Denis Savoie

Three examples of ancient "universal" portable sundials

The standard catalogue is now that of J. Bonnin, La mesure du temps dans l'Antiquité, Les Belles Lettres, Paris, 2015, accompanied by an online database at https://syrte.obspm.fr/spip/actualites/article/en-ligne

Introduction

Ancient portable sundials (see Table 1) represent only 5% to 6% of the corpus of all ancient sundials, 1 which is at present estimated to be between 500 and 600 dials. Nevertheless they must have been in rather frequent use if one is to believe Vitruvius when he writes in his De Architectura (between 35 and 25 BC): 2 "Again, following these types, many authors have left notices for the construction of travelers' sundials or portable sundials. If one wishes, one can find various kinds of projections in their works, so long as one is familiar with the drawings of the analemma." Unfortunately, none of these notices has reached us. For the gnomonists of antiquity, these horologia viatoria lent themselves particularly to the development of original models, and to the pursuit of dials intended to be usable at practically all latitudes.

One can divide ancient portable sundials into two categories:

-those that are only usable for a given latitude. This is the case with the "Portici Ham," 3 the dials found at Mainz and Ponteilla, 4 the medallion dials, 5 and generally the cylinder dials. 6 -those that are usable at multiple latitudes or at all latitudes. These include the Berteaucourt and Merida disks, dials of the "Crêt Chatelard" type, and lastly the most perfect of all, the armillary dial. 7 5 For the medallion dial in the Musei Civici di Trieste see now R. J. A. Talbert, "A lost sundial found, and the role of the hour in Roman daily life," Indo-European Linguistics and Classical Philology 23 (2), 2019, 971-988.

6

M. Arnaldi, K. Schaldach, "A roman cylinder dial : witness to a forgotten tradition," Journal for the History of Astronomy, 28, 1997, p. 107-117. 7 G. Gounaris, "Anneau astronomique solaire portative antique découvert à Philippes," Annali dell'Istituto e Museo di Storia della Scienza di Firenze, 5 (2), 1980, p. 3-18. This exceptional dial deserves a more extensive study. Three examples of ancient "universal" portable sundials However, there exists an exemplar of a medallion dial that belongs simultaneously to the categories of fixed-latitude dials and multiple-latitude dials, as we will see below.

Certain ancient dials experienced a new glory during the Middle Ages and Renaissance, in particular the altitude cylinders, which in 19th century France were called "cadrans de berger." Conversely, other portable dials vanished, and it is a matter of some interest to understand why.

Medallion dials.

The term "mediallion dial" designates small altitude sundials 4-5 cm diameter, usable for a specific latitude, and resembling small pillboxes. The rim is raised, and on the principal face is a relief portrait, generally of an emperor. An eyehole or lateral orifice, situated in the raised rim, allows the Sun's rays to enter and fall upon a small mobile ruler in the shaded interior of the box. The apparatus is used in a vertical position oriented towards the Sun. At the base of the box is a grid in the form of an angular sector, made up of hour curves and date lines. One reads the seasonal hour at the intersection of the date line-on which is the ruler-and the hour curve. There are many variants of this altitude dial: for example in the Forbach dial each face bears the same dial and each ruler is at the center of the dial. In the Rome exemplar, the ruler is off-center, and the rear face of the medallion is decorated with a portrait of the emperor Commodus.

But it is the Vienna exemplar that is most remarkable (Fig. 1). 8 Not only is one face decorated with a portrait of the emperor Antoninus Pius (138-160) with the inscription ANTONINVS AVG PIVS TR P COS III IMP II (Fig. 2), but the first "box" component is like the mater of an astrolabe, having disks installed in it that are adapted to different latitudes. The base of this first box bears a-rather crude-tracing that unquestionably resembles the hour curves of a stereographic project (Fig. 3). These curves of course have no function in the dial; this is a "learned" ornamentation whose motivation is unknown. The other part of the box is equipped with a little stud for keeping in place the disks that are furnished with a grid applicable to several latitudes. Thus there are disks for the latitudes of Rome, Alexandria, Spain, Greece, etc. The hour grids of the disks are overall rather poor. The seasonal hour curves are represented by sometimes chaotic line segments; as for the point of convergence of the date lines, it often falls to the side of the hole for the mounting. On some of the disks (for example that for Alexandria, Fig. 4), one can still read below the date lines the names of the Roman months. This portable sundial is thus a very clever system in which the traveler places a grid-disk appropriate for the locality where he is in a kind of mater, rather as if one was traveling with an astrolabe equipped with multiple plates. There is a striking parallelism between these two instruments, where the astrolabe was the subject of efforts to develop a universal version that became workable in the 11th century with the saphea of Azarquiel. 9 Let us study this dial from a modern viewpoint (Fig. 5). The most general case consists of a stud for fixing the disks and the ruler off-center. Let R be the radius of the box, whose center is O, and let C be the point of convergence of the date lines, and P the orifice through which the 8

This dial has been studied by E. Buchner, "Römische Medaillons als Sonnenuhren," Chiron, vol. 6, 1976, p. 329-348. The first mention and drawing of this dial appeared in F. Kenner, "Römische Medaillons," Jahrbuch der Kunsthistorischen Sammlungen der Allerhöchsten Kaiserhauses, vol. 1, Vienna, 1883, p. 84-85 ; one can clearly see in the drawing of F. Kenner that the dial bore a ruler as well as a pin, which have both vanished today. See also A. Schlieben, "Römische Reiseuhren," Annalen des Vereins für Nassauische Alterthumskunde und Geschichtsforschung, n ° 23, 1891, 115-128 and plate VI.

9

The principle was revived by Gemma Frisius in his astrolabe catholique. See R. D'Hollander, L'Astrolabe, Histoire, Théorie, Pratique, Institut Océanographique, Paris, 1999, p. 235-262. Savoie Figure 1. This "box" sundial preserved at the Kunsthistorisches Museum, Vienna, came from Aquileia. Dating from the 2nd century of our era, it consists of two halves of a small bronze cylindrical box (top) containing four perforated disks (bottom). On the upper half of the box one clearly sees the small metal cylinder that enables a disk to be installed, as well as the notched hole on the side that allows the Sun's rays to pass through. The four disks bear on their recto and verso the horary drawing for the latitudes of the following cities: Alexandria Aegyptus / Africa Mauretania / Hellade Asia / Hispania Achaiia / Roma ? / Ancona Tuscia / Britannia Germania.

Savoie

Sun's rays enter. Let a system of axes pass through P, such that x tends rightward and y upward. We have:

(1) where a designates the angle of aperture of the horary fan (a = 90° signifies that C coincides with O). One must fix the radius of the horary fan taking into account the eccentricity of C with a view to filling up the greatest possible surface in the box. Let E, Q, and W be the positions of the Sun at solar noon (seasonal hour 6) respectively on the summer solstice, the equinoxes, and the winter solstice. Hence we have

(2) This is also the radius of the mobile ruler revolving around C.

First of all, one aligns the ruler with the desired date. At a given moment, with the dial oriented in the plane of the Sun, a solar ray enters by the orifice P and strikes the ruler at I. The seasonal hour is read at the intersection of the date line and the hour curve. Let us seek the coordinates x and y of this intersection point.

Let h' be the noon altitude of the Sun:

(3

)
where f is the latitude of the locality and d the declination of the Sun. The altitude h of the Sun for a given hour angle H is: Three examples of ancient "universal" portable sundials 51 (4) H 0 is the semidiurnal arc, which one obtains thus:

(5)

The seasonal hour k indicated by the dial (such that 0 h corresponds to sunrise, 6 h to solar noon, and 12 h to sunset) is obtained thus: The geometrical construction is very simple. Once the radius r of the angular sector is defined, one obtains the intersection points of the hours on a date line while varying the solar altitude. Thus assumes that the maker has at his disposal a table giving the solar altitude as a function of the seasonal hour and the date. In fact, one can replace the orifice in the raised rim by a horizontal gnomon; the infinite shadow of the gnomon intersects the grid where one reads the hour according to the date (Fig. 6).

The grid that one obtains is quite harmonious. The hour curves are not excessively squeezed together as is the case if one draws the dial by true solar time. 10 It goes without saying that in the case of the Vienna dial, the tininess of the dials (to say nothing of their very crude execution), combined with the fact that one has to balance them vertically (which perhaps implies that there existed a suspension thread) renders them pure objects of prestige rather than real dials to indicate the time.

10 Such dials using equinoctial hours are apparently are unknown. The two bronze disks found in the archeological excavations in 1985 at Berteaucourt-les-Dames in Picardie (France) 11 and in 1994 at Merida (Spain) 12 date respectively from the ends of the 2nd and of the 3rd centuries of our era. The archeologists at the time, contemplating their purpose, classified them as portable sundials of a new variety, without pursuing the question further. A recent study, 13 however, has made it possible to determine their functions more precisely and to bring new clarity to these little known objects.

As one can see in Fig. 7, which represents the dial of Berteaucourt-les-Dames, the object consists of a disk of about 10 cm in diameter perforated at the center by a hole (the Merida dial has diameter 13 cm). One can divide the principal face (Fig. 8) in two parts:

-the "geographical" part, with 23 names of provinces or cities sorted according to increasing latitude from Alexandriae (latitude 30°) to Britanniae (latitude 55°). 14 -the strictly gnomonic part, which is a grid composed of four concentric curves, ascending from latitude 30° to 60° from outside to inside in steps of 10°. Seven other curves cross the latitude circles and bear labels for the twelve months of the Roman calendar, the two extreme curves being those for the solstices 15 with labels VIII K. IAN (VIII before the Kalends of January = winter solstice = December 25), et VIII K. IUL (VIII before the Kalends of July = summer solstice = June 24). The other dates doubtless correspond to the Sun's entries into the zodiacal signs. 16 On the object's rear face is a straight line, whose significance we will see presently, which extends from the central hole to the periphery. A horizontal gnomon several centimeters long must have been lodged in this hole; it must have been long enough to cast a shadow on the disk and its diameter small enough to allow a sensitive reading.

There is no horary graduation on the grid, and this allows us to conclude that the purpose of this instrument was not to show the hour throughout the day (though it could indicate noon). What the grid does clearly show is the existence of a relation between the locality's latitude and the date; hence one deduces that this instrument could have two functions, possibly at the same time:

-to indicate the solar noon for the locality -to indicate the latitude where one is Let us recall that in altitude sundials, the principle is to determine the solar time as a function of the Sun's altitude above the horizon, and that this requires knowledge of two constants: the latitude of the locality and the date. This results from the fact that this kind of dial is a practical and technical application of a formula of spherical trigonometry known in antiquity that relates the time H to the Sun's altitude h:

(21)
where d is the Sun's declination (effectively the date) and f is the latitude. This formula shows very clearly that the Sun's altitude depends on three components: the place, the date, and the time. Hence an altitude sundial intended to work throughout the Roman Empire, say over a range of 30° of latitude (about 3300 km) like the disks of Berteaucourt-les-Dames and Merida, would need either a network of curves so dense as to become illegible, or a mechanism to make it easy to use, such as for example the armillary.

