clock strikes, figures of the twelve apostles (added c.l659) file past the two large windows at the top; a cock, which crows from the upper small window after the passage of the apostles, was added in 1882. Below, is the astrolabe dial (in stereographic projection from the North Pole of the celestial sphere; the conventional astrolabe, as shown in fig. 5a, is based on a similar projection from the South celestial Pole). The arc dividing the dark (night) area of the dial-plate from the light (day) area represents the horizon. Over the dial-plate moves the ecliptic circle and two 'hands'. The Arabic numerals on the outermost (movable) horary scale are for Bohemian hours (counted from sunset); the Roman numerals within this scale are for solar time and side­ real time; and the Arabic numerals related to the curved hour-lines within this scale are for unequal (planetary) hours. One of the ' hands' terminates in a gilded hand and bears a solar symbol: the gilded hand indicates Bohemian hours and solar time; the position of the solar symbol (which slides along the 'hand') shows unequal hours and the position of the Sun in the ecliptic and relative to the horizon. The other 'hand' bears a lunar symbol which slides along the 'hand' and rotates to show the phases of the Moon and its place in the ecliptic. The pointer (tipped with a star) extending from 0° Aries on the ecliptic circle indicates sidereal time. The lower dial is a calendar dial probably added in 1490 during an extensive reconstruction by Jan Ruze; it was mechanized in 1566 by Jan Taborsky, and has since been repainted. The whole clock has undergone several alterations and reconstructions; in recent times in 1865 (with considerable alterations to the mechanism) and since May 1945 when the clock was damaged during street fighting. Staromestska radnice, Prague F IG. J7 - A reconstruction of the astrarium which Giovanni de' Dondi completed in 1364. This reconstruction, based on the description and illustrations in manuscripts of Giovanni de' Dondi's treatise on his astrarium, was made in 1958 by Thwaites and Reed Ltd., London, with the technical guidance of the late H . Alan Llyod ; the construction work was done by Mr P. W. Haward, and the engraving by Mr F. N . Fryer. The overall height of the reconstruction is 132 em.; it is made almost entirely of brass. Three of the seven dials are visible in this photograph; they are, from left to right, the dials showing the motion of Venus, Mercury, and the Moon. Below the dials can be seen the large horizontal cir­ cular band engraved with the dates of fixed feasts ; the top edge is cut with 365 teeth, corre­ sponding to the days of the year. Below, and in the centre panel of the seven-sided frame, is the calendar of movable feats ; three parallel bands of links, which appear in the 'window' of the plate, indicated the dominical letter for twenty-eight years, the feasts linked to the nineteen year lunar cycle, and the fifteen year cycle of the Roman indiction.

Museum of History and Technology, Washington, D.C. 21 the engraving of reasonably accurate scales and the fashioning of gear-wheels with, regular, triangular, teeth involved knowledge and skills of a high order. Very little is known of the processes used. The detailed financial accounts which survive relating to the construction of the large public clock and bell at Perpignan in 1356 (70) tell something of the cruder processes, but even the detailed descriptions of their clocks by Richard of Wallingford and Giovanni de'Dondi say very little of the more difficult precision work. Treatises on the manufacture of instruments are scarcely more informative. For details of early methods of scale division we have to extrapolate from Sir John Chardin's account of the traditional methods used by Islamic astrolabists in l~fahan in the seventeenth century (71). The development of new instruments, and the invention of the verge and foliot clock escapement, towards the end of the thirteenth century, are evidence that late medieval scientific theory and technology were not static. Guy Beaujouan has pointed out that, even from the eleventh century onwards, economic and technical development is reflected in the work of theologians. Hugh of St-Victor (1096-1141) in his Didascalion classifies knowledge as theory, practice, mechanics and logic, and 'mechanics' includes navigation; Ramon Lull's Arbor scientiae of 1296 includes 'De arte nautarum'. A study of such medieval encyclopaedias reveals that commerce and maritime activities become important in the classification of knowledge. Beaujouan concludes that in the medieval period there are no real compartmental divisions between the c/ercs and the praticiens (72); later, in the sixteenth and seventeenth cen­ turies, we may similarly say that there is no dichotomy between scientists and simple craftsmen (73). The life and work of one of the very few medieval instrument-makers about whom we have any information, Jean Fusoris (74), links the quest for mathematical precision with that for technical improvement. Fusoris was an ecclesiastic and an astronomer, educated at the University of Paris, who learnt also from his father who was a pewterer. Clearly, Fusoris was in many respects similar to those Islamic astronomers (in the widest sense of the word) who were also the manufacturers of astrolabes and other astronomical instruments (75). Throughout the medieval period the economic situation of the vat.:ious crafts undergoes considerable change. The proportion of merchants and craftsmen in the total population increases ; this increase, and the mobility

(70) See above. (71) HENRI MICHEL, 'Methodes de trace et d'execution des astrolabes persans', Cie/ et terre, n. 0 12 (Dec. 1941). (72) BEAUJOUAN, 'L'Interdependance ... ', pp. 7-8. (73) CIPOLLA, op. cit., pp. 32-35; cf E. G. R. TAYLOR, The Mathematical Prac­ titioners of Tudor & Stuart England, Cambridge, 1954, passim, and PRICE, Science since Babylon, ch. 3 'Renaissance Roots of Yankee Ingenuity', passim. (74) See above, n. 32. (75) See L. A. MAYER, Islamic Astrolabists and Their Works, Geneva, 1956, esp. pp. 13-14, 21. 22

of skilled labour, have not been adequately investigated. An interesting analysis by Carlo Cipolla (76) considers these factors in relation to the pro­ gress made, from the eleventh to the fifteenth century, by European technology in nearly every field. The proliferation of fire-arms, the improvements in shipbuilding and the expansion of ocean navigation after the end of the four­ teenth century are part of this technological development. The production of scientific instruments must be seen in this context wherein a found of skills, of labour, of motivation, contributes to their development and supply. By the late fifteenth century the manner of production of scientific instruments was changing rapidly. In, or shortly after, 1471 Regiomontanus established a workshop at Nuremberg for the construction of instruments. From the signatures on surviving instruments we know the names of some of the earliest makers who were producing instruments in quantity- Hans Dorn of Vienna, c. 1480, Pier Vincenzo Danti of Florence, c. 1490, the Vul­ paria family of Florence who continue into the early sixteenth century, which sees the establishment at Nuremberg of the workshop of the prolific Georg Hartmann (1489-1564) (77). As well as in Italy and South Germany, instru­ ment-making workshops were established at this time in the Netherlands where the personal and literary influence of Gemma Frisius (1508-1555) (78) of the University of Louvain led to the widespread dissemination of instruments all over Europe. Instruments designed by Gemma Frisius were made by Gerard Mercator (1512-1594), and the Arsenius family of Louvain who were related to Gemma (79). The Netherlands workshops had considerable influence on the growth of instrument-making in England (80). It was these commercial workshops, working closely with scientists, which provided the quantity of instruments which the military and land surveyors, mariners and other mathematical practitioners of the sixteenth

(76) CIPOLLA, op. cit., 'Prologue' & ch. I, passim. (77) See ERNST ZINNER, Leben und Wirken des Johannes Muller von Konisgsberg genannt Regiomontanus, 2nd ed., Osnabriick, 1968; ENRICO MoRPURGO, Dizionario degli oro/ogiai italiani ( 1300-1880), Rome, 1950, pp. 56-57 (for Danti); CARLO MACCAGNI, 'The Florentine Clock-and Instrument-makers of the Della Volpaia Family', forthcoming in Actes du XII• Congres international d'Histoire des Sciences, Paris, 1968; ZINNER, Deutsche und niederliindische astronomichen Instrumente .. . , pp. 357-368 (for Hartmann). (78) See FERNAND VAN 0RTROY, Bio-bibliographie de Gemma Frisius, fondateur de /'ecole beige de geographie, de son fils Corneille et de ses neveux les Arsenius (Academic royale de Belgique. Classe de lettres et des sciences morales et politiques. Memoires, 2. • serie, vol. IX, fasc. 2), Brussels, 1920; and A. S. OSELEY, Mercator. A Monograph on the Lettering of Maps, etc. in the 16th century Netherlands, with a facsimile and translation of his treatise on the italic hand and a translation of Ghim's Vita Mercatoris, London, 1969. (79) See OSELEY, op. cit.. Apart from the influence of Gemma's books and of his pupils (e.g. Juan de Rojas Sarmiento; see MADDISON, Hugo Helt ... ), instruments made in the Arsenius workshop were widely sold through the agency of the Plantin printing house (see COLIN CLAIR, Christopher Plantin, London, 1960, pp. 198-9; VAN OR TROY, op. cit., pp. 94-97). (80) OSELEY, op. cit., pp. 91 ff.; TAYLOR, Mathematical Practitioners ... , passim. 23 century demanded for the exercise of their profession; the instruments became more specialised in their function and were made by specialists in their manu­ facture. The techniques of engraving copper-plates for printing the gores of terrestrial and celestial globes and of engraving brass instruments are similar. It is not, therefore, surprising to find that the same men are involved in both activities - Gerard Mercator, for instance, or Humphrey Cole or Thomas Gemini or Robert Becket in England (81). The quality of the surviving instruments is eloquent testimony to the craft skills of the instrument-makers. It must also be stressed that many of these craftsmen were responsible for improvements in design of the instruments they made, for the creation of new instruments, and for the publication of numerous books and pamphlets on the use of their instru­ ments. A professional compass-maker, Robert Norman of London (fl. 1560-1596), whose experimental approach led him to the discovery of magnetic dip, is perhaps not typical, but he nevertheless held his fellow mechanicians' in high regard; in the preface to The Newe Attractive ... , 1581, he wrote:

' ... I meane ... to set doune a late experimented truth found in this [Load] Stone, contrary to the opinions of all them that haue heretofore written thereof. Wherein I meane not to vse barely tedious coniectures or imaginations, but briefly as I maie to passe it ouer, foundyng my argumentes onely vpon experience, reason, and demonstration, which are the groundes of Artes. And albeeit it maie bee saied by the learned in the Mathematicalls, as hath been alreadie written by some, that this is no question or matter for a Mechanician or Mariner to meddle with, no more then is the finding of the longitude, for that it must bee han deled exquisitely by Geometricall demonstration, and Arithmeticall Calculation, in whiche Artes they would haue all Mechanicians and seamen to bee ignoraunt ... But I doe verely think, that. .. there are in this land diuers Mechanicians, that in their seuerall faculties and professions, haue the vse of those artes at their fingers endes, and can applie them to their seuerall purposes, as effectually and more redily, then those that would moste condemne them .. .' (82).

(81) See MADDISON, 'Galileo .. .', passim.; OsELEY, op. cit., for Mercator, Cole and Gemini; on Becket, see Arthur M. Hind, Engraving in England, vol. I 'Tudor', Cambridge, 1952, pp. 221-222. (82) ROBERT NORMAN, The newe Attractiue, Contaynting a short discourse ofthe Magnes or Lodestone, and amongest other his vertues, of a newe discouered secret and subtill proper tie, concernyng the Declinyng of the Needle, touched therewith under the plaine of the Horizon. Now first founde out by Robert Norman Hydrographer, London, 1581, sig. B ir-v. The proficiency in arithmetic, geometry and algebra of the 'mechanicians' and mariners partly depended, of course, on the availability of textbooks in the vernacular. Norman, toe. cit., mentions this. 24

THE DEVELOPMENT OF NAVIGATIONAL INSTRUMENTS

The development in the sixteenth century of instruments specifically for navigation owes its impetus to the need to develop an astronomical navigation, originally to exploit fully a technique used by the fifteenth century Portuguese navigators in returning from Guinea. This tactic, known as the 'Guinea track' (later, the 'Elmina track') involved sailing in a large arc towards the west, in order to profit from the winds and currents, until the latitude of Lisbon was reached, then sailing eastwards. First adopted about 1460, the astronomical techniques required for this practice were gradually refined, and more widely applied in navigation (83). For accuracy, astro­ nomical techniques require instruments. The Piloto-Mayor of the Casa de Contratacion, founded in Seville in 1503, was charged, among other matters, with examining and certifying instruments made by pilots of the Casa. In 1523, it was found necessary to create an office entitled Cosm6grafo, Maestro de Hacer Cartas, Astrolabios y otros Ingenios de Navegaci6n (84). The supervision of the production and use of instruments was thus entrusted to experienced practical navigators. The history of instrument-making in Portugal and Spain is not yet sufficiently explored, but I suspect that the situation in those countries was, and remained, different from that in Northern Europe. In Portugal and Spain, the nature of the incentive to create an astronomical navigation, and the absence of a nascent instrument industry, resulted in the manufacture of nautical instruments remaining in the hands of the cosmographers. When the navigators of the northern countries came to adopt astronomical techniques and demand the necessary instruments, there already existed in their countries instrument workshops which could readily meet the demand. We shall now discuss some of the scientific navigational instruments that had become available in Europe by the sixteenth century, or which were developed · during that century. They will be considered roughly in their order of appearance, together with other developments in instrumentation that were later to prove valuable in navigation. It is not easy to know which instruments were of most practical use, that is, which gave the highest accuracy in use at sea. As in other fields of science and technology, many ingenious instruments and gadgets were devised by enthusiasts who often, in their

(83) See Luis MENDON<;:A DE ALBUQUERQUE, 'The Historical Background to the Cartography and the Navigational Techniques of the Age of Discovery, with Special Refe­ rence to the Portuguese', forthcoming in Annals of Science. (84) WATERS, 'Science and Techniques of Navigation', pp. 212-216; for a detailed account, see JosE PULIDO RUBIO, El Pilato mayor de Ia Casa de Contrataci6n de Sevilla. Pilotos mayores, catedrdticos de cosmografia y cosm6grafos, 2nd ed. (Publicaciones de Ia Escuela de Estudios hispano-americanos de Sevilla, vol. LVI, serie 2a, n. 0 19), Seville, 1950; see also the two papers by Marcel Destombes, cited in n. 88, below. 25 publications, made unjustified claims for their inventions. Even in the case of the better known (and presumably more popular) instruments, we may be mislead by an attempt at completeness by the author of a mariner's hand­ book, or by the inventory of a ship whose captain was purchasing as many different instruments as possible, either as insurance or for reasons of prestige. Georges Fournier, describing the 'Hemisphere Nautique' invented by Michel Coignet of Antwerp in 1581 , says, ' .. .ie concluds que l'vsage de cet Instrument est inutil sur Mer. . .', and that he had never seen it used. It will, therefore, be appropriate to introduce this section with some remarks, addressed 'To the Trauelers, Seamen, and Mariners of Englande', by William Barlow (1544-1625) in his Discours of the Variation of the Compass ... , 1581; not only because of his comments on navigational instruments, but also because the opening words exemplify the spirit of practical enquiry which is typical of the best sixteenth century navigation and instrument design:

' ... I would haue all seamen to vse suche diligence in their trauailes, that no oportunitie be omitted, when, or where any obseruation maie be made, either for the variation, or latitude of places, or of any other necessarie poincte incident to Nauigation, and thereof to keepe continuall notes & memorial!. For these obseruations, there needeth not many troublesome Instrumentes, onely for the variation, the newe Instrument in the en de of this treatise [see below] I preferre before all other. And for eleuations, a plaine Astrolabe exactly made, and a cross staffe, are sufficient. (The Globe were also a verie good and necessarie Instrument for besides many pleasaunt conclusions that maie be tried by it, it doeth lighten verie muche the conceiptes for vnderstandyng diuers important poinctes, but it is too troublesome [or otherwise not fit for euery Mariner] to be caried to the Sea). Vnto the whiche maie bee added the Topographicall Instrument [? = circumferentor ], for taking of distances, and making descriptions vpon the land. With these Instru­ mentes, and the Sailyng Cumpasse and Marine plat [= chart], (whiche are alwaies to be vnderstoode the principall, and moste necessarie Instrumentes for Nauigation, for by them onely any voiage bee maie made, but without them no Nauigation can bee performed.) the whole worlde maie bee traueled, discouered, & described' (85).