But in the present case, since there is no question of showing the time throughout the day but only solar noon, one can take advantage of a simplification of formula ( 21), observing that at where l is the Sun's ecliptic longitude, which is made to range from 0° to 360° in steps of 30°, so that one obtains the declination of the Sun at its entry into each zodiacal sign.

The grid under investigation here is a clever application of formula ( 23), in which one makes the Sun's declination vary as the "abscissa" and the latitude as the "ordinate." The read-off, whether of noon, or of latitude, takes place at the intersection of the shadow of a horizontal gnomon and a declination arc, while the instrument is suspended vertically and aligned with the plane of the Sun. This is corroborated by the straight line on the back of the instrument, which is perfectly aligned with respect to the grid, and which serves to orient the disk to the zenith, doubtless with the help of a suspension thread (Fig. 9). The graduated face is the one that is directed to the east.

The calculation of such an instrument is quite simple. One sets, starting from the hole, radius R max , which corresponds to the minimum latitude (here 30°) and radius R min , which corresponds to the maximum latitude (here 60°). Radius R for an intermediate latitude is thus obtained by a simple rule of three: If one treats the latitude as variable for a given solar declination, one gets a declination arc. If one treats the declination as variable for a given latitude, one gets a latitude circle. The declination should range from -e to +e where e is the obliquity of the ecliptic; in antiquity one generally uses e = 24°. In any case one can verify on the Berteaucourt-les-Dames disk that the angle at the vertex (Fig. 10) is indeed equal to 2 e, which corresponds to the difference in solar altitude between the winter and summer solstice at latitude 60°; the same angle is found again for the circle for latitude 30°.

In practice, such a grid does not require recourse to trigonometrical calculation; pure geometry allows one to draw it. One starts by establishing, with the help of the elementary formula (2), the values of the Sun's noon altitude for different latitudes. After drawing two concentric circles with a compass (Fig. 11), one uses a protractor centered on the center P of the circles, which is also where the gnomon will be, to trace the Sun's altitude in winter for the maximum latitude (point E) and then the altitude in summer for this same latitude (E'). One carries out the same operation for the outermost latitude circle, obtaining points A and A'. To obtain the date curves between the extremal circles, one must of course generate the altitude points for the intermediate latitudes and then join up the points by a curve.

Let us say at once that one should not look for precision instruments in these two disks: their dimensions are in the first place too slight and in the second place one should regard them more as objects of curiosity or prestige, or maybe astronomical amusement, even if they are Consider first of all the case of a traveler who wants to use this indicator to determine solar noon, thus as a portable meridian. He absolutely has to know the date and the place where he is. Let us imagine that the date is the 8th day before the Kalends of July, that is, the summer solstice, and that the traveler as at Rome at a latitude of 42° as the disk indicates (Fig. 12). After a preliminary identification of the latitude circle for 42°, the traveler has to estimate grosso modo the moment when the gnomon's shadow cuts the latitude circle and the declination curve. One can imagine that to find such a circle a thread was provided, attached to the disk's center and furnished with a sliding bead.

It is appropriate here to note that the Sun's altitude around its culmination has little variation, especially around the solstices, so that one could easily be wrong by ±15 minutes or more, and that is without taking account of the fact that the shadow of a horizontal gnomon has a certain width. In any event it is an inconvenience that one has to underline and that affects all altitude sundials: their accuracy is mediocre at noon. Now let us put ourselves in the hypothetical situation of a traveler who uses the disk to have an idea of the region where he is. Again he knows the date, but he also has to find a means of determining solar noon, for example by means of a gnomon, waiting for its shadow to be shortest (Fig. 13). Let us go back to the preceding example of a Roman traveler; at solar noon he has to find the intersection of the shadow with the date curve so that he can then read off the latitude. Here again, one can imagine that a thread furnished with a bead allows one better to estimate the place, or rather the region. But one should add right away that the instrument does not yield the longitude of the region or place. Hence one has to have already an idea of the place where one is, without which one might, for example, establish a latitude of 42° without knowing whether one is in Spain or in Italy! An attempt at a universal portable dial.

Among all the ancient portable sundials, the most numerous at present are the eleven Greek and Roman exemplars, constructed between the 1st and the end of the 6th century, of a very particular type that has tripped up many authors with regard to its functioning and hence to its theory, a bit like the case of another portable dial, in this case medieval, the Navicula de Venetiis.17 These two sundials additionally have points in common, such as that of being usable at practically all latitudes and that of not being rigorously exact except on certain dates while being theoretically very accurate throughout the year. One of these dials, lost today, was discovered in France in the 19th century, at a place called Crêt-Chatelard (département de la Loire). 18 The first to understand the working of these sundials, which had been known since the 18th century and which exhibit great variations among themselves, was the German gnomonist J. Savoie Figure 14. Roman exemplar found near Bratislava, dating from the 3rd century. The instrument is complete. Clearly visible are the mobile and curved read-off scale with its hour strokes, at the end of which is the gnomon. At the extremities of the date scale are the inscriptions VIII K. IAN and VIII K. IVL, which correspond to December 25 and June 24, the dates considered to be the winter and summer solstices in the Julian calendar.

Figure 15. Byzantine exemplar dating from the 5th-6th century, diameter 110 mm. On the gnomonic face can be seen the cursor, which enables the dial to be set according to the latitude, and the pendant ring for keeping the instrument vertical in a chosen direction. On the angular sectors appear abbreviations in Greek letters of the Latin names of the months for each half year, January to June on the upper part, July to December on the lower. The readoff scale is lost. On the back are the latitudes of 36 cities and provinces. [credit: Trustees of the British Museum].

Savoie

Let us describe with greater precision the "gnomonic" face of this dial, which, let us specify at the outset, is always used in a vertical position (Fig. 16). Its layout is in the first instance an instantiation of the celestial equator; this makes an angle with the zenith equal to the latitude of the locality. This explains why a sliding rail assemblage makes it possible to calibrate the dial in accordance with the latitude f. On each side of the equator, one traces the Sun's position right to the solstices. That is, the angle between the equator and the positions specified by the calendar corresponds to the declination d of the Sun, whose absolute value is equal to the obliquity at the two solstices.

In antiquity one uses e = 24° (cf. infra); one gets the Sun's declination as a function of the date, which is represented by the ecliptic longitude l, varying by steps of 30°:

(28)

The dial can be reduced initially (Fig. 17) to an equinoctial straight line drawn on a vertical plane exactly oriented towards the east, being mobile around its gnomon, and having the points for the hours drawn on it at intervals of 15° (tangent law: the distance of an hour point to the foot of a gnomon of length a is obtained as (a/tan H), where H is the Sun's hour angle). This equinoctial line likewise makes an angle y with the vertical passing through the gnomon which is precisely equal, on the equinoxes, to the locality's latitude. As it is drawn for the moment, the dial resembles an oriental vertical sundial with gnomonic declination 21 D = -90°, functioning only on the equinoxes.

Let us remark at once that to draw such a dial, an ancient gnomonist in possession of Ptolemy's Treatise on the Analemma 22 would have noted that the horary angle H of the Sun is the 21 The gnomonic declination D is the azimuth of the line perpendicular to the plane.

22 The edition of Heiberg de 1907 is the revised edition of the Latin text and the Greek fragments that he had already published in 1895 : Claudii Ptolemaei Opera quae exstant omnia, Vol. II, Opera Astronomica Minora, ed. J. L. Heiberg, Leipzig, Teubner, 1907, p. 187-223 et Praefatio, p. XI-XII. This edition is the standard at present. One can find Figure 17. The portable dial is here reduced to a vertical plane oriented due east and furnished with a horizontal gnomon casting a shadow on a graduated equinoctial scale.

Three examples of ancient "universal" portable sundials 63 complementary angle of the hectemoros, which last is the angle between the direction to the Sun and the cardinal east (or west) point. This hectemoros is independent of the latitude, since it is calculated as:

(29) It is interesting to make a tabular comparison of the equinoctial horary angle H, the Sun's seasonal hour angle H' (as in all ancient sundials, this portable dial shows the seasonal hour), and the complement of the hectemoros, since one observes a certain similarity, in fact a strict equivalence that-perhaps-was the origin of this portable sundial's mode of operation. On the equinoxes, the equivalence is perfect (Table 2).

Let us recall that H' is obtained thus:

(30)

Where H 0 is the semidiurnal arc obtained as:

(31)

The seasonal hour 23 k indicated by the dial (with 0 h corresponding to sunrise, 12 h to sunset) is:

H H'

90° -hecte -90° -90° -90°- 75° -75° -75°- 60° -60° -60°- 45° -45° -45°- 30° -30° -30°- 15° -15° -15° 0° 0° 0°T
able 2. Comparison of equinoctial and seasonal horary angles with the complement of the hectemoros for equinoxes.

Savoie

On the equinoxes, at our latitudes, the dial at sunrise has its gnomon pointing exactly eastward; then the shadow shifts progressively during the morning along the equinoctial line until noon, when the Sun, now in the direction of geographic south, produces an infinite gnomon shadow. Throughout the morning, the plane of the sundial has stayed perfectly fixed, with the gnomon always having a gnomonic declination of 90°. But for the dial to continue to work in the afternoon, one has to pivot its vertical plane around an axis passing through the zenith. Otherwise put, the gnomon will now point towards the south-east horizon, then the south-west horizon, finally pointing exactly westward at the moment of sunset. The plane of the dial will thus have turned 180°.

One could imagine a turning about of the dial, such that the east face becomes, after solar noon, the west face. But this operation would call for a rotation equal to 2y of the scale and the gnomon and hence a new calibration according to the date and latitude. Now none of the dials known at present bears a double graduation in latitude and in the scale of dates that would make this kind of setting possible. Moreover the user does not know a priori which part of the daymorning or afternoon-he is in.

It is well to emphasize here that right from the moment that one makes the plane of the dial pivot, thus changing its gnomonic declination, the angle between the direction to the Sun and the direction in which the gnomon points is no longer the hectemoros but another angle that we will call z: this is the angle that one reads on the dial. This angle z can be shown to be calculated thus (Fig. 18 and19): (34) where h is the Sun's altitude. Since we are at the equinoxes, one has: To sum up, on the equinoxes the operation of the dial can be divided into two phases: in the morning it is a dial with fixed horary angle is if it was a classical sundial drawn on a wall facing due east. After the Sun crosses the meridian, the user "forces" the dial by turning it in such a way that the gnomon's shadow lines up with the equinoctial line.

The relation established previously between the equinoctial hour and the hectemoros is only one hypothesis among others for explaining the principle of this portable dial; one could also Figure 19. Representation in the celestial sphere of the dial in use in the morning on the equinoxes. The Sun S, situated on the celestial equator, illuminates the portable dial, which remains immobile. On the dial, the shadow falls upon the graduation for seasonal hour 4. imagine a purely empirical approach. For that matter, we will see that a recognition in antiquity of the intrinsic error in the principle of this dial is not very probable.

H H'

If we resume the analogy between the angles but for an arbitrary date, for example for the summer solstice, for a latitude of 40° and a solar declination of +24°, we see that there is no longer an equivalence among the three aforesaid angles. One gets the following quantities for the morning, keeping in mind that cos hecte = sin H cos d (Table 3).

Additionally, the gnomon's shadow no longer falls on the equinoctial line, but below it. The inventor who conceived of this dial imagined that one should modify the inclination of the equinoctial line, and that this inclination, for a given day, was equal to the noon altitude of the Sun, namely 90° -f + d. This implies that angle y which the equinoctial line makes with the vertical passing through the gnomon equals (f -d). The purpose of this constraint is to indicate on the dial, to the extent that this is possible, the seasonal horary angle H'. Now we have seen that the dial measures the angle z, and in the general case where the Sun's declination is not zero, it can be shown (Fig. 20 or, expressed in terms of the primary parameters:

(37)

such that z has the same sign as H.

The whole principle of this dial thus rests on the relationship between z and H', using as its starting hypothesis the assumption that the deviation between these two angles (expressed on hours) would be acceptable in civil use (cf. infra). Let us observe that the principle of its operation is not transferable to a sundial that is supposed to show the equinoctial hour (Fig. 21). In other words, this dial is only useful in a society in which the civil practice is seasonal hours. This could explain why it fell into desuetude, unlike the other kinds of portable sundials which can indicate the seasonal or the equinoctial hour indifferently, such as the cylinder or the armillary, which continued to be used right through the Middle Ages and the Renaissance, and even beyond in the case of the cylinder. This fundamental point seems not to have been noticed: while the majority of ancient sundial types could have survived through the centuries despite the change in usage of hours, the portable dial studied here experienced an abrupt halt because it could not be adapted to equal hours. 24 24 An example of a truly universal portable dial is that of Regiomontanus. Resuming the preceding table (for the summer solstice), we can see that the deviation between H' and z is minimized by the solution tabulated in Table 4. The greatest deviation here between H' and z (for latitude 40°) reaches a little more than 9 minutes of a seasonal hour (Fig. 22).

One should underline the great subtlety of this portable sundial, which achieves the feat of showing, with a very acceptable error, the seasonal hour, measuring it on a scale graduated in equal angles of 15°, that is, an equinoctial scale. The considerable deviation between the equinoctial horary angle H and angle z is particularly apparent in this table; for example for H = -75° (7h), the deviation almost reaches 50 equinoctial minutes.

When one plots the deviations (H' -z) as a function of latitude and as a function of declination (Fig. 23), one finds on the one hand that the greatest deviations are at the summer solstice, and on the other hand, that the deviation increases with higher latitudes. 25 But rather curiously, the deviation always seems to reach its maximum for the same seasonal horary angle in absolute value.

To highlight this feature, it is necessary to study the derivative d(H'-ζ') / dh and set it equal to zero to obtain the precise seasonal horary angle corresponding to the maximum deviation. We obtain a rather long expression that nevertheless depends only on the semidiurnal arc:

Savoie

for high latitudes, where one observes a drop starting at f = 62°). For a latitude of 40°, this corresponds to seasonal times of 2 h 19 m and 9 h 40 m in the summer, supposing one could read the time with such precision.

When the user decides to read the time on this dial, he first has to set it in latitude by positioning the cursor on the circular scale; then he must calibrate the mobile arm according to the date (this presupposes a clamp to keep the arm fixed). The user then causes the dial to turn until the shadow of the gnomon falls upon the read-off scale. If the user is uncertain about whether it is before or after solar noon, he has to make a first reading of the time and then wait before making a second reading; if the shadow shifts away from the gnomon, it is morning, while if it shifts towards the gnomon, it is afternoon.

In addition to the intrinsic error of this dial (cf. supra), many causes can perturb the accuracy of the indicated time and even make it impossible to read off. The first cause of error is incorrect setting of the latitude: on all the portable dials that have been found, the latitudes of cities or provinces appear on the back. If broadly speaking the latitudes correspond to reality for the cities, the same does not go for the provinces, for which the latitudinal extension can be considerable. 26 26 There are additionally errors in the latitudes of cities, and one can find variants between the exemplars. Constantinople, for example, is places at 41° de latitude in the Aphrodisias exemplar but at 43° in the Samos, Memphis, and Rockford exemplars. See the table provided by J. V. Field and M. T. Wright, "Gears from the Byzantines : A Portable Sundial with Calendrical Gearing," Annals of Science, 42, 1985, p. 109-110. Three examples of ancient "universal" portable sundials

Getting the latitude wrong amounts to getting angle y wrong, hence to inclining the mobile arm at an incorrect angle y' such that y' = (f' -d), where f' is the supposed latitude and f the correct latitude. In Fig. 24 we see that the incorrect inclination brings with it a displacement of the direction in which the gnomon points from K to K'. As a result one will read off a false angle z' on the read-off scale, and this angle has to be compared to the Sun's seasonal horary angle H' for the locality f. This angle is:

(39)
In this formula, the denominator corresponds to the part set manually by the user. There are two kinds of configuration for latitude error: either the supposed latitude f' is greater than the correct latitude f, or it is less.

(1) f > f'. It is in the neighborhood of the meridian that the error is most important-in fact considerable-and the maximum maximorum takes place on the winter solstice (graph 3). Right at the meridian the false angle z' becomes:

(40) Fig. 25 displays the error H' -z' for the afternoon (the error for the morning is symmetrical but with opposite sign) when one is off by 1° in latitude (in this case the user is at 40° latitude but sets his dial for 39°). One can clearly see that between seasonal 6 h and 7 h (and hence also between 5 h and 6 h) the error is huge but decreases very quickly in such a way that one soon Savoie is within the zone where the error is in the neighborhood of -10 minutes. One should note that the user can never observe seasonal 6 h (solar noon) on the dial, even by placing it in the plane of the Sun; at this moment, instead of pointing due east (D = -90°), the gnomon is off by several degrees (in summer the deviation can significantly exceed 20°). But since the shadow covers the read-off scale completely, the user cannot realize that he is committing an error in believing that he is before or after seasonal 6 h.

(2) f < f'. In the case where the latitude to which the sundial is set is greater than the correct latitude, there results a zone of hiatus in the readability of the time since it becomes impossible to use the dial in the neighborhood of seasonal 6 h (graph 4). In fact, if the mobile arm of the dial is set such that its inclination is less than the actual noon altitude, one cannot read off the time when the Sun has an altitude greater than (90° -y'), that is, when (cos z' > 1).

In practice, this means that at a certain moment during the day, the user, no matter what how he turns his dial about, will never be able to bring the gnomon's shadow upon the readoff scale. This impossibility of making a reading, unlike the preceding case, allows him to grasp that there is a problem with the setting of the mobile arm.

Here again (see Fig. 26, where the error in latitude is 1°), it is at the winter solstice that the greatest deviations result between H' et z', and one notes that the error decreases more slowly than in the case where f > f'. Moreover, the dial is unusable for more than two seasonal hours during the day for a latitude around 40°.

One can take consideration of the error that one commits by using an incorrect orientation of the dial; but since the user is required to orient his dial so that the gnomon's shadow falls on the scale of hours-otherwise one cannot read off the time-the orientation is not a significant cause of error.

On the other hand, there is another source of error that has to be taken into account, namely the error in the date. The majority of examplars of the universal portable sundial bear a scale of dates, bounded by the two solstices, with the intermediate graduations corresponding to the entries of the Sun into the zodiacal signs. 27 Let us note in passing that the sole function of the symmetrical scale of dates that one finds on the exemplars is to refine the setting by means of a point situated at the tip of the read-off scale.

The solstices are generally placed on the 8th days before the Kalends of January and July, that is, respectively December 25 and June 24. 28 The indicated solstice dates are the classical dates according to the Julian calendar, which came into use in 45 BC. As for the equinoxes, they are set on March 25 (8th day before the Kalends of April) and September 24 (8th day before the Kalends of October). But because of the drift of the Julian year relative to the tropical year, the astronomical seasons underwent a shift as tabulated in Table 5 for the period from the 1st century through the end of the 6th century 29 In addition to this shift of the seasons there is a slow diminution of the obliquity of the ecliptic, which changed from 23° 41' in the 1st century to 23° 37' in the 6th century. This has the effect of significantly modifying the inclination of the mobile arm at the solstices, and given that the dials were engraved with an obliquity of 24°, the error ends up being a little over 0° 20' in the 6th century. Making a bad estimate of the date (or of the obliquity) on this type of portable dial amounts to applying an erroneous solar declination, and it is easy to see that this reduces to the same kind of error as introducing a bad latitude: the angle y' here becomes (f -d') where d' is the incorrect solar declination. Since the declination varies very little around the solstices, getting the date wrong by several days is inconsequential, in particular since the graduations of the dials do not allow a setting to the precise day! For example, a 6th century user who thinks that the summer solstice falls always on June 24 is committing an error of 0° 3', which is not 29 D. Savoie, "Les dates des quatre saisons," Observations et Travaux, n° 19, 1989, p. 3-6. The mean dates (largest number of occurrences of the date by century) in the present table were calculated in UT according to the algorithms given by J. Meeus, Astronomical Algorithms, Willmann-Bell, Richmond, USA, 1998. Savoie perceptible. On the contrary, the same user, if he thinks that the vernal equinox falls on March 25 rather than March 18, commits an error of close to 2° 30' in the declination, and this does become perceptible.

As has already been said, the dial is perfectly correct only on the equinoxes, and its error is absolutely imperceptible for at least a month before and after the equinox. Once again, our modern conception of the idea of precision for such a dial needs to be put in perspective. It would appear logical to compare the seasonal time indicated by the portable dial to that which would be indicated on an ancient dial that has been perfectly drawn and is in a functioning state, which plays the role of a kind of control-clock. In reality this appears unrealistic for many reasons. The first is tied to the physical difficulty of making such an error apparent, since ancient Greco-Roman sundials, with rare exceptions, lack any subdivision of the hour. This means that to know the time when the gnomon's shadow falls between two hour lines on the control-clock, one has to make an estimation that one cannot guarantee to be accurate to within 5 or 10 minutes. Hence unless the maximum error of the portable dial falls, by a felicitous stroke of luck, on a round hour number, it is practically certain that an error of 7 or 9 minutes is impossible to make visible. What is more, how can one be certain that the error does not arise from a bad setting in latitude or date rather than from the conceptual basis of the dial? In fact it is legitimate to ask whether the inventor or inventors of this portable dial were conscious that it was, in an ideal sense, false.

We should thus seriously consider the possibility that this dial was considered in antiquity to be perfectly exact. For lack of documents, one cannot know whether its invention resulted from a theoretical investigation or by chance or from a combination of the two. But if one recalls that it is not a precise instrument for time measurement, one has to conclude that it is doubtless the best candidate for being the famous πρὸς πᾶν κλίμα of which Vitruvius speaks,30 and that it fulfilled in a very satisfactory way its mission of giving a good notion of the time while traveling over a vast extent of latitude. It constitutes one of the very are examples of sundials that sank into obvlivion when unequal hours progressively gave way to equinoctial hours.