(85) W[ILLIAM]. B[ARLOW]., A Discours of the Variation of the Cumpas, or Magnetica/1 Needle ... And is to be annexed to The Newe Attractiue of R. N. [see above, n. 82], n.p. [London], 1581, sig. * ijv- * iijr. The quotation from Fournier is from Hydrographie contenant Ia theorie et Ia pratique de toutes les parties de Ia navigation, 2nd ed., Paris 1667, p. 388. On Coignet, see ZINNER, Deutsche und niederliindishe astronomiche Jnstrumente, pp. 281-282. 26

a) The mariner's quadrant

The earliest known representation of a quadrant intended for use by mariners occurs in the 1563 (posthumous) edition of Va1entim Fernandes' Report6rio dos tempos (first published at Lisbon in 1518). The illustration (fig. 18) occurs at the beginning of a chapter on ' ... o regimento pera se poder

fl Scsucfco f(6itn€ntopna f6! podcrrclJtr pclo ~uodrantt ou :tttlrolab\opela dircHa ~o JA.oltc

~~~~~~~~~~S~bcr~srt:o o alturg qqunndotcmHl vo 1Ro2tf q tanto mote Cfiilf tnUVtO ~ ao dtc como QOUCO, 1 p9lo coft>{;lltOU f11llCfic,po~q t\1 do b£ bu.~ S~bcr.lo q 6!!1\ ltirb~ toda\aa bo:~o nao dt~n o "f\oltc i bit~ ~\tura. ~ 3)tc,ao \3uardao n~ cab£~ ~~ tC bo f\ozu.):~~\,1. graoa 'l bfi ur~o,-r ell~ na fc ba 'Ot meter €tn cot~,po1 c.1ufn va qugntidadc qbe lHquwa, 1 bo ~ar n.1m (t;s~ura a tom or dta conta, -r ntTi b:.lG 'OC f ~~ ... £r no outroa a\tunl9 q tomQf(G.:Bo {\lhlfdao dt"ndo na h=­ ~l£il t:fqnird~,acbaraeo 1RoltC (m.rn:v}.~rgoa.ee foHm ~9 suarl\ n1:) "" \utea -oo \1(( ,rquc.rdo,ocb~roo o 1Ro2tc (m.]:,:~.r.

FIG. 18-The quadrant illustrated in Valentim Fernandez, Report6rio dos tempos, Lisbon, 1563 (a posthumous edition). The two sight-vanes can be seen on the top radial edge; no plumb-line and bob are shown, but would have hung from the apex. Most of the quadrant's surface is occupied by the scale of 90° along the arc and by the extended divisions at 5° and 10° intervals. Towards the apex is a diagram of unequal hours (cf fig. 5b) and perhaps a solar declinations scale, so that the quadrant might be used as a sundial (the type of horary quadrant known as quadrans vetus), if the plumb-line were provided with a sliding bead .

reger pelo Quadrante ou Astrolabio pela estrella do Norte'. Compared with the medieval quadrant shown in figure 6, the quadrant illustrated in Fernandes' book has a horary scale (unequal hour diagram) which has been reduced to occupy a much smaller area of the instrument (86); the simple scale of degrees

(86) FoNTOURA DA CosTA, op. cit., p. 21. Horary quadrants (i.e. quadrants pri­ marily intending for telling the time by the sun) continued to be made throughout the six- FrG . 19 - A mariner's astrolabe, ? Spanish, c. 1588 , of brass; diam.: .178 mm .; thickness: 14 mm. at the top, 16 mm. at the bottom; weight: 2270 gm. The sights on the alidade are characteristically set close to the centre (cf. fig . 20). Found at Valencia, Ireland, in J 845, possibly from a wreck of the Spanish Armada. Waters, The Sea- or Mariner's Astrolabe ... , type Ia. National Maritime Museum, Greenwich (The photograph is of the facsimile in the Museum of the History of Science, Oxford.)

27 along the arc has, however, been emphasized by lengthening the divisions at so and 10° intervals. Used in conjunction with the sights and a plumb-line, the function of this instrument was primarily to measure the altitude of a celestial body, e.g. the Pole Star. The last pages of the 1563 edition of Fernandes' Report6rio include a section on how to navigate with the quadrant and describe a method which was by then already superseded. The pilot, on leaving Lisbon, is instructed to mark where the plumb-line falls while observing the Pole Star with the Guards of the Little Bear east-west in rela­ tion to that star. When some days later, at sea, he wishes to ascertain his distance from Lisbon, he should find the difference in degrees between the original position of the plumb-line and that of a new observation, and convert to distance on the basis of 1° = 16 2/3 leagues (87). There is, of course, no theoretical reason why such a quadrant should not have been used at sea for several centuries previously: the instrument was available and the concept of latitude familiar to astronomers. However, the use in navigation of the quadrant is associated with the development of the technique of 'running down the latitude'.

b) The mariner's or sea astrolabe (88) The illustration (fig. 19) shows a mariner's astrolabe, possibly Spanish, c. 1588 (89). As in Fernandez' quadrant, there is clearly the reduction to essentials of an instrument intended for practical use. The mariner's astrolabe is not a planispheric astrolabe; there is no stereographic projection of the celestial sphere, nor a zodiac/calendar scale, a shadow-square, or a horary diagram on the back. It consists simply of an alidade moving over a scale of degrees for measuring altitudes. Much care, however, was taken to render teenth and seventeenth centuries; the horary scales are often of considerable complexity (e.g. the quadrants named after Edmund Gunter and Henry Sutton). See HIGGINS, op. cit., pp. 344, 346; MADDISON, 'Early Astronomical and Mathematical Instruments .. .', passim. (87) The significance of this passage in connexion with the account sent to Martin Behaim by Diogo Gomes of his voyage to Guinea in 1460 has been discussed by ALBUQUERQUE, op. cit. Gomes' quadrant was of wood. (88) See DAVID WATERS, The Sea- or Mariner's Astrolabe (Agrupamento de Estudos de Cartografia Antiga, serie Separatas n. 0 XV), Coimbra, 1966; MARCEL DESTOMBES, 'Un Astrolabe nautique de Ia Casa de Contrataci6n (Seville, 1563)', Revue d'histoire des sciences et de leurs applications, vol. XXII (1969), pp. 33-64; and MARCEL DESTOM11ES, 'Deux astrolabes nautiques inedits de J. et A. de Gois, Lisbonne, 1603, 1648', in this publication. To the lists of surviving mariner's astrolabes given by Waters and Destombes ('Un Astrolabe .. .', pp. 42-44 & n. 1, and 'Deux astrolabes .. .'), there should be added ten other mariner's astrolabes which have been recently discovered: two English examples of the sixteenth­ century, one found at Layme Bay, Dorset, the other in Guernsey, both of which are now at the National Maritime Museum, Greenwich; a ? Portuguese example, ? sixteenth-century, found in Bermuda; five of as yet unknown origin from a wreck of 1552 in the Gulf of Mexico, one of which is dated 1550; and two recovered by Robert Stenuit from the wreck (1558) of the Girona of the Spanish Armada (information from Lt-Cdr D. W. Waters), Destom­ bes, 'Un Astrolabe .. .', pp. 45-48, gives a list of early illustrations of mariner's astrolabes. (89) National Maritime Museum, Greenwich, n. 0 IC 318. 28 it suitable for use on board ship: the body of the astrolabe is very thick and it is therefore heavy (90), and the thickness increases towards the bottom, so that it hangs well; the body is perforated so as to offer minimum resistance to the wind; the ali dade has the sights set closely together to facilitate the taking of solar readings (91). The illustration (fig. 20), from Pedro de Medina's Regimento de navegaci6n, 1563, shows a mariner's astrolabe in use for deter­ mining the meridian altitude of the sun. The mariner's astrolabe was deve­ loped during the last decades of the fifteenth century. In 1497 Vasco da Gama had a large astrolabe of wood, as well as smaller brass astrolabes. Joao de Barros described (92) how, after five months voyage, at first landfall in the Bay of St Helena, the large astrolabe was taken ashore and hung in a tripod in order to determine the altitude of the sun:

' ... sayo em terra por fazer agm'ida & assy tomar a altura do sol. Porque como do vso do astrolabio pera aquelle mister da nauega~am, auia poco tempo que os mareantes deste reyno se aproueitaua, & os nauios eram pequenos: nam confiaua muyto de atomar dentro nelles por causa do seu arfar. Principalmente com hum astrolabio de plio de tres palmos de diametro, o qual armauam em tres paos a maneira de cabrea por melhor segurar a linha solar, & mais verificada & distincta­ mente poderem saber a veradeira altura daquelle Iugar: posto que leuassem outros de latam mais pequenos, tam rusticamente come~ou esta arte que tanto fructo tern dado ao nauegar .. .' (93).

The earliest illustration of an astrolabe for nautical use is on a chart drawn by Diego Ribero in 1525 (94). The drawing, however, depicts an

(90) 2270 gms. Cf. the weights of other mariner's astrolabes given in the table in WATERS, The Sea- or Mariners Astrolabe ... , ad finem. GEORGES FOURNIER, op. cit., p. 369, wrote of the mariner's astrolabe: 'C'etait un gros cercle d'airain de 10 a 20 livres que l'on fait lourd afin qu'il resiste mieux au vent en agitation du vaisseau, et se mette plus promptement de niveau, et s'y tiene plus constamment: l'alidade se termine en un point aux extremites, les pinnules ne sont distantes que d'un pouce du centre'. (91) Mariner's astrolabes were graduated to read either altitudes or zenith distances, sometimes both; see DESTOMBES, 'Un Astrolabe nautique ... ', pp. 50-51; and WATERS, The Sea- or Mariner's Astrolabe ... , passim. (92) JoA.o DE BARROS, Asia ... Dos fectos que os Portugueses fizeram no descobrimento e conquista dos mares et terras do Oriente, 1." decada, Lisbon, 1552, livro 4, cap. vi, f. 41 v. (93) This passage continues (ff. 41 v-42r) with Barros' puzzling account of Joao Il's three advisers on navigational problems, Mestre Rodrigo, Jose Vizinho and Martin Behaim. On this so-called junta, see E. G. RAvENSTEIN, Martin Behaim. His Life and his Globe, London, 1908, pp. 12-13, 20; cf. the opinion expressed by WATERS, 'Science and the Techni­ ques of Navigation .. .', p. 207. (94) Archivio Castiglioni, Mantua. The chart is dated but not signed. Three other charts by Ribeiro bear similar illustrations: Thuringische Landesbibliothek, Weimar, 1527 (not signed) and 1529 (signed); Bibliotheca Vaticana, 1529 (signed) (DESTOMBES, 'Un Astrolabe nautique .. .', p. 45 & n. 3). On the Vatican chart, the illustration is entitled, 'Astrolabio maritimo para saber las alturas delas tierras' (WATERS, op. cit., p. 15 & fig. 2) . 29 astrolabe made from a solid plate of metal or wood and there is a shadow­ -square in the lower half; in fact, the drawing could equally well show the

ORJ ZO'NT£

FIG. 20- A mariner's astrolabe in use for determining the meridian altitude of the Sun. The illustration is reproduced from Pedro de Medina, Regimiento de navegaci6n, Seville, 1563.