The dial can be compared-without presuming a priori a line of descent-to another later instrument of Arabic or rather Persian origin,31 the "ancient quadrant" (quadrans vetus), one of the earliest references to which goes back to Hermann le Boiteux (1013-1054),32 and which was diffused in Europe especially thanks to Master Robert Anglès (Robertus Anglicus)33 and Sacrobosco34 (Fig. 27). This consists simply of an adaptation of a diagram of unequal hours-a grid that was in wide use notably on the backs of planispheric astrolabes-to a sighting system complemented by a weighted thread. Otherwise put, the ancient quadrant is a "universal" altitude sundial since from observation of the altitude of the Sun one deduces the unequal hour, no matter what date and latitude of the locality.

This quadrans vetus presents remarkable properties which call to mind those of the ancient universal portable dial: it is not rigorously exact except at the equinoxes, 35 it has to be adjusted to the noon altitude of the day, its equinoctial path is valid at (nearly) all latitudes, and it indicates the seasonal hour subject to exactly the same approximation as the ancient universal portable dial.

Let us briefly describe this sundial. It is a quadrant of a circle bearing a sighting system (pinnules on one of its sides, a plumb line fixed to the point of convergence of the hour lines, graduation of the limb in 90°), six circular arcs meeting at the instrument's top and constituting hour lines that divide the limb into six sectors of 15°. In the 12th century, a zodiacal calendar was added in the form of a mobile circular sector along the limb, allowing the solar noon altitude to be obtained as a function of the date; this is what was named the cursor. It served as a kind of table of solar declination.

On the day of observation, one calculates the altitude of the Sun's culmination at the place of observation, which one finds (for example by means of a bead sliding along the plumb line) on the line for seasonal hour VI; then one sights the Sun by holding the quadrant vertically. The entire dial is tilted, except of course for the plumb line. The sliding bead will now show the seasonal hour (Fig. 28).

35 This point did not escape J.-B. Delambre, Histoire de l'Astronomie du Moyen Age, Paris, 1819, p. 243-247. J. Drecker approaches the problem but in a more obscure manner in Die Theorie der Sonnenuhren, op. cit., p. 86-89. See also R. D'Hollander, L'Astrolabe, Histoire, Théorie, Pratique, op. cit., p. 213-216. Figure 28. Principle of setting and use of the quadrans vetus. Knowing the latitude of the locality and the Sun's declination, one calculates the Sun's noon altitude (90° -latitude + declination), which one locates on the graduated limb. One now extends the plumb line, which cuts the circle for unequal hour VI at a point that one finds by means of a sliding bead. When this setting is complete, one sights the Sun; the position of the bead enables one to read off the unequal hour on the network of curves.

Savoie

It is easy to show by plane trigonometry that the angle that one reads off on the dial is not the seasonal horary angle T but a different angle-let us call it T'-whose formula is: (41) where h is the Sun's altitude and h m is its noon altitude, that is, 90° -f + d. Hence we have: (42) or, again, (43) One sees at once that the expression for T' is the same as that for z in the ancient universal portable sundial. If for example one calculates the error committed on the summer solstice (d = +23° 26') on a quadrans vetus calculated for the University of Puget Sound (f = 47° 15' 44'') one obtains the data tabulated in Table 6.

It goes without saying that, by way of contrast, the difference (H -T'), that is, the equinoctial hour angle minus the "hour angle" of the dial yields considerable deviations: one cannot read off the equinoctial hour on such a sundial. Here one meets again one of the particularities of the ancient universal portable dial, with the difference that one could have adapted the quadrans vetus to equinoctial hours, but at the cost of suppressing its "universality," since such a sundial depends on the locality's latitude;36 the hour lines remain circular arcs but they do not converge at the angle of the quadrant. Moreover, the cursor no longer has real meaning since its purpose is to render the dial usable universally. While we wait for future archeological excavations to provide us with new portable sundials from antiquity-perhaps of a new type-we should recall the intent of these "universal" portable dials. They are witnesses first of all of remarkable originality and imagination in gnomonics, even if the principle on which they are based is relatively simple: to determine the time from the Sun's altitude. There are few scientific instruments that made it possible to deploy so many clever devices, for which there was need of a collaboratoin of applied technology, trigonometry, and geometry. The Middle Ages and the Renaissance would continue along this route opened by the gnomonists of antiquity, with dials in which esthetics assumed a major role, as in the Navicula, the Capucin, and the "Universal" of Regiomontanus. More surprisingly, one finds again even in the Age of Enlightenment this tendency to conceive of new universal portable sundials; it suffices to consult the Supplément à l'Encyclopédie [of Diderot and D'Alembert] and its superb plates,37 where the author describes unpublished portable dials38 some of which were due to the German mathematician Johann Heinrich Lambert (1728-1777).

Did these ancient universal dials serve in the "real world" to determine the time? Emmanuel Poulle, connoisseur of medieval astronomy, concluded bluntly that astronomical instruments (astrolabes, quadrans vetus, …) constituted a pedagogical resource and incidentally a tool for calculation, but in no way a resource for observation. I absolutely share this view and I think that the same applies to the majority of ancient portable dials: they are objects of prestige and curiosity. As I have said above, their small dimensions make the read-off of the hour very difficult, not to say impossible; the crudeness of the drawing in the case of some of them, and in the case of others the uncertainness or inexactness of the locality where they were used and the shift in the dates of the seasons in the Julian calendar-all this makes highly improbable any precise determination of the time. Doubtless there would be much to say about this concept of "precision" in antiquity and even in the Middle Ages, and it is a safe bet that we impose modern concepts on these portable sundials that are totally anachronistic so far as concern the results that the ancients expected to obtain. 39

Figure 2 .

 2 Figure 2. Outside face of the box, bearing a relief portrait of Antoninus Pius.

Figure 3 .

 3 Figure 3. Inside face of the half of the box, bearing a drawing resembling a stereographic projection. The reason for its presence in this dial is unknown.

Figure 4 .

 4 Figure 4. Disk showing the horary drawing for the latitude of Alexandria. One can clearly see that the hole is displaced relative to the drawing and that the latter is quite crude. Below the lines are the names of the months.

Figure 5 .

 5 Figure 5. Diagram showing the principle of the "box" altitude dial: with it held vertically in the solar plane, the rays enter at P and strike the mobile ruler (which is very narrow); one reads off the hour at the intersection of the ruler and the drawing. The latter is contained within a triangular zone, with points E, Q, and W being the positions of the spot of light at solar noon (seasonal hour 6) respetively on the summer solstice, the equinoxes, and the winter solstice. The date lines converge on C, which is the mounting point of the ruler, while the hour arcs form a fan extending from the lowest arc (noon) to the center (sunrise/sunset).

bFigure 6 .

 6 Figure 6. Modern reconstruction of the "box" altitude dial for a latitude of 38°. The rays enter by the lateral notch and strike the ruler, which is calibrated according to the month (here δ = -11.47°, zodiacal signs Pisces/Scorpio). If one considers the time to be in the afternoon, it is seasonal 8 h. The red circular arc corresponds to solar noon; the red straight line in the middle corresponds to the equinoxes.

Figure 7 .

 7 Figure 7. Bronze disk of diameter 10.4 cm, discovered in a Gallo-Roman villa at Berteaucourt-les-Dames, a locality in the north of France in Picardie, département de la Somme. The object dates from the 2nd century of our era.

Figure 8 .

 8 Figure 8. Drawing faithfully reproducing the inscriptions and drawing of the Berteaucourt-les-Dames disk. The upper part consists of a grid where one recognizes the names of the months; the rest of the disk is filled by a list of 23 Roman provinces, and occasionally cities, accompanied by their increasing latitudes. This progressive list begins with ALEXAND(riae) [latitude] XXX and ends with BRITANN(iae) [latitude] LX. The disk is perforated by a hole at the center.

Figure 9 .

 9 Figure 9. Photo of the rear face of the Berteaucourt-les-Dames disk. A gnomon was likely inserted in the hole to cast a shadow on the grid figuring on the other face of the disk. On the rear face shown here, a groove along the radius of the disk enables one to adjust it in the direction of the zenith.

Figure 10 .

 10 Figure 10. Modern representation of the grid. It comprises four concentric circles indicating the latitude (from 30° to 60°), crossed by seven date curves.

Figure 11 .

 11 Figure 11. Geometrical drawing of the grid. Arcs EE' and AA' are respectively the arcs for latitude 60° and 30°. Arcs EA (the curve for the winter solstice) and E'A' (for the summer solstice) are in red.

Figure 12 .

 12 Figure12. The gnomon's shadow (red) cuts the summer solstice curve at latitude 42° (broken circle).

  translation facing the Latin in R. Sinisgalli, S. Vastola, L'analemma di Tolomeo, Edizioni Cadmo, Firenze, 1992. See O. Neugebauer, HAMA, Springer-Verlag, Berlin-Heidelberg-New York, 1975, t. II, p. 840-841 and D. Savoie, Recherches sur les cadrans solaires, Brépols, Turnhout, 2014, chap. IV. 23 If one keeps to the classical definition, the seasonal hour has no meaning beyond the polar circles (latitude 90• ± obliquity) at certain times of year because the Sun can be circumpolar.

Figure 18 .

 18 Figure 18. Representation by spherical trigonometry (viewed from the zenith) of the portable dial in use on the equinoxes. P is the north celestial pole, Z the zenith, K the tip of the gnomon.

Savoie

Figure 20 .

 20 Figure 20. Representation by spherical trigonometry of the principle of the portable dial. The dial measures angle ζ whereas it is set as a function of angle ψ.

Figure 21 .

 21 Figure 21. Representation in the celestial sphere of the portable dial in use in the morning on the winter solstice. The dial measures angle ζ which approximates a division by 6 of the semidiurnal arc described by the Sun. The Sun (at S) illuminates the dial, which is oriented to the southwest. The gnomon's shadow falls upon the graduation for seasonal hour 3.5.

  Deviation (H' -ζ) for different latitudes on the summer solstice.

  , H' undergoes a gentle fluctuation of a few minutes as a function of the Sun's declination and the latitude, but always remains very close to a seasonal horary angle of ±55° (except 25 Around the polar circles, the dial becomes unusable for the most part because of the huge error caused by the latitude.

Figure 24 .

 24 Figure 24. Principle of the calculation of error in latitude, represented in spherical trigonometry. A bad setting of the read-off arm of the dial introduces a false angle ψ', so that instead of measuring angle ζ, the dial measures ζ'.

Figure 25 .

 25 Figure 25. Error in reading the time for φ = 40°, φ' = 39°.

Figure 26 .

 26 Figure 26. Error in reading the time for φ = 40°, φ' = 41°.

Figure 27 .

 27 Figure 27. Illustration of the quadrans vetus from Orontius Finnaeus, De solaribus horologiis et quadrantibus, Paris, 1560, Book II, p. 143. On this ancient quadrant can be seen the sighting system consisting of pinnules, and the limb graduated in 90° with a dentate scale. Below the limb, the author has added a zodiacal calendar establishing the correspondence between the days of the year and the degrees of the zodiac occupied by the Sun on each day. Six circular arcs meeting at the top represent the hour curves.

Table 5 .

 5 Shift of dates of solstices and equinoxes in the Julian calendar.

	Autumnal equinox	Sept. 25	Sept. 24	Sept. 23	Sept. 22	Sept. 22	Sept. 21
	Winter solstice	Dec. 22	Dec. 22	Dec. 21	Dec. 20	Dec. 19	Dec. 19

Table 6 .

 6 Calculation of error of time determinations on the quadrans vetus on the summer solstice, latitude 47° 15'.

	H	T	T'	Error in minutes T -T'
	0°	0°	0°	0
	15°	11.443°	12.364°	3.7
	30°	22.886°	24.659°	7.1
	45°	34.329°	36.810°	9.9
	60°	45.773°	48.727°	11.8
	75°	57.216°	60.299°	12.3
	90°	68.659°	71.379°	10.9
	105°	80.102°	81.771°	6.7

J. L.Massy, Gallia, t. 43, fascicule 2, 1985, p. 481-482. This disk, discovered in a Gallo-Roman villa is preserved at the Musée de Picardie at Amiens. It is in much better condition than the Merida disk. See also C. Hoët-van Cauwenbergue, E. Binet, "Cadran solaire sur os à Amiens (Samarobriva)," Cahiers Glotz,XIX, 2008, p

. 123-124. 12 J. Arce, "Viatoria pensilia. Un nuevo reloj portatil del s. III D. C. Procedente de Augusta Emerita (Mérida, Espana)," Merida Tardorromana(300-580 d. C.), 2002, p. 217-226. This disk is preserved at the National Museum of Roman Art of Merida (Estremadura). The latitude circles are effaced; six date arcs survive.13 See D. Savoie and M. Goutaudier, "Les disques de Berteaucourt-les-Dames et de Mérida : méridiennes portatives ou indicateurs de latitude?", Revue duNord, t. 94, n° 398, 2012, p. 115-119. 14 The Merida disk bears 19 names of provinces in contrast to 23 for that of Berteaucourt-les-Dames. On the latter, there are some exceptions to the increasing order of the latitudes. On the geographical labels inscribed on portable sundials, see C. Hoët-van Cauwenbergue, "Le disque de Berteaucourt-les-dames (cité des Ambiens) et les listes gravées sur les cadrans solaires portatifs pour voyageurs dans le monde romain," Revue duNord, t. 94, n° 398, 2012, p. 97-114. 15 See F. K. Ginzel, Handbuch der Mathematischen und TechnischenChronologie, vol. 2, Leipzig, 1911, p. 179-181 et p. 282. The solstice dates given here are the classical dates in the Julian calendar that came into use in 45 BC; as for the equinoxes, they are fixed on March 25 (VIII before the Kalends of April) and September 24 (VIII before the Kalends of October). At the beginning of the 3rd century of our era, because of the shift of the Julian year relative to the tropical year, the astronomical seasons began on the following dates (see Table5below): vernal equinox on March 21, summer solstice on June 23, autumnal equinox on September 24, and winter solstice on December 22. Hence the user of the instrument would commit a slight error in retaining the common dates.

See C. Eagleton, Monks, Manuscripts and Sundials, The Navicula in Medieval England, Brill, Boston, 2010. The calculation of the error in read-off on the Navicula was made by J. Kragten, The Little Ship of Venise -Navicula deVenetiis, Eindhoven, 1989.

18 This dial was described by V. Durand, followed by a restoration and-erroneous-instructions for use by general De La Noë : "Cadran solaire portatif trouvé au Crêt-Chatelard," Bulletin et Mémoire de la Société Nationale des Antiquaires de France, t. 7, mémoires 1896, Paris, 1897, p. 1-38. De La Noë, who does not hesitate to characterize as "crude" an earlier attempt at explication by Baldini (cf. infra), had absolutely no understanding of this dial, which he placed horizontally.Figure13. Method of use of the Berteaucourt-les-Dames disk. The disk is suspended in the plane of the Sun. One can here see that the horizontal gnomon casts a shadow upon the grid, cutting the curve for latitude 50° at the equinoxes (red).

Vitruvius, De Architectura, Book IX, chap. VIII, 1, gives a description of sundials, attributing them to inventors, and speaks of a dial "for all latitudes" (in Greek in the text). See the translation by J. Soubiran, Les Belles Lettres,Paris, 1969, p. 30.

See D. King, "A Vetustissimus Arabic treatise on the Quadrans vetus," Journal for the History ofAstronomy, xxxiii, 2002, p. 237-255 et F. Charette, Mathematical instrumentation in fourteenth-century Egypt and Syria, Brill, Leiden-Boston, 2003, p. 211-215.

Study of the texts of this period, including the one allegedly by Hermann le Boiteux, enabled J.-M. Millas Vallicrosa to demonstrate that there actually existed two types of quadrans : the vetustissimus, which was older than the vetus. See the important study by J.-M. Millas Vallicrosa, "La introduccion del cuadrante con cursor en Europa," Isis, t.XVII, 1932, p. 218-258.

33 The Latin and Greek text were edited by P. Tannery, Le Quadrant de Maître Robert Anglès, (Montpellier, XIII è siècle), Notices et extraits des manuscrits de la Bibliothèque Nationale, Paris, t. 35, 1897, 2 è partie, p. 561-640. See, however, the remarks and criticisms by W. R.Knorr (cf. infra

).34 One should consult the fundamental study by W. R. Knorr, "The Latin Sources of Quadrans vetus and What They Imply for Its Authorship and Date," Texts and Contexts in Ancient and Medieval Science : studies on the occasion of John E. Murdoch's seventieth birthday, E.Sylla and M. McVaugh, Leiden, New York, Köln, Brill, 1997, p. 23-67.

The procedure for constructing a quadrant for equal hours is given, for example, by Jean Fusoris (1365-1436) : see E. Poulle, Un constructeur d'instruments astronomiques au XV è siècle : Jean Fusoris, H. Champion, Paris, 1963, p. 71-73. A good example of a quadrant for equal hours (and unequal hours) may be found in Orontius Finnaeus, De solaribus horologiis et quadrantibus,Paris, 1560, Book II, p. 151.

Supplément à l'Encyclopédie ou Dictionnaire Raisonné des Sciences, des Arts et desMétiers, t. 2, Amsterdam, 1776, p. 97-106.

See Y. Massé, De l'analemme aux cadrans de hauteur, 2009, available from the author: 2 ruelle de la Ravine 95300 Pontoise, France.

Having executed an exemplar of the ancient universal sundial of 19 cm diameter in wood, I can confirm that it would yield the unequal hour with very good accuracy. However, none of the dials that have come down to us reach these dimensions; of the eleven known examples, half are 6 cm in diameter and the other half 11 cm.

Drecker at the beginning of the 20th century. 19 Several studies have been published since on the subject, the most thorough to date being that of M. T. Wright in 2000. 20 These dials are quite simple in appearance (Fig. 14 and15). They are disks of between 5 and 12 cm diameter. On one face names of cities or provinces are inscribed with their latitudes. On the other face are engraved labels pertaining to months (notably equinoxes and solstices). The mobile scale for reading off the time is not inscribed with numbers; it is curved, and the gnomon is at its extremity. On the disk's periphery, a sliding rail assemblage, under which the latitudes to which the instrument can be set are marked, allows a cursor or pendant ring to be slid to calibrate the dial for the place where it is to be used.

19 J. Drecker, Die Theorie der Sonnenuhren, op. cit., p. 64-66. Drecker was also the first to estimate the error in the read-off of the time as a function of the date and latitude. Two earlier authors (Baldini and Woepcke) had already studied this dial but they were completely misguided about its operation: G. Baldini, "Sopra un'antica piastra di bronzo che si suppone un orologio da sole," Saggi di dissertazioni accademiche publicamente lette nella nobile Academia Etrusca di Cortona , vol. III, Rome, 1741, p. 185-194 ; F. Woepcke, Disquisitiones archaeologio-mathematicae circa solaria vetrum, (Diss. Inaug.), Berlin, 1842, p. 14-19. In their defense, one should note that the model of dial on which they based their arguments was incomplete, the gnomon situated at the end of the read-off scale having been lost. 20 M. T. Wright, "Greek and Roman Portable Sundials -An Ancient Essay in Approximation," Archive for History of Exact Sciences, vol. 55, 2000, p. 177-187. Wright, who curiously does not cite Drecker, employs a Vitruvian analemma in his trigonometrical demonstrations, which is admirable. We may also cite the brief study by F. A. Stebbins, "A Roman Sundial," Journal of the Royal Astronomical Society of Canada, vol. 52, 1958, p. 250-254, who has the merit of having explained clearly how one used these portable dials. See also the classic and very good article by D. J. de Solla Price, "Portable Sundials in Antiquity, including an Account of a New Example from Aphrodisias," Centaurus, 1969, vol. 14, p. 242-266. Many authors, more specialized in archeology, have concentrated on the geographical lists that appear on the backs of the dials, which in some cases give as many as 36 places. Attention should also be drawn to an inscribed marble slab found at Aquincum, Hungary, and sometimes miscalled tabula gromatici, which appears to have been a set of templates for constructing this type of dial; see P. Albèri-Auber, "The Aquincum fragment," The Compendium: Journal of the North American Sundial Society 25 (2), 2018, 13-24.


Maria João Valente
email: mvalente@ualg.pt

Cleia Detry
email: cdetry@letras.ulisboa.pt

Cláudia Costa
email: cmcosta@ualg.pt

Claúdia Costa

Naroa Garcia-Ibaibarriaga

Jone Castaños
email: jcastanosdlf@yahoo.es

Aitziber Suárez
email: aitziber.suarez@ehu.eus

Pedro Castaños
email: pedrocastanos@yahoo.es

Salvador Bailon
email: salvador.bailon@mnhn.fr

Xabier Peñalver

Sonia San José

José Antonio Mujika

Juan Rofes
email: juan.rofes@mnhn.fr

Xabier Murelaga
email: xabier.murelaga@ehu.eus

Naroa, CASTAÑOS, Jone, SUÁREZ-BILBAO García-Ibaibarriaga

Aitziber, CASTAÑOS, Pedro, BAILON, Salvador, PEÑALVER, Xabier, SAN JOSÉ Sonia

In Valente

Maria João

Detry

Cláudia Cleia, Costa

Jone Castaños, Aitziber Suárez-Bilbao

FOREWORD OF THE EDITORS

Keywords: Cave-use, Vertebrates, Palaeoenvironment, Upper Palaeolithic, Epipalaeolithic, Cantabrian Range

Praileaitz I cave is located on the northern Iberian Peninsula and preserves a long sedimentary deposit spanning between 21 and 10 ka BP. Excavated since 2000, the use of the cave by humans seem to be different from other caves known in the Basque Country. The Lower Magdalenian singular anthropic remains suggests that this space would have been occupied most probably for worship activities instead of most common domestic purposes. The study of both macromammal and microvertebrate remains stresses the common use of this cave by both carnivores and avian predators.