National Maritime Museum, Greenwich

back of a planispheric astrolabe (95). If this be indeed a mariner's astrolabe, one might postulate an evolution from the back of a planispheric astrolabe to the characteristic nautical instrument. More probably the conceptual origin of the mariner's astrolabe is to be found in a similar graduated circle

(95) Ribera's drawing of a quadrant on the Vatican chart of 1529 is hardly an example of a specifically nautical instrument either; it is a typical horary quadrant (see above, n. 86). 30 equipped with an alidade which was used by medieval astronomers (96). The link between a planispheric astrolabe and the mariner's astrolabe appears to extend no further than the identity of the names.

c) The nocturnal (97)

During the sixteenth century, there was developed the nocturnal or noctur/abio, an instrument for determining the time at night by observation of the apparent rotation of a or fJ ('the Guards') Ursae majoris, or of fJ Ursae minoris, about the Pole. No detailed history of this instrument appears yet have been attempted. Some would, perhaps, seek to derive it from the very ancient Chinese circumpolar constellation template (98), but its immediate origin is probably to be found in medieval mnemonic diagrams serving a similar purpose. There is also a curious medieval device, known as the polar sighting tube, with the use of which the development of the nocturnal may be connected. The exact purpose of this tube is unexplained, but its existence is recorded as early as the tenth century when Gerbert of Aurillac sugges­ ted its use for correct identification of the Pole Star (99). The drawing (fig. 21) from the twelfth century Ms. Chartres 214 (173), containing a text of the Sententiae astrolabii, is interesting because of the diagram surrounding the Pole Star. The divided scale suggests some attempt at the determination of time with the aid of the sighting tube and the position of circumpolar stars. Towards the end of the thirteenth century, Ramon Llull described an astrolabium nocturnum or sphaera horarum noctis (100) which consisted of a single disc, perforated at the centre and engraved with concentric scales of the months and of the 24 hours, correlating the midnight positions of fJ Ursae minoris throughout the year (101). By sighting the Pole Star through

(96) See EMMANUEL PouLLE, 'Les Conditions de Ia navigation astronomique au xv• siecle', in this publication. (97) There is no general history of the nocturnal, but see JosEPH NEEDHAM and WANG LING, Science and Civilisation in China, vol. 3, 'Mathematics and the Sciences of the Heavens and the Earth', Cambridge, 1959, pp. 332-339; and CLARE VINCENT and BRUCE CHANDLER, 'Nightime and Easter Time. The Rotations of the Sun, the Moon, and the Little Bear in Renaissance Time Reckoning', The Metropolitan Museum of Art Bulletin, April, 1969, pp. 372-384. (98) NEEDHAM, foe. cit .. (99) RoBERT EISLER, 'The Polar Sighting-Tube', Archives internationales d'histoire des sciences, 2• annee, n. 0 6 (jan. 1949), pp. 312-332; Gerbert's text is cited on p. 313 & p. 323, n. 8. See also HENRI MICHEL, 'Les Tubes optiques avant le telescope', Ciel et terre, LXX• annee, n.os 5 & 6 (1954). There is, of course, no question of the use of lenses in these tubes; but cf. Robert Hooke's pole-finding telescope of 1687 (NEEDHAM, op. cit. , vol. 3, p. 262). (100) RAM6N LLULL, Opera omnia, Mainz, vol. I, 1721, 'Medicina', sec. x, cap. XXXVI, met. 30. (101) FONTOURA DA COSTA, op. cit., pp. 38-39. 31 the central hole and noting against which hour the star stood, the time could be found by counting how many hours were before or after the midnight position at the time of year. The Leal Conselheiro (1428-1437) of D. Duarte

n... lUf

FIG. 21 - A polar sighting-tube in use, perhaps as a nocturnal. An illustration from MS Chartres 214 (173), which was written in the first half of the twelfth century. The manuscript contained several treatises on astronomy and mathematics, including the Sententiae astrolabii (composed of fragments borrowed from various authorities, especially Gerbert of Aurillac (after 940-1003) and Hermannus Contractus (1013-1054). This illus­ tration may have been between the text of the Sententiae and a work of Gerbert which follows. The manuscript was completely destroyed during World War II. See Catalogue general des manuscrits des bibliotheques publiques de France . Departements, vol. XI 'Char­ tres', Paris, 1890, pp. 109-110; and op. cit., vol. LIII 'Manuscrits des bibliotheques sinistrees de 1940 a 1944', Paris, 1962, pp. 2-5

Formerly in the Bibliotheque municipale, Chartres mentions a similar device (l 02). Pierre Garcie's Grant Routier of 1483 and 1484 has a figure marking the quarters of the sky and a table of 24 1/2-monthly positions at midnight of the guards (103), and such diagrams are found in the Regimento de Evora, the Livro de Marinharia of Joao de Lisboa (1514) and many other works (104) (fig. 22). In the sixteenth century, Robert

(102) FONTOURA DA COSTA, op. cit., pp. 40-41. (103) D. W. WATERS, The Rutters of the Sea. The Sailing Directions of Pierre Garde. A Study of the First English and French Printed Sailing Directions, New Haven (Conn.) & London, 1967, pp. 40-41 & illus. (from 2nd ed., 1521). (104) FONTOURA DA COSTA, op. cit., pp, 41-44; Luis MENDONCA DE ALBUQUERQUE, 0 Livro de marinharia de Andre Pires (Agrupamento de Estudos de Cartografia Antiga, 32

Norman, described an equally crude nocturnal (105) which consisted of a small iron ring held firm at the centre of a larger ring by four equally spaced radial threads; the larger ring had 24 (or 32) equally spaced spikes on its circumference and was aligned on the celestial meridian by either pair of threads which formed a diameter. This instrument, which had to be used

J\.-1 f .:..~

o,. ·J'.. '"::-> · t- ·~ ...... _, I I I ~ ~ ~ ..]::< 0

FIG. 22- A diagram (roda das horas), giving (on a 24-hour scale) the midnight positions throughout the year of fJ Ursae minoris, from the Livro de Marinharia (1514) of Joao de Lisboa (MS belonging to the Livraria da Casa Palmela). Reproduced from A. Fontoura da Costa, A Marinharia dos Descobrimentos, Lisbon, 1933, fig. 24 (see also op. cit. pp. 482-483, item 61 M).

with a table of midnight pos1t10ns throughout the year, is a curious late survival of the most elementary form of nocturnal, by then long superseded. The devices (figs. 23 and 24) on the lids of small equinoctial dials, ? 15th cen­ tury (106), are the only recorded surviving examples on instruments of the simple type of nocturnal described by Llull; these devices have index-arms for aligning on the star used to determine the time. The lid of another equi­ noctial dial (fig. 24), probably c. 1500 (107), bears a fully developed nocturnal: two concentric discs, one of which is adjustable to the date, thus glVlng a direct reading of the time. The earliest known nocturnal as a separate

serie Mem6rias, n. 0 1), Lisbon, 1963; Luis MENDONc;:A DE ALBUQUERQUE, Os Guias nauticas de Munique e Evora (Agrupamento de Estudos de Cartografia Antiga, serie Mem6rias n. 0 4), Lisbon, 1965; TAYLOR, The Haven Finding Art ... , pp. 145-148. (105) TAYLOR & RICHEY, The Geometrical Seaman ... , p. 62. (106) See also above, & figs. lOa and lOb. (107) Above, & fig. lOc. FIG . 23 - The simple form of nocturnal, on the hinged lid of the equinoctial dial (? 15the century), shown in fig. 1Oa ; the index arm also serves as a catch to keep the lid shut. From the outer, uninscribed, 24-hour scale (with 20 minute divisions), the lines marking every 2-hours are continued towards the centre to form a scale of the J 2 months (very faintly marked by their initial letters). In use, the Pole Star was sighted through the central hole and the index arm turned till it pointed towards {3 Ursae minoris. As the scale of months gave the midnight position of that star, it was only necessary to count the number of hours before or after the midnight position on the date of observation in order to find the time. This nocturnal resembles that described by Ram6n Llull.

Mnseum of the History of Science, Oxford F1o . 24- The simple nocturnal on the hinged lid of the equinoctial dial (? 15th century), shown in fig. lOb. The design is similar to that of the nocturnal shown in fig. 23, and its method of use is identical. (For photographic reasons, the engraving has been temporary filled with white material.) Museum of the History of Science, Oxford FIG. 25 - The nocturnal on the hinged lid of the equinoctial dial (? c. 1500) shown in figs. 1Oc and 11. This is a fully developed nocturnal with a separate hour-scale and an index which is set to the date. The position of the index-arm, after an observation has been made, then gives the time directly (cf fig . 27)

Museum of the History of Science, Oxford FIG. 26 - A nocturnal, signed en the back, 'LA YRENTIYS YYLPARIA. FLO RENT'. 1511'; gilt brass; diam.: 77 mm. A second, larger, rotatable disc is missing from between the existing disc and the main plate. During reassembly the original index arm appears to have been replaced by the present 'alidade' and no central hole provided in the rivet (cf the nocturnal in fig. 27). Museo di Storia della Scienza, Florence FIG. 27- A nocturnal, signed on the back, 'EVFROS!N' VVLPARlA . FLORENTIN' LAVRENTII FILl' ANNO. M.D.XVI.'; brass. Dr. Carlo Maccagni has pointed out that part of this inscription replaces an earlier inscription which read, 'CAMILL' & BEN­ VENTVS VVLPARIAE FLORENTINI LAVRENTI FILl! ANNO . M.D.XVI'. In use, the index (inscribed, 'MEDIA NOX') on the larger rotatable disc was set to the date on the scale on the main plate; the nocturnal was them held up and the Pole Star sighted through the central hole; then, the index arm (inscribed, 'HOROLOGIVM NOC­ TVRNVM') was moved until it appeared to align with the Guards (a & {J Ursae majoris); the time could then be ascertained from the position of the index arm over the 24-hour scale on the larger disc. The smaller disc is cut with twenty-four notches, some of which are numbered anti-clockwise from its index. If the index of this disc were aligned with that of the larger disc, the number of hours before or after midnight could be determined in the dark by counting the notches; the numeration of the notches, if visible, was merely an aid to reading hours before midnight.

National Maritime Museum, Greenwich

33 instrument is that made in 1511 by Laurentius Vulparia of Florence (108) (fig. 26). Nocturnals are fairly common instruments in the sixteenth and seventeenth centuries. Georges Fournier, in his Hydrographie, first published at Paris in 1643, describes two types of nocturnal, the conventional type 'duquell'Alidade est simple' (as in figs. 25 & 27) and a variant 'dont l'Alidade est croisee' (fig. 28). Somewhat similar to the latter is the peripo/e (fig. 29), invented in 1671 by an ecclesiastic named Loysel, which defines the declination circle of the Pole Star by the eccentric traced by the small sighting hole as the inner ring is rotated. The purpose of this becomes clear if we consider Fourniel's definition of a nocturnal: 'Nocturlabe est vn instrument par lequel a toute heure de la nuict on peut trouuer combien l'Estoile du Nord est plus haute ou plus basse que le Pole. On peut aussi seruir pour s<;auoir quelle heure il est'. For Fournier, then, the prime purpose of a nocturnal was not time-telling, but location of the Pole from an observation of the declination of the Pole Star. This is precisely the function of the diagrams, known as rodas do norte (fig. 30), which are found in the nautical guides of the sixteenth century, such as the Regimento of Munich, c. 1509. In these diagrams, eight positions of the Pole Star on its declination circle are written at the extremities of eight equidistant radii of a circle corresponding to the rhumbs occupied, at the equivalent time intervals, by {3 Ursae minoris. These diagrams, and simple instruments based on them, are adaptations of the primitive 'sky-clock' diagrams and early forms of nocturnal; their histories are inextricably linked. Fournier said that Pedro Nunez 'maintient que ces Nocturlabes ne sont pas Instruments vniuersels [i.e. usuable in any latitude]', but politely disagreed. Nevertheless, he was not particularly impressed with the nocturnal as a nautical instrument:

'Cet instrument est grandement necessarie, puis qu'il est impossible d'auoir de nuit sur Mer, la hauteur du Pole, & Latitude de quelque lieu, si on ne s<;ait de combien l'Estoile a laquelle on opere, est plus basse ou plus haute que le Pole, au moment que se fait !'operation. Aussi les Pilotes en font tant de cas qu'ils se persuadent qu'en son bon vsage consiste l'vn des plus grands secrets de la marine. Voire lors qu'vn Hydrographe interroge quelqu'vn deuant Messieurs I'Amiraute pour connoistre s'il est capable, & suffisamment instruit pour gouuerner vn Vaisseau, & estre passe Maistre Pilote, c'est leur plus ordinaire demande: & semble qu'il suffit pour estre tenu habille homme s'il s<;ait combien l'Estoile du Nord est plus haute ou plus basse que le Pole a chaque Run

(108) Museo di Storia della Scienza, Florence, no. 1305. Another early nocturnal is that made in 1516 by Eufrosinus Vulparia (fig. 27), now in the National Maritime Museum, Greenwich. Both nocturnals have horary quadrants on the back. On Laurentius and Eufrosinus Vulparia, see MACCAGNr, op. cit .. 3 34

FIG. 28- A nocturnal dont l'Alidade est croisee, illustrated in Georges Fournier, Hydro­ graphie, 2nd ed., Paris, 1667, p. 392. Fournier gives instructions for using this nocturnal to find the difference in altitude between the Pole Star and the Pole, and to ascertain the time. FIG . 29 - 'Peri pole lnuente par Loysel Eclesiastique 1671 ', a form of nocturnal; brass ; diam.: 130 mm . The side shown is entitled 'Horologe aux Etoiles'. The cross-arm attached to the scale of hours can rotate with the scale of months, which in turn can rotate within the main frame. ]n use, the date is set to the index line above the inscription on the handle; the radial bar marked with a star and the word 'Claire' (below the 12 o'clock numeral marked 'minuit') serves as the index-arm. The sighting-hole is eccentrically placed and defines the declination circle of the Pole Star. The other side of the instrument is entitled, 'Mouuement de !'Etoile Polaire', and is similar to the side shown but, on the rectangular piece between the arms, is engraved with a picture of the constellation Ursa minor.