In recent decades, there have been great developments in the study of past human-animal interactions, clearly demonstrated by the influx of researchers to the Meeting of Iberian Zooarchaeology (EZI, or Encontro de Zooarqueologia Ibérica), held April 2017 in Faro, Portugal. Its organisation was a joint effort of three Portuguese Research & Development Units in Archaeology -CEAACP1 , ICArEHB2 and UNIARQ3 and was hosted by the University of Algarve. This volume, entitled New Trends in Iberian Zooarchaeology, is the final product of that meeting.

One of the highlights of EZI 2017 was the closing keynote given by Arturo Morales, Full Professor at the Universidad Autónoma de Madrid, and a researcher with vast experience. That keynote serves as the basis for the first text of this volume. Here, Morales leads the reader on a brief yet motivating chronological journey through the development of zooarchaeology as a discipline in the Iberian Peninsula from 1975 to the present day, following his personal experiences in the field.

After this introduction, the articles begin with a set dedicated to prehistory. Naroa Garcia-Ibaibarriaga and colleagues summarise what is known for the Praileaitz I, a cave located in the Basque Country, throughout the Solutrean to the Epipaleolithic sequence. Esteban Álvarez-Fernández and colleagues review zooarchaeological materials (both molluscs and vertebrates) from an intervention carried out in the 1930s at Cova del Solà del Pep and give us a glimpse into the final phase of the Mesolithic period in Catalonia. The paper presented by Nelson Almeida and colleagues focus on two cave assemblages located in central Portugal dominated by leporid remains. Their article explores the possibility that such remains were accumulated by non-anthropogenic agents, namely carnivores, despite the well-documented human occupations in the caves. Carlos Pimenta and colleagues analyse the small vertebrates from the Chalcolithic site of Penedo do Lexim, located in Portuguese Estremadura. Using the Habitat Weighting Method, and comparing its results with other Chalcolithic sites in the region, they were able to identify the coexistence of two bioclimatic domains (Atlantic and Mediterranean).

Finally, Rafael Martínez Sánchez and Dolores Ruiz Lara present the study of fauna recovered in two ditches at La Minilla (Córdoba) during the Middle-Late Copper Age. These materials show features indicative of possible "banquets" (i.e., collective consumption during a festive occasion).

Next, we explore protohistory, starting with Íris Dias and colleagues describing fauna from the Late Bronze Age of Outeiro do Circo in South interior Portugal. The assemblage is dominated by domestic animals and hunting seems to have been a minor activity. Rafael Bolado and colleagues present the zooarchaeological results of El Ostrero, a shell midden located in Cantabria and dated between the eighth and fourth century BC. In addition to cattle, pigs, sheep and goats, they recorded the abundance of oysters collected in an estuary.

Ana Beatriz Santos and Nuno Mota describe a small assemblage dating from the first and second centuries AD in downtown Lisbon, an area with few zooarchaeological studies from the Roman period. Domestic animals such as cattle, caprine and swine dominate the collection, in addition to a significant presence of red deer which, together with leporids, is indicative of wild game in the Roman Olisipo. From the North of Portugal, Vera Pereira and colleagues describe a faunal assemblage from Torre Velha (Castro das Avelãs), near Bragança, in the Roman province of Gallaecia, a region with few known faunal data so far. This is the territory of the Zoelas, and the materials date from the first and second centuries AD, the first phase of Roman occupation. Livestock is abundant, but hunted game is also present (leporids, red deer and red partridge). Thierry Argant describes more than two thousand faunal remains, most from unclassified mammals, from another Portuguese site also in Northern Portugal: Vale do Mouro (Meda). The fauna comes from the last phases of occupation of a Roman villa in the fourth century AD. The identified fauna is quite diverse, both domestic and wild. The author suggests that some animals, such as cattle, were obtained through a network with other local settlements.

For the Medieval period, Patrícia Aleixo and colleagues present a classic study on materials collected in an intervention carried out in the city of Loulé (Southern Portugal) with Almohad chronology. The faunal assemblage is unusual for the area and period, displaying a large number of red deer and rabbit remains. The authors suggest the deposits may result, at least partially, from unusual (perhaps festive) meals. Idoia Grau and colleagues studied an unusual assemblage from Vitoria-Gasteiz (province of Álava, Basque Country, Spain), dated from the 13th and 14th centuries. It mainly consisted of sheep and goat horncores for manufacturing handles or other objects at an iron-working workshop.

The last two articles concern methodological issues. Esteban García-Viñas and colleagues write of their experience of immersing modern bones in seawater to study the taphonomic processes (erosion and chemical change) in the fauna collected in two shipwrecks dated from the 16th and 17th centuries and located in the Bay of Cádiz.

In all, this volume shows the diversity of themes in Iberian zooarchaeology, one of the greatest values of the EZI conferences. We hope it will be a valuable contribution to the knowledge of zooarchaeology in the Iberia Peninsula.

Maria João Valente

Cleia Detry Claúdia Costa Loulé, Lisbon and Faro, September of 2022

Introduction

The Vasco-Cantabrian region is worldwide known for its rich Palaeolithic archaeological heritage. The archaeological record shows that the population of the time display a certain interest in transcendental matters, as the abundant and variety of rock and cave art manifested -places like Ekain [START_REF] Ochoa | Más que pinturas de caballos en la Cueva de Ekain (Deba, Gipuzkoa): los grabados digitales paleolíticos en Europa Occidental[END_REF]), Danbolinzulo (Iriarte-Chiapusso et al. 2015) or Astuigaina (Iriarte-Chiapuso et al. 2017), among others. In Praileaitz I cave (Deba, northern Iberian Peninsula), archaeological remains such as lithic industry, stone tools and faunal remains are scarce when compared with other archaeological sites in the region -as those of Amalda [START_REF] Altuna | La Cueva de Amalda (Zestoa, País Vasco): ocupaciones Paleolíticas y Postpaleolíticas[END_REF]), Ekain [START_REF] Altuna | El yacimiento prehistórico de la Cueva de Ekain[END_REF], Santimamiñe [START_REF] López-Quintana | La cueva de Santimamiñe: revisión y actualización (2004-2006) (Bizkaiko Arkeologi Indusketak 1)[END_REF], among others. On the contrary, pigments, personal ornaments, and hearths are well represented (Peñalver et al. 2017a). All the evidence may suggest that ritual activities could have been performed in this cave although we can only guess the what they consisted of. The excavations carried out between 2000 and 2009 in Praileaitz I cave revealed a singular sequence for the Vasco-Cantabrian region of Spain. The detailed results of these investigations were recently published in a monograph (Peñalver et al. 2017a). This paper presents the first archaeozoological synthesis combined with the data provided by other archaeological records (i.e. tools and ornaments). Data will be compared with anthracological and palynological data from Praileaitz I cave in order to synthesize the study of palaeoenvironmental and archaeological information and reconstruct the occupational history of this unique cave.

General setting and site description

The archaeological site of Praileaitz I is located in the municipality of Deba (Gipuzkoa, northern Iberian Peninsula), in the lower part of the Deba river valley (Figure 1a). It is located at 55 m.a.s.l, on the right bank of a meander formed near the mouth of the river. The cave opens onto the NE side of the Praileaitz hill, which is practically destroyed due to the presence of an active quarry (Figure 1b). From a geological point of view, the site is located in an area characterized by Aptian-Albian (Cretaceous) shelf carbonates with rudists (Urgonian Complex). The scarce vegetation of the area is composed mostly of Cantabrian Holm oak and mixed Atlantic Forest, together with large Pinus radiata plantations (Peñalver et al. 2017a). The entrance of the cave, oriented NW, has a triangular shape and is 6 m high and 2.5 m wide at the base (San [START_REF] Jose | Praileaitz I haitzuloa[END_REF]. The cave runs approximately 100 m long in NE direction, and is divided into three independent, semi-circular, chambers joined by sub-horizontal vestibules. The entrance opens to a vestibule (an area of 34 m2 and a maximum height of 10.4 m), where the most complete stratigraphic sequence has been recorded. On the northwest, there is a small gallery named Northwest Gallery. To the south of the Vestibule, there is the access to the 1st Inner Room, of 43 m2, 7 m diameter, and a maximum height of about 2.25 m (Figure 1c). The 2nd Inner Room (42 m2 and a maximum height of 1.57 m) was completely covered by a stalagmitic crust. From this point, the cavity extends into various galleries that have not been excavated but contain cave paintings (García-Diez and Ochoa 2017). These are a set of red dots and lines spread randomly over the surface that are traced with the fingers. They have been considered Palaeolithic without any other marker to specify more accurately their chronology.

The cave was discovered in 1983 by M. Sasieta and J. Arruabarrena, who carried out preliminary archaeological prospections during the 80s. These yielded scant lithic remains and some animal bones. Since 2000, and up to now, systematic excavations have been conducted focused on the use of the cave (Peñalver et al. 2017c).

Material and methods

Excavation

During 2000-2009 field seasons, about 191 m2 from different areas of the cave were excavated using standard archaeological and palaeontological techniques (Peñalver et al. 2017b). In order to facilitate the understanding of the space, six excavation areas were defined: Ledge, Vestibule, Northwest gallery, Transit area between Vestibule and 1st Inner Room, 1st Inner Room and 2nd Inner Room (Figure 1b; see Appendix 1 for more information about the studied area). Since the works had been carried out in distant areas with different characteristics, the numbering of the layers do not correspond between zones, although they have been stratigraphically correlated with the establishment of standardized layers (see Appendix 2a and 2b).

More than 450 tool objects of a different kind were recovered (Mujika-Alustiza 2017), including 29 perforated, and mostly decorated, lithic and bone pieces (Peñalver and Mujika-Alustiza 2017).

Chronology

Several samples from different fossiliferous layers and areas have been dated by different methodologies and laboratories (Peñalver et al. 2017b). The absolute datings obtained from bone remains or charcoal have been complemented with the archaeological information from the successive excavation campaigns. In this way, different phases of occupation have been identified, ranging from the Solutrean to the Epipalaeolithic (between 21 to 10 Ka BP; Appendix 3).

Palaeontology

More than 25.500 macromammal complete or fragmentary bones and teeth were recovered at Praileaitz I cave. Each remain has been studied individually and identified anatomically and taxonomically whenever possible [START_REF] Castaños | Estudio de la fauna de macromamíferos del yacimiento de Praileaitz I (Deba, Gipuzkoa)[END_REF]. The quantification was defined by the number of remains (NR) and the minimum number of individuals (MNI). In the case of certain species (Spanish ibex, wolf and chamois), the minimum number of elements (MNE) and the minimum number of animal units (MAU) have been also analysed. Bones were measured following [START_REF] Driesch | Das Vermessen von Tierknochen aus vor und frühgeschichtliche Siedlunge[END_REF].