Museum of the History of Science, Oxford

35

ou trait du compass. En quoy ces bonnes gens se trompent lourdement, tel instrument n'ayant Ia iustesse qu'ils se persuadent, comme ie demons­ treray en ce traitte, bien que ie ne vueille leur en oster entierement l'vsage, puis qu'ils peuuent par fois en tirer de l'vtilite, & que les operations de Mer ne demandent vne rigoureuse iustesse Mathematique' (109).

d) The azimuth compass (111 ).

4l

FIG. 30- Roda das alturas do norte, for Lisbon, from Valentim Fernandez, Report6rio dos tempos, Lisboa, 1518. The head (caber,:a) of the man represents North, and eight altitudes of the Pole Star on its declination circle are given at the extremities of the eight radii corresponding to rhumbs occupied by f3 Ursae minoris.

It is clear from the works of Robert Norman and William Barlow (to name but two) that much care was taken in the sixteenth century to improve the functioning of the magnetic compass, though Barlow could still write, in the chapter (X) 'Of the fashioning of the compasse needle' in his Magneticall Advertisements, 1616, that:

'The Compasse needle, being the most admirable and vsefull instru­ ment of the whole world, is both amongst ours and other nations for the most part, so bungerly and absurdly contriued, as nothing more. And

(109) FouRNIER, op. cit., pp. 391-393. An example of Loysel's instrument is in the Museum of the History of Science, Oxford, n.° F. 245. On the rodas do norte, see FoN­ TOURA DA CosTA, op. cit., pp. 44-60; ALBUQUERQUE, 'The Historical Background ... '; ALBUQUERQUE, Os Guias nduticas ... ; and TAYLOR, The Haven-Finding Art ... , pp. 163-164. 36

therefore... [ haue thought good... to employ my best endeauor, to aduance this noble instrument towards its highest perfection .. .'.

Barlow gives detailed instructions for marking a steel needle and tempering it, and discusses the form of the needle which is attached to the fly; some, he says, prefer a square needle, others a loop (or extended oval), but ' ... now a dayes, a narrow straight plate (being somewhat broader in the middle) is in great request: Of these three I holde the loope or ouall forme (if it be well made) to bee the best. . .'. He remarks that Simon Stevin put the needle on the upper face of the fly, and says that the needle and fly must not be heavier than necessary (therefore, not more than six inches in diameter), because of the wear on the pin; the latter must be kept sharpened and the capital (the boss of the fly which rests on the pin) must fit well. In the next chapter, on a variation of azimuth compass, Barlow says that the glass (of the inner box of the compass) should be of good thickness and strength, but yet clear, and suggests the use of those glasses imported from Venice for looking glasses before the foil is applied (110). Barlow's 'Sayling Compasse fitted for obseruing at Sea the variation, amplitude of either sunne or starres, capes or trendings, &c.' described in the same chapter, like the two variation compasses illustrated in his Discours of the Variation of the Cumpas, 1581 (111) (fig. 33), represent important steps in the development of the azimuth compass, an instrument which derives ultimately from an instrumento de sombras described and illustrated in the Tratado da sphera of Pedro Nunez, published at Lisbon in 1537 (fig.32) (112). In 1514, Joao de Lisboa had written on magnetic variation (a subject about which there was still much confusion)in his Tratado da algu/ha de marear (113).

(110) BARLOW, Magneticall Aduertisements ... , pp. 66 ff. A typical 16th. century compass (with fly) appears in the portrait reproduced in fig. 31 . SCHUCK, op. cit., e.g. pl. 5, illustrates various shapes of the needle placed under the fly . (111) B[ARLOW]., Discours, sig. B i v & Givr. (112) On the azimuth compass, see E. G. R. TAYLOR and M. W. RicHEY, The Geome­ trical Seaman. A Book of Early Nautical Instrumellls, London, 1962, pp. 31-33, and WATERS, The Art of Navigation ... , pp. 70-71; illustrations of azimuth compasses and instructions for their use are found in many late seventeenth and early eighteenth century publications, e.g. WILLIAM LEYBOURN's, Cursus mathematicus ... , London, 1690, and JOHN SELLER's, Practical Navigation ... , London, 1699. For Nunez' shadow instrument, see Luis DE ALBUQUERQUE, 'Jnstrumentos abacos e graficos na nautica portuguesa dos seculos XVI e xvrr. III. Instrumento de sombras', Vertice. Revista de cultura e arte, vol. XXVII, n.0 287 (Agosto 1967), pp. 531-539 ; TAYLOR, The Haven-Finding Art ... , pp. 181-182. The shadow instrument was also described and illustrated in NuNEZ' De Arte atque navigandi libri duo, Coimbra, 1573, and this is the text discussed by ALBUQUERQUE, op. cit., There are other editions of the relevant tratado. See FONTOURA DA CosTA, op. cit., pp. 419, 422-423, & 426, bibliography n.0 5 32A-35A. A shadow instrument was used by D. Joiio de Castro on his voyage to Goa in 1538; see D. JoXo DE CASTRO, Obras camp/etas (ed. by Armando Cortesiio and Luis de Albuquerque), vol. I, Coimbra, 1968, pp. 127 ff. (113) Jacinto Inacio de Brito Rebelo (ed.), Livro de marinharia. Tratado da agulha de marear de Joiio de Lisboa, Lisbon, 1903; see WATERS, 'Science and the Techniques of FIG . 31- Edward Fiennes, Lord Clinton and Saye, Lord High Admiral, 1562. Artist unknown. For a description and provenance, see Mrs Reginald Lane Poole, Catalogue of Portraits in the Possession of the University, Colleges, City, and County of Oxford, vol. I, Oxford, 1912, p. 168 , where the subject of the portrait is described as an unknown navigator. The subject holds a magnetic compass which has a characteristic fly.

Ashmolean Museum, Oxford

37

Felipe Guillen had produced in 1519 an instrument for finding magnetic variation (114) and Magellan was also provided with an azimuth measuring

FIG. 32 - Instrumento de sombras, illustrated in Pedro Nunez, Tratado da sphera, Lisbon, 1537. A horizontal plate, a b c d, has inset a magnetic compass. In the centre of the plate at e, there is a vertical style which casts a shadow of the sun on a scale of degrees around the circumference of the plate (the lines fe and ge show two possible positions of the shadow, and are referred to in Nunez discussion of the use of the instrument. The compass, set in the northern half of the plate has a south-pointing needle (cf fig. 2).

Navigation .. .', pp. 224-5; and FONTOURA DA COSTA, op. cit., pp. 482-483, bibliography n. 0 61 M. (114) WATERS, 'Science and the Techniques of Navigation .. .', p. 225. 38 instrument (115). Nunez' 'shadow instrument' was used to measure azimuths of the sun when at equal altitudes before and after midday; if any difference between the azimuths was found, this was halved to give the variation of the compass-needle from the meridian.

a

b

FIG. 33- Two variation compasses illustrated in William Barlow, Discours of the Variation of the Compass ... , London, 1581 (appended to Robert Norman, The newe Attract­ ive ... , London, 1581). a) On sig. Bi 11 • This compass differs from the instrumento de sombras of Nunez (fig. 31) by having, i.a., a string-gnomon inst(ad of a vertical style. The initials 'R.N.' on the base-plate are those of Robert Norman. b) On sig. Givr. This compass was devised by Barlow as an improved version; he calls it, 'A new Instrument for the Variation'. Barlow's book concludes with an advertisement that both sorts of compass may be obtained from Robert Norman, who was a professional compass-maker.

(l15) WATERS, foe. cit.. FIG. 34 - Azimuth compass, signed on the scale surrounding the compass, 'Rich: Glynne Londini Fecit', c.l706; brass, in an oak box with iron handles; length of box: 52.5 em. The hand-coloured engraved compass-card is signed, 'Made by I: Sellars & C. Price Hydro­ graphers to ye Queen Compass Makers to Nauy Royall, Waping', and 'R. Spofforth Sculp.'. The compass is mounted on gimbals within the box. To determine the azimuth of the sun, the alidade was directed towards the sun until the shadow of the string gnomon fell upon the line engraved on the alidade. The hinged arm supporting the string is perforated by a vertical slit which could serve as a back-sight (in conjunction with the string) for direct observations. The scale carries a transversal division of the arc (cf fig . 55).

Museum of the History of Science, Oxford FrG . 35- A Portuguese amplitude compass, made in Lisbon in 1711 by Josep' da Costa Miranda. Opposite sides of the painted wooden box containing the fly are fitted with windows and sights for taking solar bearings. The mounting screws are visible on the outside of the box. Whipple Science Museum, Cambridge FIG. 36 - The fly of the Portuguese amplitude compass illustrated in fig. 35.

Whipple Science Museum, Cambridge

39

The instrument was hung in cords or mounted in gimbals to insulate it from the movement of the ship. Gimbals are sometimes known as the Cardan suspension, though even Girolamo Cardano (1501-1576) himself did not claim the invention (116). Gimbals were known to medieval techno­ logy and are depicted in the 'Sketchbook' of Villard de Honnecourt, c. 1235 (117); Leonardo da Vinci, c. 1500, envisaged their use for a compass (118). Although gimbals were occasionally thought to provide the answer to all problems arising from the motion of a ship (119), they were of considerable importance in the development of marine technology; the history and applications of this form of mounting would repay detailed investigation. No early examples of the variation of azimuth compass have survived; a typical later compass of this type is here illustrated (fig. 34). It was made about 1706 by Richard Glynne and has a compass card sold by Jeremiah Sellar and Charles Price, all of London (120). The gimbal-mounted compass box bears a string-gnomon for ascertaining the sun's azimuth. An amplitude compass made in Lisbon in 1711 by Josep' da Costa Miranda (121) is also illustrated (figs. 35 and 36); the compass-box is again gimbal-mounted. Both compasses have the customary fly (122). It was in the sixteenth century that the foundations were laid for the science of terrestrial magnetism with its far-reaching effects on the design of the marine compass. Nearly 350 years separate the two classic early writings on magnetism, the Epistola de magnete of Petrus Peregrinus (123) and William Gilbert's De magnete published in London in 1600 (124), though in the previous century particular aspects of magnetic phenomena had received attention

(J 16) See BEDINI & MADDISON, op. cit., p. 38, n. 120. (117) See THEODORE BowiE (ed.), The Sketchbook of Villard de Honnecourt, 2nd ed., New York, 1962, p. 28 (a hand-warmer with a gimbal mounting of seven rings). (118) See JOSEPH NEEDHAM and WANG LING, Science and Civilization in China , vol. 4, part. II 'Mechanical Engineering', Cambridge, 1965, pp. 228-236, for a survey of Chinese and European references to the gimbal-mounting. ScHUCK, op. cit., pl. 24, fig Sa & b, illustrates an early (1571) gimbal-mounted compass by Hans Gobe. (119) Cf. the illustration of a gimbal-mounted marine chair in JACQUES BESSON, Livre des instruments mathematiques et mechaniques, 1571-2, reproduced in TAYLOR & RICHEY, op. cit., p. 94, fig. 34; and see SILVIO A. BEDINI, 'The Instruments of Galileo Galilei', Ga/ileo. Man of Science (ed. by Ernan McMullin), New York, 1968, pp. 379-380, for Galileo's attempts to improve observations at sea by insulating the observer from the motion of the vessel. (120) Museum of the History of Science, Oxford. (121) Whipple Science Museum, Cambridge. On Josep da Costa Miranda, see DESTOMBES, 'Deux astrolabes .. .'. See the comments on this compass by Lt-Cdr D . W. Waters in the 'Discussiio' at the end of this article. (122) See above. (123) See above. (124) On Gilbert, see DUANE H. RoLLER, The De Magnete of William Gilbert, Amsterdam, 1959. 40 from mariners and writers on navigational topics in Portugal, Spain, England and the Netherlands (125). Apart from his debt to Petrus Peregrinus, Gilbert's methods derived from practical compass-makers such as Robert Norman. Norman's book, The Newe Attractive, 1581, describes the author's discovery of magnetic dip:

'Hauyng made many and diuers compasses, and vsing alwaies to finish and ende them, before I touched the needle, I found continually, that after I had touched the Irons with the Stone, that presently the North poinct thereof would bende or Decline downwards vnder the Horizon in some quantitie ... ' (126).

The hopes that were focused on the use in navigation of this discovery are expressed in the laudatory address by Edward Wright (?1558-1615) (127), which prefaces Gilbert's book:

' ... you will stimulate all wide-awake navigators to give not less study to observation of dip than of variation. For it is highly probable, if not certain, that latitude, or rather the effect of latitude can be determined much more accurately (even when the sky is darkest) from the dip alone, than longitude or the effect of longitude can be found from the variation even in the full light of day or all the stars are shining, and with the help of the most skilfully and ingeniously contrived instrument. .. '; previously he had remarked, when speaking of variation:

'And thus, thanks to this magnetic indication, that ancient geographic problem, how to discover the longitude, would seem to be on the way to a solution; for, the variation of a seaboard place being known, that place can thereafter be very easily found as oft~n as occasion may require, provided its latitude is not unknown'.

Gilbert's experiments were conducted with lo~dstones, and with a load­ stone ground to a spherical shape he was able to demonstrate magnetic dip (128). Such loadstones are called terellae and two, probably of the

(125) See HELLMANN, op. cit.; BALMER, op. cit.; FONTOURA DA COSTA, op. cit., pp. 153-184; and Gilbert's unfavourable comments on magnetic observations by seamen (GILBERT, op. cit., pp. 265-267). (126) NoRMAN, op. cit. (See above & n. 82), p. 8. (127) On Wright, see TAYLOR Mathematical Practitioners ... pp. 181-182; and Dic­ tionary of National Biography, art. 'Wright, Edward', (128) GILBERT, op. cit., xliii & xxxix; on attempts to determine latitude by measuring variation, see WATERS, The Art of Navigation ... , passim. FtG. 37- Two terellae (loadstones ground to a spherica l shape). a) An armed terella, with steel pole-pieces and brass mounting,? 18th century; 74 x 70 mm. overall, excluding suspension ring. The terella is a plain sphere. b) A terel/a in a velvet-lined fish-skin case, l 8th century; diam. of terella: 58 mm. The terella is engraved with lines corresponding to 'latitude' and ' longitude'. Museum of the History of Science, Oxford

41

18th century, are illustrated here (fig. 37) (129). One of these terellae is armed; the other bears lines corresponding to lil}es of 'latitude' and 'longitude'.

e) The mechanical clock as an aid to navigation

Alas, for the hopes of Edward Wright- the measurement of magnetic variation failed to contribute to the solution of the intractable longitude problem (130). However, it was in the sixteenth century that what was to prove the most practical solution was first proposed. In 1530 at Louvain and Antwerp, there was published Gemma Frisius' De principiis astronomiae et cosmographiae. The very short chapter XVIIJ of part 2 of this book is entitled, 'De nouo modo inueniendi longitudinem' and describes concisely how to determine longitude by comparing local time with standard time:

'In our century we see certain small and ingeniously constructed time-pieces being made which, because of their exiguous size, are a very small burden to the wayfarer. They often keep going continuously up to 14 hours and will, if you assist [sc. by winding them], even be moved by a quasi-perpetual motion. With their aid, the longitude is found in the following way. First, before we start on our journey, let it [sc. the time-piece] most accurately record the time [= standard time] at the place from which we start. Then see that it does not stop on the journey. At the end of a journey of 15 or twenty miles, if you want to know by how much in longitude we are distant from the place where we started, wait until the hand of the clock reaches precisely the mark of any hour. At that moment find out the time [=local time], with the aid of an astrolabe or of our globe, of the place at which we then are. If that time be to the minute the same as that shown by the horoscopium [ = here, the astrolabe or globe, instruments indicating the time by direct observation], it is certain that we are still on the same meridian or the same longitude, and that we have travelled either towards the South or towards the North. But if there be a difference of an hour or of some minutes, then these must be reduced to degrees, or to the minute of the degrees, as we have shown in the preceding chapter, and thus the longitude is to be found. By this art, I could find the lon­ gitude of [distant] regions, also if unknowingly I had been taken a thousand miles away did not know the distance: but the latitude must (as always) first be known'.

(129) Museum of the History of Science, Oxford, n. 0 5 2410 (armed) and 57-84/271. (130) Cf. HENRY BoNo, The Longitude Found: or, a Treatise shewing An Easie and Speedy way, as well by Night as by Day to the Longitude, having but the Latitude of the Place, and the Inclination of the Magneticall /nclinatorie Needle, London, 1676 ; see BALMER, op. cit., pp. 186 ff. 42

In the 1553 edition of Gemma's book, this chapter became the nineteenth (instead of the eighteenth) and the following sentences were added at the end:

'We have previously taught that it [? sc. the latitude] may, without knowing the time, be ascertained in various ways. But then, a timepiece that would remain constant in spite of a change of air could indeed be [a] most exquisite [thing]. For that reason it will be useful to employ on long journeys, and especially during voyages, large water-clocks, or sand-clocks [ = sand-, or hour-glasses], which will accurately divide the whole day [into equal spaces], whereby the errors of other time-pieces may be corrected' (131).

It is clear from this text that Gemma had fully appreciated the advantages of the small clocks or watches from Germany (Nuremberg 'eggs' they were called because of their ovoid or round cases, often like pomanders, and were made to be hung about the neck), invented perhaps no more than thirty years earlier. Spring-driven, they could easily be carried about, unlike a weight­ driven clock. The problem of transporting a pendulum clock while it was going did not exist, for the pendulum had yet to be invented. These watches, of course, had no balance-spring either- simply a verge and balance-wheel escapement. Needless to say, they were inaccurate as time-keepers. Perhaps Gemma came to realize that his suggested use of clocks for finding longitude was impractical in view of the imperfections of horological science in his day, and that is why he added in the 1553 edition of his book the proposal that one sort of time-piece should be checked by another. As the early portable clocks had only an hour-hand, Gemma suggests, for greater pre­ cision in noting standard time, that his reader should wait until the hand reaches exactly one of the hour divisions of the dial, to avoid the estimation of quarters or minutes. When finding local time an astrolabe or globe was to be used, and specially with the former instrument it was easier to read divisions of the hour. The illustration (fig. 38) shows a small portable clock of c. 1540 (132) of the type to which Gemma refers. It was to be over 200 years before the problems were satisfactorily overcome by the development of the marine chronometer; in doing so science and technology were profoundly changed.

(131) GEMMA FRJSIUS, op. cit., (author's translation); see A. PoGo, Gemma Frisius, his Method of Determining Differences of Longitude by Transporting Timepieces (1530), and his 'Treatise on Triangulation (1533)', Isis, vol. XXII (1935), pp. 468-486 (-506). REY PASTOR, op. cit., p. 96 refers to the determination of longitude by transporting clocks as 'metodo que suele atribuirse a Alonso de Santa Cruz pero en verdad pertenance a Fernando Col6n (1524)', but gives no source. On the later history of the marine chronometer, see RUPERT T. GouLD, The Marine Chronometer. Its History and Developmellt, London, 1923; and HUMPHERY QUILL, John Harrison. The Man who found Longitude, London, 1966. (132) Museum of the History of Science, Oxford, n. 0 B.l. FrG . 38 - A ? German portable alarm clock, not signed but with pillars of the movement in the form of the letters '1' and 'Z', c. 1550; gilt brass tambour case, with hinged, pierced cover, decorated with animal and human figures, including boar-hunting scenes around the side: steel and brass movement ; diam.: 50 mm. The dial is for ordinary and Italian hours, with touch pins and with an alarm setting dial in the centre. The photograph of the movement shows the verge escapement and the stackfreed. The movement has two trains, for going and for the alarm; there is no motion work.

Museum of the History of Science, Oxford FrG. 39 - An armillary sphere, with sights, not signed, but certainly from an Arsenius workshop (the engraving, design and the satyr figures are characteristic of Arsenius work­ manship), c. 1560, gilt and silvered brass, and bronze Atlas figure; overall height: 46 em. There are pointers indicating the positions of 16 fixed stars. The pin-hole sights are attached to the innermost ring of the complex of rings within the sphere, and are visible in the photo­ graph. The ring, to which the ring with sights is attached, is pivotted so as to compensate for the supposed trepidation of the equinoxes.

Museum of the History of Science, Oxford FIG. 40 - An astronomical ring, signed, 'Nepos Gemmae Frisy [ = Gualterus Arsenius] Louany fecit 1567', gilt brass; diam.: 100 mm. The vertical, meridian, ting is engraved at the top with a latitude scale. The instrument may be adjusted for use in any latitude by fixing the suspension piece (by means of the two screws) in an appropriate place on the ring (coarse adjustment) and sliding the suspension piece before tightening the screws (fine adjustment). An 'equatorial' ring is hinged to the meridian ring and opened at right angles when in use; this ring also bears an ecliptic/calendar division . Within is pivotted a third ring within which rotates a fourth, concentric ring bearing sights, thereby providing for observational measurements of altitude and azimuth.

Museum of the History of Science, Oxford FIG. 41 - A universal equinoctial hanging dial, not signed, c. 1480 (a later inscription read, 'MARTIN FREY REGENSPURE 1590'), brass ; 95 mm. square. A rare type of dial (see n. 137). Around the edge of the circular hole in the square plate slides a ring carrying a disc on which is pivotted an alidade. To use the instrument, the sliding ring is first set to the latitude by means of the latitude scale marked on the square plate. The ali dade is set to the declination by means of ·the zodiac scale on the disc. The instrument is then suspended and disc is turned until the sights are directed towards the sun. The distance between the notch on the sliding ring and the notch in the centre of the zodiac scale is then measured by the small ruler (kept in the slots at the bottom of the plate) which is marked with a scale of chords. The chords are numbered as hours so that the time may be read directly. Museum of the History of Science, Oxford FIG . 42 - A universal equinoctial ring dial, signed, 'Hilkiah Bedford at Holborn Conduit [London]', c. 1670, brass ; diam.: 135 mm . The vertical meridian ring is engraved at the top with a latitude scale along which the suspension piece can slide so as to adjust the dial for use in any latitude. In use, the equatorial ring is opened at right angles to the meridian ring. The bridge pivotted within the meridian ring carries a sliding cursor which can be adjusted to the date or to the solar declination (the side shown here bears the date scale; that shown in fig. 43 the declination scale). The dial is self-orientating; it is held so that the meridian ring lies roughly north-south and both the meridian ring and the bridge are turned until sunlight, passing through the hole in the cursor, falls on the hour-scale on the equatorial ring. The spot of light then indicates the time.

Museum of the History of Science, Oxford FIG. 43 - The nautical ring (armi/a ndutica) on the back of the meridian ring of the universal equinoctial ring dial shown in fig . 42. To use the nautical ring, the dial is folded flat, and the suspension piece moved until it is at the zero point of the latitude scale. A pin is inserted at A, and the ring is directed towards the Sun so that the shadow of the pin falls on the scale of degrees, indicating the solar altitude.

Museum of the History of Science, Oxford 43

f) The universal equinoctial ring dial

Gemma Frisius' craftsmen relatives, the Arsenius family, made a number of armillary spheres which included sights · for observational purposes (133) (fig. 39). Simplifying the essentials for observation of such a sphere, G~mma invented an astronomical ring, of which an example made by Gualterus Arsenius in 1567, is shown in figure 40 (134). This instrument includes facilities for latitude adjustment, sights on a movable ring, equatorial and meridional fixed rings, and star names. Gemma's Annuli astronomici ... vsus ... , was published in Paris in 1558 (135). In the dedicatory preface, written in 1554, Gemma said:

' ... Concerning our [astronomical] ring, I may frankly own ... that this is not entirely my invention. However, if it is praiseworthy to add to and to extend an invention, then in this matter 1 put forward my name. For we have so improved the ring, which up till now showed only the hours of the day and the four regions of the Earth, that it now emulates any mathematical instrument. For whatever others have written at length in various places about quadrants, cylinder-dials, and astrolabes, is now brought together in one ring .. .' (136).

Despite Gemma's enthusiasm, the astronomical ring did not, to judge from the examples which survive, become very popular. It, nevertheless, inspired the invention in the seventeenth century of the only form of sundial that was of much use to seamen, the universal equinoctial ring-dial (fig. 39) (137).