Since sampling for micropalaeontological analysis was not carried out, some of the samples taken for the sedimentological study have been used to recover disarticulated small vertebrate fragments (Table 1). The sediment was processed with the water-screening method using a 0.5 mm mesh. The fragments were identified following the general criteria of systematic palaeontology (e.g. [START_REF] Bailon | Amphibiens et reptiles du Pliocène et du Quaternaire de France et d'Espagne mise en place et évolution des faunes[END_REF][START_REF] Bailon | Différenciation Ostéologique des Anoures (Amphibia, Anura) de France, Fiches d'ostéologie animale pour l'archéologie[END_REF][START_REF] Daams | The dental pattern of the dormice Dryomys, Myomimus, Microdyromys and Peridyromys[END_REF][START_REF] Heinrich | Zur biometrischen Erfassung eines Evolutionstrends bei Arvicola (Rodentia, Mammalia) aus dem Pleistozän Thüringens[END_REF][START_REF] Reumer | Ruscinian and early Pleistocene Soricidae (Insectivora, Mammalia) from Tegelen (The Netherlands) and Hungary[END_REF][START_REF] Van Der Meulen | Middle Pleistocene smaller mammals from Monte Peglia (Orvieto, Italy) with special reference to the phylogeny of Microtus (Arvicolidae, Rodentia)[END_REF]. Specific attribution of the small vertebrates is based on the best diagnostic cranial and/or postcranial diagnostic element. The fossils were quantified using the MNI method, taking into account the side whenever possible. Additionally, with the fossil remains collected during excavation campaigns with a 2 mm sieve, we have estimated the distribution of remains throughout the Vestibule area, 1st Inner Room and 2nd Inner Room [START_REF] Garcia-Ibaibarriaga | Estudio de los microvertebrados del yacimiento de Praileaitz I (Deba, Gipuzkoa)[END_REF]. In order to reconstruct the environment at Praileaitz I cave, we used the MNI of each small mammal taxa and their relative proportion in the assemblage, considering the autoecological affinities of each taxon in accordance with [START_REF] Cuenca-Bescós | Paleoclima y paisaje del final del Cuaternario en Cantabria: Los pequeños mamíferos del Mirón (Ramales de la Victoria)[END_REF], [START_REF] Pemán | Aspectos climáticos y ecológicos de los micromamíferos del yacimiento de Erralla[END_REF], and [START_REF] Sesé | Aportación de los micromamíferos al conocimiento paleoambiental del Pleistoceno superior de la Región Cantábrica: Nuevos datos y síntesis[END_REF].

Results

Macromammals

Out of +255.500 macrommal remains studied, 20.5% could be identified at the genus and/or species level [START_REF] Castaños | Estudio de la fauna de macromamíferos del yacimiento de Praileaitz I (Deba, Gipuzkoa)[END_REF]. Regarding the distribution of the remains according to areas (Table 2), the largest assemblage of remains (both determined and not determined) was recovered at the Vestibule (NR = 11.670, Identified NR= 2373). On the contrary, the Transit area has provided the smallest amount of remains (NR = 908, of which 82 were determined).

The 5247 remains identified correspond to 22 species, being ungulates the most abundant group (NR = 3690), represented by seven species (Figure 2, Table 2). The assemblage is dominated by Capra pyrenaica (NR = 2282), especially in the Solutrean and Lower Magdalenian levels of the Vestibule, Transit area and 1st Inner Room. Most of these remains (77.3%) correspond to immature individuals (i.e. infantile, juvenile and subadult age groups). Large bovids and reindeer are barely represented, while horse and roe deer are each represented by four and one remain, respectively. Carnivores are worse represented in terms of the number of NR (1519) but are nonetheless taxonomically more diverse with fourteen species recorded (Figure 2, Table 2). Canids are the best represented predators in Praileaitz I cave with fox as its main representative in all areas and levels, followed by felids. The presence of the mustelids is practically testimonial Taphonomic analysis of macromammals evidenced that almost of the ungulates' long bones are mostly complete and exhibit gnawing marks, especially in the epiphyses. More than 80% of the bones and teeth correspond to infant or juvenile individuals of deer, goat and Pyrenean chamois. Therefore, the assemblage has little or nothing to do with an accumulation of bones as result of a human consumption. In addition, the relative frequency of carnivores in the Ledge (NR = 25.8%) and the Vestibule (NR = 31%) is similar to that identified at other deposits that served exclusively as carnivore dens, such as Sima de Labeko Koba and Unikoté I (Castaños and Castaños 2017). Furthermore, the anatomical representation of carnivores indicates that most animals died in the cave, while in the case of the ungulates the skeleton is not complete, in view of the almost complete absence of backbones and ribs. For these reasons, we consider the large mammal assemblage of Praileaitz I primarily related with the predatory activity of different carnivores, mostly with canids. In general, human action is barely observed on bones.

Small vertebrates

Based on the residue extracted for the sedimentological study, we studied the small vertebrate assemblage from the Solutrean to the Mesolithic periods (Garcia-Ibaibarriaga et al. 2017). The assemblage comprises 83.662 identified and unidentified disarticulated bone fragments (teeth, isolated mandibles, skull fragments, and postcranial bones). The identified assemblage at the genus and/or species level correspond to 676 individuals (MNI), representing a total of 18 taxa (Figure 3 and 4; Table 3).

When relative proportions of the different skeletal elements are observed, it is possible to differentiate two groups in the assemblage. In one group (samples from the 1st Inner Room and V1 and V2) all the skeletal elements are represent, whereas in the second group some of them are missing (samples V3, V4 and V5). The relative proportion of isolated teeth is higher in the first group (nearly 60% of the remains). Regarding the distribution of the remains, in the Vestibule they were accumulated only in some squares, most probably related with the fact that birds of prey concentrate pellets around their nesting and roosting sites. On the contrary, in the inner rooms and samples V3, V4 and V5, bones and teeth are randomly distributed, suggesting a water flow transport of these remains from the Vestibule.

The assemblages from each area of the cave provide evidence of different palaeoenvironments depending on the chronology. The samples from the 1st Inner Room (Solutrean and Lower Magdalenian) Rangifer tarandus are dominated by species associated with open humid areas, such as Sorex araneus-coronatus and Microtus (Alexandromys) oeconomus. These levels have provided the few amphibian and reptile remains recovered in the site. In the Vestibule, the open-meadow species are still dominant during the Lower Magdalenian, although Microtus (Microtus) arvalis prevails. Finally, during the Epipaleolithic, the few remains obtained belong to Apodemus sylvaticus-flavicollis, Sorex araneus-coronatus and Talpa sp., although the scarcity of the remains (MNI = 5) does not allow a proper palaeoenvironmental reconstruction.

2 1 3 3 2 1 3 2 1 1 1 1 Capreolus capreolus - - 1 1 - - - - - - - - Ursus arctos - - 14 2 - - - - - - 7 1 Ursus spelaeus 26 4 6 4 2 1 - - - - 60 3 Ursus sp. - - - - - - - - - - 18 2 Crocuta crocuta 9 3 - - - - - - - - 5 1 Panthera pardus 8 2 6 1 13 1 1 1 2 1 - - Lynx lynx 7 2 24 3 4 1 2 2 - - 2 1 Lynx spelaeus - - 3 1 - - - - - - - - Lynx sp. - - 23 4 - - - - 8 2 - - Felis silvestris 1 1 2 1 - - - - - - 1
Meles meles 2 1 - - - - - - - - - - Mustela nivalis - - 2 2 - - - - - - 2 1 Mustela putorius 1 1 - - - - - - - - - - Mustela erminea - - 2 1 1 1 - - - - - -

Lithic and bone tools

The number of recovered lithic objects is less than 100 remains at each level, making a total of 416 lithic artefacts (Mujika-Alustiza 2017). With the exception of 16 bone elements, flint is clearly the dominant raw material. They are generally well preserved, since only 12 cases (3.1%) display an intense patina (Tarriño Vinagre 2017). This raw material was collected mostly from the Flysch (NR = 306), Treviño (NR = 14), Urbasa (NR = 10), and Chalosse (NR = 8), although flint from two other North Pyrenees sites has been identified anecdotally (Tercis, NR = 3; Salies-de-Béarn, NR = 1). The functional analysis applied to the lithic remains from the Lower Magdalenian level reveal their use in butchering processes (Clemente [START_REF] Conte | Análisis funcional de los restos líticos tallados de la cueva de Praileaitz I (Deba, Gipuzkoa)[END_REF].

The bone industry is still more limited. It is worth highlighting a perforated baton found in the Vestibule because of its material (reed), shape (sinuous pattern) and the presence of two perforations (Mujika-Alustiza 2017). It belongs to the end of the Final Magdalenian or the beginning of the Epipalaeolithic (a bone sample from the same level was dated at 10740±50 BP).

Personal ornaments

The recovery of a set of pendants made with river stones of unique shapes is of a great intereset [START_REF] D'errico | Les galets perforés de Praileaitz I[END_REF]. All these remains correspond to the Lower Magdalenian, and they were found distributed throughout the Vestibule and the 1st Inner Room (Peñalver and Mujika-Alustiza 2017). Twenty-one of them present human-made perforations at one end, while other five display natural perforations. Additionally, 18 pendants were decorated with sets of notches on their edges or various patterns engraved on their flat faces. Fourteen elements were found in a series at the northwest of the 1st Inner Room, and considered as part of a necklace (Peñalver and Mujika-Alustiza 2017) or cloth decorating elements [START_REF] D'errico | Les galets perforés de Praileaitz I[END_REF]. Particularly noteworthy is a thin bright black pebble with a rhomboid shape, reminiscent of the rounded Palaeolithic 'Venus' figurines found in several locations throughout Europa (Peñalver and Mujika-Alustiza 2017).

Discussion

Palaeoenvironmental reconstruction

The Praileaitz I cave sequence is associated with a period from the beginning of MIS2, as well as the beginning of the MIS1. The sedimentological, and biotic studies provide information about the changes in the environmental conditions throughout the stratigraphic sequence.

The charcoal data indicate the predominance of Quercus subg. Quercus in all the stratigraphic levels and a low taxa diversity (Ruiz-Alonso and Zapata 2017). This pattern suggests that the area was characterised by large forest masses of oaks. Based on ecological and biogeographical data, Quercus is well adapted to harsh climatic conditions, but in summer it requires moisture in the soil. Unfortunately, The microvertebrate assemblage attests all throughout the sequence to an environment clearly dominated by open landscape [START_REF] Garcia-Ibaibarriaga | Estudio de los microvertebrados del yacimiento de Praileaitz I (Deba, Gipuzkoa)[END_REF], although there is a clear increase in the arboreal component from the base of the sequence (sample S3) to the top (samples V1 and V2), as suggested by the notorious increase of A. sylvaticus-flavicollis. Cold, rigorous climatic conditions during the Solutrean (sample S3) are evidenced also by the presence of the willow ptarmigan (Lagopus lapopus; Moreno-García 2017), species considered as indicative of cold climate during the Quaternary (Mourer-Chauvire 1993). The samples dated to the Lower Magdalenian (sample S2, S1, V7 and V6) indicate slightly warmer conditions. The few small vertebrates present in the Epipalaeolithic levels (A. sylvaticus-flavicollis, S. araneus-coronatus and Talpa sp.) can be associated with dense forest areas.