(133) See above & n. 20. D. Joiio de Castro mentions (op. cit., p. 129 & n. 23) the use on his voyage to Goa in 1538 of an altitude-measuring instrument known as a poma, which is clearly a derivative of the armillary sphere. (134) Museum of the History of Science, Oxford, n. 0 57-84/24; the instrument is signed, 'Nepos Gemmae Frisy Lovany fecit 1567'. (135) In Annuli astronomici, instrumenti cum certissimi, tum commodissimi, vsus, ex variis authoribus, Petro Beausardo, Gemma Frisio, Ioane Dryandro, Boneto Hebraeo, Burchardo Mythobio, Orontio Finaeo, vna cum Meteoroscopio per Ioane Regiomontanum, & annulo non vniuersali M. T. autore, Paris, 1557, repr. 1558, and in other publications (see VAN 0RTROY, op. cit., pp. 172-175). (136) Op. cit., sig. fii (author's translation). Although the form of the astronomical ring clearly derives from the armillary sphere, Gemma refers here to an earlier 'ring' which 'showed only the hours of the day and the four regions of the Earth'. Perhaps he was thinking of the equinoctial dial with its compass in the base (see above & figs. 9, 10 & 11), or the simple ring dial (see below & n. 141). However, there is in the Museum of the History of Science, Oxford, n. 0 G. 83, a very rare type of equinoctial dial which may have a place in the history of the astronomical ring. It is an equinoctial hanging dial of c. 1490, which bears, in a later hand, a now partly erased inscription which formerly read, 'MARTIN FREY [REGENSPURE 1590]'. This dial has no hour ring and the time is ascertained by means of a ruler engraved with chords numbered for the hours (fig. 41). (137) Museum of the History of Science, n.0 77. The invention of the universal equinoctial ring dial is attributed to the English mathematician, William Oughtred (1574-1660), 44

The sighting ring was removed, and a bridge gnomon (adjustable for solar declination) was placed between the poles. Such dials, which are self­ -orienting and fairly easy to use on. board ship, became popular in the later

FIG. 44 - A nautical ring (armila ruiutica) illustrated in Simao de Oliveira, Arte de navegar, Lisbon, 1606, p. 62. The side of a fiat ring, equipped with a suspension ring, bears a scale of 90° with its apex at A (thereby doubling the size of the scale compared with a scale of 90° drawn in one quadrant of the circle). At A, a very thin style is placed perpendicular to the plane of the ring, so as to cast a shadow on the scale when the ring is directed towarsd the Sun. Cf. fig. 43 . Reproduced from the article by Luis de Albuquerque cited in n. 138. half of the seventeenth and in the eighteenth century. Most English examples of the universal equinoctial ring dial have engraved on the back of the meridional ring a 'nautical ring' (see fig. 43), an instrument described by Simao de Oliveira in his Arte de navegar, published in Lisbon in 1606 (fig. 44). Oliveira's text follows closely a description of this armila nautica who referred to it as the 'general horological ring' ; see The Description and Use of the Double Horizontal/ Dyall ... Invented and Written by W. 0. Whereunto is added, The Description of the generall Horologicall Ring, London, 1652. The instrument-maker, Henry Wynne, later wrote an account of this type of sundial, and on the title-page of his publication named Oughtred as the inventor of the portable version: The Description and Uses of the General Horological-Ring or Universal Ring-Dyal. Being the invention of the late Reverend Mr. W. Oughtred, as it is usually made of a portable pocket size ... , London, 1682. For details of such dials, see H . 0. HILL and E. W. PAGET-TOMLINSON, Instruments of Navigation. A Cata­ logue · of Instruments at the National Maritime Museum [Greenwich] with Notes upon their Use, London, 1958, pp. 42-50. William Bourne, writing in 1574, recommended the use of a universal equinoctial dial (a type of sundial fixed on a base in which is set a magnetic compass- see fig. 10); see WILLIAM BouRNE, A Regimenter for the Sea, and other Writings on Navigation (ed. by G. R. Taylor) (Hakluyt) Society, 2nd ser., n.° CXXI), Cambridge, 1963, pp. 266-270; cf. the use of sundials by D . Joao de Castro in 1538 (op . cit., passim & nota C, pp ~ 285-289). 45 given by a Jesuit professor, Francisco da Costa, who taught in the Aula da Esfera of the Colegio de Santo Antao, Lisbon, in the last decade of the sixteenth century. Costa thought that the instrument was of value for use at sea:

'Considerando os instrumentos que os astronomos inventaram, assim para tomar a altura do Sol como para outras observa<;5es, e pondo os olhos s6 naqueles que podem servir no mar, acho que se deve entre todos o primeiro Iugar a armila miutica ... pois se algum se pudera com­ parar com ele era o astrohibio ... ; porem a este leva a vantagem par ter cado grao duas vezes maior em una mesma circumferencia, e em nao ter os embara<;os e deten<;as da dioptra; pelo qual esperamos sera de todos admitido, como ja alguns, assim estrangeiros como naturais o fazem, e poem-no nas costas dos astrolabios desocupados ... ' (138).

This type of 'nautical ring' uses the same principle as, but is different m form from, another type of 'nautical ring', called anel nautico by Luis Albuquerque. Whereas the former has the scale engraved on the flat side of a ring on to which the shadow of a pin (placed normal to the side of the ring) is cast by the sun, the latter has the scale engraved on the broad inner circumference of the ring on to which a spot of sunlight falls through a hole drilled opposite through the ring. The anel nautico was described by Pedro Nunez in his De arte atque ratione navigandi libri duo, Coimbra, 1573, and by John Davis in The Seaman's Secrets ... , London, 1595 ·(fig. 45). The latter explained the instrument thus:

'There hath beene great paines taken by many, for the enlarging of the degrees contained in an Astrolabe, among which there is a proiec­ tion to convey the degrees of a Quadrant into the concavitie of an Astro­ labie, whereby these degrees shall be double, to any other Astrolaby, of the same quantity, so that the Sunbeam, pearcing a hole made in the side of the Astrolabie, is thereby carried to the degrees noted, in the opposite concaue part ... '.

Nunez' ring and his instrumento de sombras were the two instruments which he thought would be of particular service to navigators (139). Fournier,

(138) Lufs DE ALBUQUERQUE, 'Instrumentos abacos e graficos na nautica portuguesa dos seculos XVI e xvn: IV Armila nautica', Vertice. Revista de cultura e arte, vol. XXVII, n. 0 288 (Setembro 1967), pp. 618-624; and HILL & PAGET-TOMLINSON, op. cit., p. 44 . . The scale, constituting the 'nautical ring' is mentioned by WYNNE, op. cit., but not by OuGHT­ RED, op. cit .. (139) See Luis DE ALBUQUERQUE, 'Instrumentos, abacos e graficos na nautica por­ tuguesa dos seculos xvr e xvu: I Anel nautico', Vertice. Revista de cultura e arte, vol. XXVI, n.os 271-272 (Abril-Maio 1966), pp. 282-297. The quotation from Davis is from the sixth impression, London, 1643, sig. F2r. 46 too, spoke well of this instrument, which he called, 'Anneau gradue': 'Cet Anneau est preferable a I' Astrolabe'. In its general design and mode of

. •"' ...... ---- ,.,. .. ~- • iJ' ...,_ I I ---- .•• -, # ,,:• .... # •• ,.,,,, • . ~ .. ,,,,,, _, ,_ _. ~" ~ # ,• I I I .....,.• · , .· , ,.# .,':.'•• ~ ~.. *·, ,' • J 1 t# , -" , , • i : : • .. . . .~, ... ,' .: : •, • I I · o •• • I ' • .· ,•. •• , .I ••

FIG. 45 - A nautical ring (anel ndutico) illustrated in John Davis, The Seaman's Secrets ... , London, 1643, F2v. The principle of this nautical ring is similar to that of the rings shown in figs. 43 and 44, but the scale of 90° is engraved on the inner circumference of the ring, not on the flat side, and light from the Sun falls through a hole pierced in the circumference instead of casting a shadow. (Cf the poke dial shown in fig. 46). This is the type of nau­ tical ring described by Pedro Nunez in his De arte atque ratione navigandi libri duo; Coimbra, 1573. operation, this ring is reminiscent of the simple ring or 'poke' dial of which examples survive from the medieval period to the eighteenth century (140) (fig. 46).

f) The cross-staff(141)

In the sixteenth century, other altitude-measuring instruments for navi­ gation came into use. One of these is the cross-staff (or balestilha), also called

(140) FoURNIER, op. cit., p. 372. On the 'poke' dial ,see PRICE, 'Precision Instru­ ments .. .', pp. 597& 598; HIGGINS, op. cit., p. 348 . (141) See BERNARD R. GOLDSTEIN. 'Preliminary Remarks on Levi Ben Gerson's Contributions to Astronomy', The Israel Academy of Sciences and Humanities, Proceedings, FrG. 46 - A ring or poke dial, signed, 'HIERONIMVS . VVLPARIA FLORENTI­ NUS . FA . ANO . D.M.C.LXVI.AD', and, 'G. V. F.', gilt brass; diam. 163 mm . The inner circumference of the ring is engraved with parallel scales of Italian hours (i. e. equal hours counted from sunset up to 24) for the months of the year. In use, the ring (which can only be used in latitude 43° 13', for which it was designed) is directed towards the Sun, so that sunlight passing through the hole in the circumference (at A) falls on the hour-scale.

Museum of the History of Science, Oxford ..·

Olt.IZONT£

FIG. 47 - A cross-staff use for determining the altitude of the Pole Star, when the Guards (a & fJ Ursae majoris) are in a particular position. The illustration is reproduced from Pedro de Medina, Regimiento de navegacion, Seville, J 563.

National Maritime Museum, Greenwich 47

Jacob's staff (142). The illustration (fig. 47) is from Pedro de Medina's Regimiento de navegaci6n, 1563. The cross-staff was not a new instrument -it was probably invented by the Judaeo-Provenc;al philosopher and. scientist Levi ben Gerson (1288-1344) who described it in his Sefer tekunah, of which the part describing the cross-staff was translated from Hebrew into Latin by Peter of Alexandria in 1342 (143). Regiomontanus and his patron, Bernhard Walther, knew of Levi's treatise and a Jacob's taff (radius astro­ nomicus) was used by Walther for many of his astronomical observations at Nuremberg from 1476 to 1504 (144). It does not appear, however, that the cross-staff was used by seamen before the sixteenth century; the first navi­ gational works to mention it are those of Joao de Lisboa and Andre Pires, both writing before 1520 (145). A distinction needs to be made between

vol. III, n.0 9 (1969), pp. 239-254, esp. 244-246. 253-254; Luis DE ALBUQUERQUE, 'Instru­ mentos, abacos e graficos na mi_utica portuguesa dos seculos xvr e xvn: II Balestilha', Vertice. Revista de cu/tura e arte, vol. XXVI, n. 08 277-278 (Outubro-Novembro 1966), pp. 706-728, and vol. XXVII, n. 08 280-281 (Janeiro-Fevereiro, 1967), pp. 70-90; and WATERS, The Art of Navigation ... , passim, (142) The terminology is complex, and many different names are found (ALBUQUER­ QUE, op. cit., passim.). I do not think it is always possible to distinguish the Jacob's staff (or radius astronomicus) from the cross-staff ( balestilha) as instruments; these terms refer unambi­ guously to an altitude measuring instrument consisting of a bar or rod (staff) with a sliding transversal bar. That the nature of the scales engraved on the main bar changed in the course of time and that seamen used an instrument of this type from which altitudes could be read directly in degrees of arc, cannot be

c

FIG. 48- Baston astronomique de Gemma Frison as illustrated by Georges Fournier, Hydrographie, 2nd ed., Paris, 1667, p. 385 (see n. 142). The narrower arm of the single transversal carries a sliding sight vane which is used, in conjunction with a special division of that arm, for determining altitudes of less than 15° (see Fournier, foe . cit.). FIG. 49 - A cross-staff made by Gualterus Arsenius, who signed the instrument, 'Nepos Gemmae Phrisy Louany fecit an6 1571.', i.e. 'Made by the nephew of Gemma Frisius, at Louvain, year 1571 '; brass. Only the baton survives, and portions of the sections into which it divides are shown in the photographs above; a scale of degrees of arc; scales of Antwerp and Louvain linear measure; a guide mark for the transversal and a scale of unequal parts (non-linear); a scale of equal parts (linear); and the signature.

British Museum, London FIG. 50- A nautical cross-staff of wood, left by Jacob van Heemskirck and Willem Barentszoon in the 'Behouden Huis' at Nova Zembla in 1956 or 1597. Their possessions were rediscovered in 1871 and 1876. Rl}ksmuseum, Amsterdam 49 the form of cross-staff described by Levi ben Gerson and that used by seamen. The former had scale divisions which could not be read directly in degrees of arc, and seamen would have required a table to convert the readings obtained into degrees. The navigational type had a scale which gave readings in degrees, and it is the origin of this form which of particular interest in the history of navigation. The earliest surviving examples of any type of cross­ staff are two made by Gualterus Arsenius, nepos Gemmae Frisii (146) (one of these is shown in fig. 49); presumably, they were not intended for nautical use. The earliest surviving nautical cross-staff is probably the wooden instrument left by Jacob van Heemskirck and Willem Barentszoon

(146) A cross-staff in the Instituto de San Isidro, Madrid, signed by Gualterus Arsenius, 1563, ' ... of wood and brass. The longitudinal piece was in two sections, made of a square brass tube with a wooden core. The wood core projected about four inches from the first section so as to fit into the second tube (hollow for about four inches), thus joining them. The combined length was about four feet, six inches. There were two scales. The single cross piece was of brass, mounted to the staff by a fitting which also formed a double sight. There were also two sliding sight vanes for the cross piece which was marked with a symmetrical scale. The inscriptions read "Locus * status trans­ uero" and "Nepos Gemmae Frisii Louani fecit 1563. G.A." (Private communication, 18 February 1969, from Mr and Mrs Roderick A. Webster, The Adler Planetarium, Chicago). Of the other cross-staff only the baton survives; it is in the British Museum, London, and is illustrated in fig. 49. It is signed 'Nepos Gemmae Phrisy [i.e. Gualterus Arsenius] Louany fecit ano 1571'. No examples of this type of cross-staff were known to VAN 0RTROY, op. cit., pp. 359-360. John Dee (see below & n. 167) returned to England from the Netherlands in 1547 with a radius astronomicus and an annulus astronomicus of the types associated with Gemma Frisius (Dictionary of National Biography, art. 'Dee, John'). Tycho Brahe had a cross-staff made by Gualterus Arsenius and criticised the wooden core: 'We do not altogether reject the use of a radius, specially on journeys, since it is easily transported and may be packed into quite a small box ... I have such an instrument. .. made of carefully joined brass plates, but inside it is wooden ... I had my craftsman construct another radius also entirely of brass, but hollow, without any wood inside. For wood has the property that if it is not subjected to a special treatment it will force the brass plates with which it is covered to bend in the direction in which the wood itself is bending on account of its own instability and the changing influence of the air .. .'. Tycho goes on to criticise the scale division of the Arsenius instrument and the accuracy of the cross-staff as an observational instrument: 'I made equidistant divisions on it, making use of transversal points [see below], according to my custom, in order that it might fulfil the same purpose as a five-figure sine-table, and in every respect give better results than Gemma's radius ... , the latter being provided with a non-uniform division arranged in another way which is, incidentally, erroneous ... Frankly, however, no matter how this radius is constructed it cannot. .. give stellar distances precisely in accordance with reality, not even the smaller distances up to 15 degrees, not to mention, the greater ones where the error is still larger. . .' (RAEDER et a/., op. cit., pp. 96-97). Both Levi ben Gerson (GoLDSTEIN, op. cit., pp. 245-246) and Thomas Harriot (see below, & n. 155) were also aware of optical problems involved in the design and use of the cross-staff. 4 50 m the 'Behouden Huis' at Nova Zembla in 1596 or 1597 (fig. 50) (147). It has been suggested (148) that the navigators' interest in the cross-staff was aroused by acquaintance with the Islamic kama/ (149) (fig. 51), also known as the tavoletas da india, which is mentioned by both Joao de Lisboa and Andre Pires (150) .

...... ~ ...... ~ ...... , --.------______: ...

FIG. 51- A drawing of a kama/ (tabuas da india) reproduced from A. Fontoura da Costa, A Ciencia nautica dos Portugueses na epoca dos Descobrimentos, Lisbon, 1958, p. 45. At the centre of the flat wooden plate, there is attached a string, divided by means of appropriately spaced knots, giving readings in numbers of isba'. In use (the principle of which is similar to that of the cross-staff), the bottom edge of the plate was aligned on the horizon and the top edge on the celestial body the altitude of which was to be ascertained. The knot which, when held between the teeth of the observer, kept taut the string indicated the altitude.

A well-known passage of Joiio de Barros describes Vasco da Gama's first encounter with his pilot, AI:tmad b. Majid. The pilot, unimpressed with Vasco's instruments, refers to the kama/, the use of which Barros compares to the cross-staff:

«E amostrandolhe Vasco da Gama o grande astrolabio de pao que leuaua, & outros de metal com que tomaua a altura do sol, nam se

(147) Rediscovered, with other instruments, in 1871 and 1876. Now in the Rijks­ museum, Amsterdam. (148) E.g. WATERS, 'Science and the Techniques of Navigation', p. 210, n. 13. (149) TmBETS, op. cit., points out that this term is not used in the survivig Islamic treatises. (150) ALBUQUERQUE, 0 Livro de marinharia de Andre Pires ..• , pp. 133 ff. 51

espantou o mouro disso: dizendo que aJguuns pilotos do mar roxo vsauam de jnstrumentos de latam de figura triangular & quadrantes com que tomauam a altura do sol, & principalmente da estrella de que se mais seruiam em a nauega<;am. Mas que elle e os mareantes de Cambaya & de toda a India, pero que a sua nauega<;am era per certas estrellas assy do norte como do sui, & outras notauees que cursauam per meyo do ceo de oriente a ponente: nam tomauam a sua dis tan cia per jnstrumentos semelhau<;es aquelles mas per outro de que se elle seruia, o qual jnstrumento lhe trouxe logo amostrar, que era de tres tauoas. E porque da figura & uso dellas tratamos em a nossa Geografia em o capitulo dos jnstrumentos da navega<;am, baste aquy saber que seruem a elles naquella opera<;am que ora acerca de nos serue o jnstru­ mento aque os mareantes chamam balhestilha, de que tambem no capitulo que dissemos se dara razam delle & dos seus jnuentores» (151).

There is some evidence that English seamen thought that the mariner's astrolabe was most convenient for use when the sun was above 50° or so of altitude but that otherwise they preferred the cross-staff. John Davis said that:

' ... there can be no invention that can establish the certainty of the use of either Quadrant or Astrolabie at the Sea, for unlesse it be in very smoth water, there can be no certainety of any observation by those instruments, whereby the Seaman may rest assured of the altitude which he seeketh, but the observations made by the Cross staffe are without all distrust of errour, and therefore no Instrument may compare with the excellencie of this Crosse staffe for the Seamans use' (152).

f) The backstaff(l53)

There were problems in using the cross-staff efficiently. Thomas Harriot (1560-1621), the English mathematician and friend of Sir Walter Raleigh, showed how to correct the parallax error which arises because the eye is not on the axis of the staff (I 54). Harriot sought to redesign the instrument,

(151) JoA.o DE BARROS, op. cit., 18 decada, livro 4, cap. vi, ff. 46v-47r; quoted i.a., by CosTA BROCHADO, 0 Piloto arabe de Vasco da Gama, Lisbon, 1959, pp. 19-20. On AJ:unad b. Majid, see naBETTS, op. cit., and works there cited; also T. SHUMOVSKli, op. cit., and T. SHUMOVSKli, Fifteenth Century Arabian Marine Encyclopedia (XXV International Congress of Orientalists. Papers presented by the USSR Delegation), Moscow, 1960. (152) DAVIS, op. cit., f. F2v (1643 ed.). (153) WATERS, The Art of Navigation ... , passim; and HILL & PAGET TOMLINSON, op. cit., pp. 10-13; TAYLOR & RICHEY, op. cit., pp. 49-51. (154) TAYLOR & RICHEY, op. cit., p. 40; on Harriot, see A. C. CROMBIE, J. V. PEPPER, D. B. QUINN, J. W. SHIRLEY and R. C. H. TANNER, 'Thomas Harriot (1560-1621): an original practitioner in in the scientific art', T.L.S. ( = Times Literary Supplement), n.0 3530,23 Octo­ ber 1969, pp. 1237-1238, and references there cited; WATERS, The Art of Navigation ... , 52 but it is with the name of John Davis, c. 1595, that the improved version, called a backstaff (or Davis quadrant), is associated (155). The method of

FIG. 52 - A backstaff (or Davis quadrant) in use. The illustration is reproduced from Samuel Sturmy, The Mariner's Magazine .. . , London, 1669, p. 86 .

use, which accounts for the name, is clear from the illustration (fig. 52) (156). The backstaff ultimately inspired the invention of the sextant, by way of Robert Hooke's reflecting instrument of 1666, Isaac Newton's instrument of

passim, esp. appendix n. 0 30. 'Thomas Harriot's Contribution of the Art of Navigation', pp. 5484-591; and the quotation from Hakluyt at the beginning of this article. (155) WATERS, The Art of Navigation ... , pp. 205-206, & 302-306. (156) Earlier, more simple, forms of the backstaff are illustrated in DAVIS, op. cit., sigs. E4V & F1 r (1643 ed .). An early illustration of a Davis backstaff, in its customary form, is to be found in a manuscript of George Waymouth's 'Jewell of Artes', 1604 (British Museum Add. MSS . 19889). See WATERS, Art of Navigation ... , pp. 301 ff. & pl. LXXI. F10. 53- A tidal volvelle on an unusual navigational instrument, probably of Portuguese or Spanish origin, c. J 650 (see n. 0 J 60). The centre is silvered except for an eccentrically placed circular dark area. Above this, attached to the alidade, is a disc with a circular hole. Surrounding the silvered area is a disc engraved with three concentric scales. The· outermost scale is numbered from J to 30. If the alidade is rotated until the proportion of light (silvered) and dark areas visible through the hole correspond to the observed phase of the Moon, its age is given on the scale. The two inner scales give the tidal establishment of an unidentified port. Museum of the History of Science, Oxford FIG. 54- An English sector, not signed, c. 1597, brass with steel points; length of arm 280 mm. The arms are engraved with a scale of proportions; the arc bears scales of use in gunnery. Museum of the History of Science, Oxford 53

1700, and the octants of John Hadley (1682-1744) and of Thomas Godfrey (J 704-1744) of Philadelphia (157).

g) The sector (158)

The increasing accuracy in n'avigation in the sixteenth century and the consequent mathematization of the techniques involved, resulted in the use of a number of ancillary instruments (159). One of these was the sector (160) which was gradually evolved during this century from the proportional compass. It was used in the solution of problems for which later the slide­ rule was used (161), and is based on the principle of equal triangles. The sector is commonly associated with the name of Galileo who called his sector, compasso geometrico e militare, indicating the practical uses to which it might be put, and published a description of it in 1606. The sector illustrated (fig. 54) is earlier than Galileo's, probably about 1597, and carries information for gunner's on the scale. Later, sectors were specially made with scales of value to mariners, e.g. meridional parts for use with the Mercator projection. The back of the sector illustrated (fig. 55) bears an interesting transversal division of the scale, permitting its more accurate reading. Similar trans-

(157) TAYLOR & RICHEY, op. cit., passim. ; and EDMOND GUYOT, Histoire de Ia deter­ mination de l'heure, La Chaux-de-Fonds, 1968, pp. 41-45. (158) See MADDISON, 'Galileo .. .'. (159) Discussion of a number of instrumental aids to the navigator, both of the late medieval period, and of the sixteenth century, has been omitted from this paper - e.g. ordinary mathematical compasses or dividers, the sand-glass, the transverse board, the lead and line, and the instrumental forms (volvelles) of tide tables. For these see generally WATERS, The Art of Navigation ... , passim., and references there given. On fig. 53 is reproduced a detail, showing a tidal volvelle, from an unusual navigational instrument, probably of Portuguese or Spanish origin, c. 1650, now in the Museum of the History of Science, Oxford, n. 0 57-84/269. This instrument combines characteristics of the mariner's astrolabe, with a shadow-square, an unequal hour diagram, a zodiac/calendar scale, and certain star declin­ ations; see MADDISON, Hugo Heft .. . , p. 53 & n. 116, & figs. 9 & 10. On tide tables & vol­ velles, see D. GERNEZ, 'Les indications relatives aux man~es dans les anciens livres de mer', Archives internationales d'histoire des sciences, n. 0 7 (avril 1949), pp. 671-691; and WATERS, op. cit. Also excluded from this survey are the numerous esoteric and little used nautical instruments which were devised during the sixteenth century; see above and cf ROBERT DuDLEY, Dell'Arcano del mare ... libri sei, Florence, 1646. (160) Much confusion has occurred in the translation into English of the name for this instrument in various European languages. What has been called, in English, since at least 1598, a sector (in GERMAN, Kreissektor) is in Italian called a compasso di propor­ zione (and similarly in the other Romance languages). The English phrase proportional compass (and the German, Proportionalzirkel) refers to what in Italian is known as a compasso di riduzione (and similarly in other Romance languages). (161) ANTHONY N. B. GARVAN, 'Slide-rule and Sector: a Study in Science, Techno­ logy and Society', Ithaca. 26 VJJI 1962-2 IX 1962. Actes du dixieme C011gres international d'Histoire des Sciences, Paris, 1964, .vol. I, pp. 397-400 & illus. between pp. 308- & 309 . 54 versals are found on back-staves and other instruments of the period. An Italian nautical MS of 1438 already uses a double line of alternately placed dots ...... in a graphical traverse table with a scale of miles, thereby forshad- owing this type of transversal apparently first used by Richard Chancellor on instruments he designed as Chief Pilot in 1552/3 (162). This is the ancestor of the modern diagonal scale. In 1542, Pedro Nunez had used a system

1

FIG. 55- A portion of a scale of degrees of arc divided with transversals, from the sector shown in fig. 54. The transversals are equivalent to a division of the scale to 10 minutes of arc.

Museum of the History of Science, Oxford of concentric arcs, divided into decreasing numbers of equal parts [90-89- 88 ~ 45], better suited to a scale of arc. The nonius, as this is called, was the precursor of the vernier, described by Pierre Vernier in 1631 (163). The sector illustrated is almost identical to that described in 1598 by Thomas Hood (fl. 1582-1598) who, following a Privy Council recommendation that citizens should be instructed in military matters, was appointed to a mathematical lectureship in London (164). A speech he gave in London on 4 November 1588 well illustrates the growing appreciation, during the Renaissance, of the value of applied science. Commenting on the utility of astronomy (which he considers 'but a parte of the Mathematicall science'), arithmetic and geometry, he concludes:

' ... Then if Geometrie reache so high that it can iustly measure the Cape of heauen: no doubt on earth it performeth most excellent thinges.

(162) WATERS, The Art of Navigation ... , p. 304; TAYLOR and RICHEY, op. cit., p. 77. (163) See MAURICE DAUMAS, Les Instruments scientifiques aux XVII• et XVIII• siec/es, Paris, 1953, pp. 249 ff.; cf. Raederet a/., op. cit., pp.141 ff. forTycho's discussion of transversal. (164) TAYLOR, The Mathematical Practitioners ... , p. 179; Dictionary of National Biography, art. 'Hood, Thomas'. 55

Let Geographie witnesse in vniuersall Mappes, let Topographie witnesse in seuerall Cardes, let Hydrographie witnesse in the Mariners plat, you your selues may witness in Martiall affaires, let the Gunner witnesse in planting his shot, witnesse the Suruerior in measuring land, witnesse all those, that labor in mines, and those that practice conueying of water, whose skill being tolde vs, we would scarcely beleeue, it were it not lying at our doores' (165).