The most abundant species among the ungulate remains are the Iberian ibex (Capra pyrenaica) and the chamois (Rupicapra pyrenaica), especially in the Solutrean and Lower Magdalenian levels. This is in agreement with the cave location in a rocky, mountainous area [START_REF] Castaños | Estudio de la fauna de macromamíferos del yacimiento de Praileaitz I (Deba, Gipuzkoa)[END_REF]) and the general climatic conditions. In terms of abundance, they are followed by red deer, which mostly inhabits open deciduous woodland or broadleaved woodland interspersed by large meadows [START_REF] Lovari | Cervus elaphus. The IUCN Red List of Threatened Species[END_REF]). In addition, cold-adapted species such as the reindeer (Rangifer tarandus) have been identified in levels with harsh climatic conditions, especially during the Solutrean.

Site function

The position of Praileaitz I is somehow strategic because of its location close to the coast corridor (currently flooded), which probably was used by hunter-gatherer groups as a transit area (Edeso-Fito and Mujika-Alustiza 2017). Human occupations of the cave were sporadic and most probably of seasonal character, as it is suggested by the abundance of carnivores throughout the entire stratigraphic sequence.

The first well contextualized human evidences at Praileaitz I cave correspond to Solutrean and Magdalenian periods. The lithic and bone industry is rather scarce, but clearly attributable due to the recovery of remains assigned to these periods by their techno-typology. Because of this reason, Praileaitz I cave was probably used as a secondary settlement, dependent or related to other caves. In this way, the near sites of Urtiaga (Mujika-Alustiza 1993) or Ermittia [START_REF] Esparza | Reflexiones en torno a la estratigrafía de Ermittia (Deva, Guipúzcoa)[END_REF] have yielded more archaeological remains, despite the fact they have been also considered as seasonal settlements.

Human occupation of the cave during the Lower Magdalenian remains sporadic, and not consistent with the characteristics of the hunting sites. No raw material processing sequence has been identified, neither other activities such as carcass processing. However, singular characteristics seem to occur. In this period, the Vestibule seem to have worked as the main occupational area, where a soil formed by abundant clasts of limestone of small size was probably created by anthropic activity (Peñalver et al. 2017c). Additionally, and distributed among different areas inside the cave, a variety of ornamental elements of remarkable homogeneity was found, some of them located near a hearth. These all findings do not seem to have a direct relationship with daily life, and might maybe they respond to worship activities that we are not able to fully identify at this point (Peñalver et al. 2017c).

All in all, the cavity seem to have been recurrently visited but always sporadically during the Upper-Final Magdalenian and Epipalaeolithic. This explains the scarce human activity, which was apparently restricted to the Vestibule, Transit Area and the 1st Inner Room.

Conclusions

Praileaitz I cave (Deba, Gipuzkoa) offer a remarkable sequence that begins in the Solutrean and spans to the Lower Magdalenian, Upper-Final Magdalenian and Epipalaeolithic.

According to the taxonomic and chronological information from the different areas of the site, human presence in the cavity has been very sporadic, occasional, with short periods of occupation as suggested by the low number of industrial remains, slightly manipulated fauna and the low diversity of wood used as fuel. During uninhabited periods on the part of humans, the cavity was used as a den of different carnivores and as a birds of prey shelter. Therefore, it was used for short-term occupations involving few individuals and alternating with animal predators occupations, similar to what happens in relatively close deposits such as Astigarraga, Ekain, Amalda, Zerratu, Labeko Koba or Lezetxiki. The archaeological sequence described for the Lower Magdalenian depicts a more complex use of the cave, since the singularity of the remains (a large number of decorated pendants of unique characteristics, the formation of a soil and the reduced number of evidences recovered) pointed out that this space would have been occupied for non-domestic purposes, probably related to ritual activities.

The palaeoenvironmental reconstruction reported in this study indicates that hard and cold climatic conditions dominated at the base of the sequence, i.e. Solutrean, with significant humidity variations. These conditions seem to persist during Lower Magdalenian, though a trend towards a decrease in environmental humidity is observed. Finally, the arboreal component increases during the Epipalaeolithic, stablishing forest or woodland landscape.

  1. General photo of the participants at EZI 2017; 2. Opening session (April 26th); 3. Opening keynote (April 26th) by Marta Moreno García; 4. General view of the participants during the oral presentations; 5. Official reception at the cloister of the Convent of Our Lady of the Assumption in Faro, offered by the Municipal Museum of Faro; 6. Researchers having a good time at the reception; 7. General view of the posters presented at EZI 2017: 8. The Organizing Commission addressing the participants.

Figure 1 -

 1 Figure 1 -Location and general view of the site. a: Geographical location of Praileaitz I cave (Deba, Basque Country). b: General view of the limestone quarry in which the site is located. On the right, framed in white, you can see the exact location of the cavity. c: Plan view of Praileaitz I Cave (Deba, Basque Country). In dark grey the location of the squares where the sedimentological samples were retrieved.

Figure 2 -

 2 Figure 2 -Some large mammal fossil remains from Praileaitz I cave (Deba, Basque Country). a: Phantera pardus right mandible, labial view; b: Cervus elaphus left talus, plantar view; c: Cuon alpinus left mandible, lingual view.

Figure 3 -

 3 Figure 3 -Some small mammal fossil remains from Praileaitz I cave (Deba, Basque Country). a-b: Microtus (Microtus) arvalis left m1; c: Microtus (Microtus) agrestis left m1; d: Microtus (Terricola) sp. right m1; e: Microtus (Alexandromys) oeconomus left m1-2; f: Chionomys nivalis left m1; g: Arvicola amphibius right m1-2; ha-h2: Clethrionomys glareolus right m3; i: Apodemus sylvaticus-flavicollis right m1-3; j: Glis glis right p4; k: Talpa sp. right humerus; l1-l2: Crocidura russula right mandible and; m1-m2: Sorex minutus left mandible and condyle; n1-n2: Sorex araneus-coronatus left mandible and condyle. Scale bars = 1 cm (figure k) and 1 mm (other figures).

  Naroa Garcia-ibaibarriaGa, JoNe castaños, aitziber suárez-bilbao, Pedro castaños, salvador bailoN, Xabier Peñalver, soNia saN José, José aNtoNio MuJika, JuaN rofes, Xabier MurelaGa

	Humans, macromammals and microvertebrates
	during Pleistocene and Holocene in Praileaitz I
	cave (Deba, northern Iberian Peninsula)

Table 1 -

 1

	Identification	Standardized Layer	Area	Chronology	Sediment weight
	V1	1	Vestibule	Superficial
	V2	3	Vestibule	Superficial
	V3	5	Vestibule	Epipalaeolithic
	V4	7	Vestibule	Epipalaeolithic	1998,1 g
	V5	9	Vestibule	Epipalaeolithic
	V6	11	Vestibule	Lower Magdalenian
	V7	11	Vestibule	Lower Magdalenian
	S1	7	1st Inner Room	Lower Magdalenian
	S2	7	1st Inner Room	Lower Magdalenian	1336,1 g
	S3	13	1st Inner Room	Solutrean

Relation of the acronyms used for each small vertebrate sample from Praileaitz I cave (Deba, Basque Country), their stratigraphic location, chrono-cultural attribution and weight of the sediment.

  1

	Canis lupus	96	5	242	8	182	4	6	2	13	2	19	1
	Cuon alpinus	7	2	17	4	8	2	-	-	-	-	-	-
	Vulpes vulpes	42	3	281	11	198	8	14	2	61	3	69	1

Table 2 -

 2 Number of remains (NR) and minimum number of individuals (MNI) of macromammals from Praileaitz I cave (Deba, Basque Country).

  Naroa Garcia-ibaibarriaGa, JoNe castaños, aitziber suárez-bilbao, Pedro castaños, salvador bailoN, Xabier Peñalver, soNia saN José, José aNtoNio MuJika, JuaN rofes, Xabier MurelaGa too few pollen grains were recovered so that the study is considered statistically insignificant (fewer than 250 specimens) to make a comparison of palynological and anthracological records at Praileaitz I cave. The available data suggest the presence of open landscape with low forest cover dominated by pine during the Solutrean, and low presence of juniper and birch (Iriarte-Chiapusso 2017).

	Humans, macromammals and microvertebrates
	during Pleistocene and Holocene in Praileaitz I
	cave (Deba, northern Iberian Peninsula)

Universidade do Algarve; CEAACP -Centro de Estudos de Arqueologia, Artes e Ciências do Património.

ICArEHB -Interdisciplinary Center of Archaeology and Evolution of Human Behaviour.

UNIARQ -Centro de Arqueologia da Universidade de Lisboa.

Acknowledgements

We received financial support from the Research teams GIU15/34 and IT-622-13 of the University of the Basque Country and the PALEOGATE project of the Spanish Science Ministry (HAR2014-53536-395 P). A. Suárez-Bilbao has a predoctoral fellowship from the Basque Government (PRE 2014 1 345). We thank the anonymous reviewers for their careful reading of our manuscript and their insightful comments and suggestions.

Clethrionomys glareolus

Appendix 1. Studied areas

Ledge

It represents the area located to the East of the entrance. Nineteen layers of 2 cm were excavated in 22 squares of 1x1 m, identifying six stratigraphic levels (named I-VI). Given the scarcity of lithic tools, it was not possible to establish a well-defined chronocultural sequence. Even so, two distinct phases were identified: the upper dated to Azilian-Final Magdalenian and the lower dated to the beginning of Upper Palaeolithic (40,853 cal BP).

Vestibule

This is a zone in which the excavation area has been widened on several occasions, especially after the removal of a large block of stone that obstructs part of the entrance. In total, 48 squares have been excavated in this area. The 26 layers were synthesized in seven archeostratigraphical layers (0-VI) that range from the Solutrean to the Epipalaeolithic.

Northwest gallery

The excavated area affects to 17 squares. It has been excavated 19 layers that can be grouped into seven levels (levels I-VII). The accumulation of archaeological materials against the wall, and the specific characteristics of this space, suggest that the layers from this area do not have a direct relationship with those identified in the Vestibule, except for Level V (related with Level IV from the Vestibule).

Transit area between vestibule and 1st Inner Room

Like the Vestibule, this zone was excavated in several phases of successive extensions. The excavated area has affected to 17 squares, including a hearth of large extension. The 26 layers can be grouped into five levels (I-V) that extended from Solutrean to Epipalaeolithic.

1st Inner Room

The archaeological works in this zone were carried out at 48 squares. Five levels (I-V) were differentiated in this room, which have been dug into 16 layers. Three of these levels have been adscribed to a cultural period: Epipalaeolithic (Level II), Lower Magdalenian (Level IV) and Solutrean (Level V).

2nd Inner Room A large stalagmitic column occupies 10 squares, totally or partially, in the centre of the room. Even so, the excavated area has affected 42 squares. Eighteen layers, divided into nine stratigraphic levels, have been differentiated (levels I-IX). The deposit of this area may have been altered, with the sediment being probably transported by water flow from more outer areas of the cave.

Appendix 2.

STANDARDIZED LAYER EXCAVATED AREA

Ledge