Such sentiments are parallelled in the long and extremely interesting 'Mathematicall Praeface' which John Dee {1527-1608), who took such an interest in navigation~! science, wrote in 1570 to the first English translation of Euclid, by H. Billingsley. Dee surveys all the arts and sciences in which mathematics could be useful. Of navigation he says:

'What need, the Master Pilote, hath of other Artes, here before recited, it is easie to know: as, of Hydrographie, Astronomie, Astrologie, and Horometrie. Presupposing continually, the common Base, and foundation of all: namely Arithmetike and Geometrie. So that, he be able to understand, and judge his own necessary instrumentes, and furniture Necessary: Whether they be perfectly made or no: and also can, (if nede be) make them, hymselfe. As Quadrantes, The Astronomers Ryng, The Astronomers staff, The Astrolabe universal. An Hydro­ graphical Globe. Charts Hydrographicall, true, (not with parallell Meridians). The Common Sea Compas: The Compas of variacion: The Proportionall, and Paradoxall Compasses (of me Invented, for two Moscovy Master Pilotes, at the request of the Company) Clockes with spryng: hourehalfe houre, and three houre Sandglasses: & sundry other Instruments: And also, be hable, on Globe, or Playne to describe the Paradoxall Compasse: and duely to use the same, to maner of purpose, whereto it was invented. And also, be hable to Calculate the Planetes places for all tymes. Moreover, with Sonne Mone or Sterre (or without) be hable to define the Longitude & Latitude of the place, which he is in: So that, the Lon­ gitude & Latitude of the place, from which he say led, be given: or by him, be knowne, whereto, appertayneth expert meanes, to be certified ever, of the Ships way. &c ... Sufficiently, for my present purpose, it doth appeare, by the premisses, how Mathematicall, the Arte of Navi­ gation, is: and how it nedeth and also useth other Mathematical Artes: And now, if I would go about to speake of the manifold Commodities,

(165) A Copie of the Speache: mad by the Mathematicall Lecturer, unto the Worship­ full Companye present. At the houve of the Worshipfull M. Thomas Smith, dwelling in Gracious Street: the 4. of November, 1.5.8.8., London, n.d. (S.T.C. 13694), sig. B. iijr; see FRANCIS JOHNSON, 'Thomas Hood's Inaugural Lecture .. .', Journal of the History of Ideas, vol. 3 (1942). 56

commying to this Land, and others, by Shypps and Navigation, you might thinke, that I catch at occasions, to use many wordes, where no nede is' (166).

CONCLUSION

The navigators of the 16th century had indeed benefited from the astro­ nomical and mathematical sciences, as is shown by the array of 16th-century instruments illustrated on the title-page of the 1584 Leyden edition of Lucas Janszoon Waghenaer's Spieghel der Zeevaerdt (fig. 56). There was more to come. Already in sixteenth century England, the reflecting telescope had its first tentative beginnings at the hands of Leonard Digges (d. 1571), and the refracting telescope was to be invented in Holland about 1604 (167). Developed and popularised by Qalileo, this instrument was not only to revolutionize astronomy but, added to navigational and other practical instruments, was to provide the means of a much more precise astronomical navigation. But the flow of benefits was two-way. If the navigators learnt from the astro­ llOmers and mathematicians, so were these to profit. In meeting the demand for instruments, from the navigators, the military surveyors and gunners, the land and mine surveyors, and other trades and professions, the whole economic and social organisation of the instrument-trade was to change. From the medieval astronomer/craftsman, the sixteenth century sees the move towards workshops, the sole function of which was to make and sell instru­ ments (e.g. the Arsenius family in Louvain). In the next century, this process was intensified so that there emerged specialist suppliers of particular classes of instrument, who might sometimes sub-contract their manufacture. The clock-makers were under increasing pressure from the navigators to solve the longitude problem, but were also under social pressures for, as Cipolla has pointed out (168), as more and more people obtained clocks and watches, so it became necessary fur other people to possess them; the machine created the conditions for its own proliferation. The craftsmen who made instru­ ments and the clockmakers who met the need for even more precise workman­ ship by creating new tools, such as the dividing engine in the seventeenth and

(166) H. Billingsley (trans!. & ed.), The Elements of Geometrie of the most auncient Philosopher Euclide of Megara ... , London, 1570, sigs. diiijV-Aj'. On Dee, see CHARLOTTE FELL SMITH, John Dee, London, 1909; and I. R. F . Calder, 'John Dee studied as an English Neoplatonist', 2 vols., unpublished Ph. D. thesis, London University, December, 1952. (167) For discussion and references, see MADDISON, Galileo ... ; also MARJORIE NICOLSON, Science and Imagination, Ithaca (N.Y.), 1956, repr. 1962, esp. ch. I & IV, which give a large number of useful references, and G. L'E. TURNER, 'The History of Optical Instruments. A Brief Survey of Sources and Modern Studies', History of Science, vol. 8 (1969) (forthcoming). (168) CIPOLLA, op. cit., ch. I, passim. 57

FIG. 56- The title-page of Lucas Janszoon Waghenaer, Spieghel der Zeevaerdt ... , Leyden, 1584. The navigational instruments depicted include a mariner's astrolabe, a nautical quadrant (i.e. engraved only with a scale of degrees of arc), lead and line, a magnetic compass, a cross-staff, 'one-handed' dividers (compasses), and a sand-glass. Between the celestial and the terrestrial globes (at the top), several mariners are looking in a mirror (Spieghel). 58 eighteenth centuries (169), thereby establishing a preciSion tool tradition that was adequate to match that of scientific endeavour. Among the instruments inextricably linked to the development of modern science and technology and its economic and social consequences, the mariner's astrolabe has an important place. In it, scientific theory and craft technology are indeed combined in response to practical needs, and ' ... em este reyno de Portugal se achou o primeiro vso delle em a nauegar;am' (170).

(169) See MAURICE DAUMAS, 'Precision Mechanics', A History of Technology, (ed. by Charles Singer, E. J. Holmyard, A. R. Hall and Trevor I. Williams), vol. IV, Oxford, 1958, pp. 379-416. The fascination with machines that is evident during the Renaissance, and which often led to the design rather than the construction of many ingenious devices, has only been touched upon here in regard to the mechanical clock, an eminently practical device which, as the marine chronometer, eventually became an important navigational instrument. Nevertheless, the subject is of importance for the general context of craft practice in which effective navigation developed. See, for example, WmTE, op. cit., ch. III; BERTRAND GILLE, Les lngenieurs de Ia Renaissance, Paris, 1964; A. G. KELLER, A Theatre of Machines, Lon­ don, 1964 (for Jacques Besson, Agostini Ramelli, & Vittorio Zonca); and FAUSTO VERANZIO, Machinae novae (ed., with introd., by Umberto Forti) (Classici italiani del pensiero scienti­ fico, vol. I), Milan, 1968. Finally, it shoud be remarked that no development of astrono­ mical navigation would have been possible, in spite of the design of new instruments, or of the invention of printing with the consequent dissemination of textbooks of navigation, without a concurrent increase in the literacy of the navigators. See CARLO M. CIPOLLA, Literacy and Development in the West, Harmondsworth, 1969. (Cipolla, pp. 22-23, give some details of illiteracy in the Venetian navy from the 15th to the 17th centuries); see also R. A. SKELTON, The Seaman and the Printer, in this publication. (170) BARROS, op. cit., f. 41 V.

Acknowledgments. As well as my indebtedness to the authors whose works I have cited above, I wish, to acknowledge the help I have received in the preparation of this article from: Professor Luis Mendon~;a de Albuquerque, Coimbra; Mrs. D. P. Allen, Oxford; Senor R. Barreiro-Meir6, Madrid; Monsieur Guy Beaujouan, Paris; Dr & Mrs J.D. Bergsagel Manchester; the late P. G. Coole, London; Dr. Zdenek Horsky, Prague; Dr. H. P. Lattin, Tiburon; Dr. Carlo Maccagni, Pisa; Dr. J.D. North, Oxford; Monsieur Emmanuel Poulle, Paris; Mr. A. Turner, London; Mr. G. L'E. Turner, Oxford; Cdr D . W. Waters, R. N., Greenwich; Mr. & Mrs. R. L. Webster, Winnetka; and my wife. I also wish to thank the following for permission to reproduce illustrations: the Visitors of the Ashmolean Museum (fig. 31); the Directeur, Bibliotheque royale, Brus- . sels (fig. 1); the Trutees of the British Museum, London (fig. 49); the Direttrice, lstituto e Museo di Storia della Scienza, Florence (fig. 26); the Regents of the Smithsonian Institution, Washington, D. C. (fig. 17); the Trutees of the National Maritime Museum, Greenwich (figs. 20, 27, 47, & 52); Mrs G. Newton, Derby (fig. 15); the Director, Rijksmuseum, Amster­ dam (fig. 50); the President and Council of the Royal Society of London (fig. 13); the Curator, Whipple Science Museum, Cambridge (figs. 35 & 36). 59

DISCUSSAO

A. TEIXEIRA DA MoTA. - Em relar;iio com este tao interessante trabalho do Dr. Mad­ dison, afigura-se significativo que ei-Rei D. Joiio II- a quem tanto deve o progresso da nautica- tenha escolhido para emblema do duque de Viseu, futuro D. Manuel I, pre­ cisamente a esfera armilar, que viria a tornar-se urn simbolo nacional, figurando ainda hoje na bandeira de Portugal. Aponta-se tambem que a pratica portuguesa no dominio da construr;iio de instrumentos nauticos no seculo xv1 parece ter raiz ou afinidade maiorquina, ja que frequentemente os mestres de cartas de marear eram tambem construtores de agulhas de marear e outros instrumentos nauticos, e a sua actividade exercia-se sobretudo dentro das atribuir;oes conferidas aos Armazens da Guine. Finalmente, anota-se que a mais antiga descrir;iio de urna agulha de marear;iio e a que vern no «Tratado da Agulha de Marear>> de Joiio de Lisboa (1514).

DAvm WATERS.- In these scientific inventions, I have learnt over the years to search always for the man who first puts an idea into a practical, useful form. Thus, for instance, we know that Abraham Zacuto made sea-astrolabes for Vasco da Gama's voyage, and that these instruments were made specially for it. Here, probably is the inventor of the first sea-astrolabe; similarly we know the name of the first inventor of an instrument for measur­ ing variation: Joiio de Lisboa. It was an invention of fundamental importance to the advan­ cement of navigation and nautical science. The simple nocturnal illustrated by Robert Norman was earlier illustrated in a Dutch leeskaart now in Harvard University Library, of an edition of the 1560's but probably first published on 1544 by Anthony Anthoniszoon. The Portuguese compass of 1711 which he illustrated is an amplitude compass, for finding the variation by observing the sun's bearing at sunrise or sunset and comparing it with amplitude tables. Such tables were first published by the Piloto-Mayor of the Casa de Contratacion, himself a Portuguese early in the 17th century. The seaman of the 16th century (certainly the English ones) always distinguished between the astronomical Jacob's Staff, which was graduated in tangential parts which had to be converted by means of a table into degrees and minutes and the balestrella or cross­ staff for use at sea and which was described by Martin Cortes in his Breve Compendia de Ia Esphera, of 1551. Reverting to the question of astrolabes and quadrants, the inventory of Magellan's Expedition of 1519 records the provision of: «6 quadrantes de madeira feitos por Rui Faleiro»; «l'astrolabio de madeira feito pelo referido Faleiro»; «Pago ao dito.Magalhiies por 6 astrolabios metalicos com as respectivas reguas»; <

R. A. SKELTON.-I was interested in Dr. Maddison's account of the commercial development of instrument-making in the xv1th century. The location of industries was doubtless governed by social factors (as suggested by Dr. Hooykaas) and by economic factors such as the availability of raw material (metals, silica, etc.). It is known that about 1500 Nurnberg sundials were exported to Lisbon regularly and in bulk. The distribution of instruments from such local centres presumably throws some light on their typological development and cross-breeding in design and construction. I wonder whether this line of research has been pursued by historians of technology. The commercial character of the industry in Mercator's time is illustrated by his complaint that he had been diverted from «philosophy» by the need to earn his living as an instrument-maker. 60

A. CoRTESAO.- I sincerely regret that the short time at our disposal does not allow for a full discussion of this most important paper. The hour is late, 11nd I just want to express to Dr Maddison - and I am sure I interpret the opinion of all present - our deep gratitude and admiration for his scholarly work, which is undoubtedly one of the most remarkable brought to this meeting. Unfortunably Dr Maddison could do no more than give us a very brief resume of his paper, but I am sure that all who have read or will read it in full will entirely agree with what I have said. Thanks you Dr Maddison and you all .

..

I

.• I \ I I ,rI

f

•

Ult ItO. ~- ·---- -~

I~ ••••!"''"'"'. "' "'"'"'"' u ~:~ ·~-

KNOWN SEA-ASTROLABES

1 Palermo 1540 ~~]. ' _ Z Dundee 15!'15 3 Krabbe 158Z 4 Greenwich c. 1588 5 Kron borg lSOO 6 Oxford (Vera Cruz) c. 1600 7 Barlow (Manila) 1602 8 Hoffman (Champlain's) 1603 9 Florence 1608 10 Tenri Un i vers~le 1609 11 St. Andrew ~ r 161S 12 Skokloster I 1626 13 Skokloster 11 c. 1626 1~ Skokloster m c. 1626 15 BATAVIA I ante 1629 . 1S BATAVIA TI ante 1629 . . . . .:~· ~ 17 Caudebec 1632 . ~11· ~·~

18 Coimbra University c.1675 • ' • • • a r-.__;1.-.r''---'~. 19 Felix ea,riY 18th c. a-1, ...... -.. ._._~~...... '"'"'-' \ \ Fig. 6-The surviving sea- or mariner's astrolabes known, • I ·

.. lilt Mat

______.. ---- ' ~ •• t62t

._ -._- . -

11675

------.--- .... -...... ~

• • .... , .!' ...... ,...... w. • ~;:::;E=:==:==:==S=:==:==:==:_IP>' B.Acim,...... ". ....t965 · o 16 was destroyed by bombing in 1940).