1. the Influence of the Difference ‰Ê Between the Astronomical and the Angles Is ±3” and in Measuring Distances Is ± 3Mm ± 3Ppm

ON THE DATE OF THE KATHOLIKON OF DAPHNI MONASTERY. A NEW APPROACH BASED ON ITS ORIENTATION

GEORGE PANTAZIS National Technical University of Athens School of Rural and Surveying Engineering Department of Topography Athens, Greece email: [email protected]

MARIA PAPATHANASSIOU National and Kapodistrian University of Athens Faculty of Mathematics Department of Algebra and Geometry Athens, Greece email: [email protected] Received: 21 - 11 - 2004 Accepted: 26 - 4 - 2005 *to whom all correspondence should be addressed

ABSTRACT The exact date of the foundation of the Katholikon of Daphni monastery is unknown. Based on the stylistic data of its mosaic decoration the archaeologists suggest that its mosaics date to the end of the eleventh century, which is either a terminus ante quem for the construction of the Katholikon or the mosaic decoration is contemporary to this construction. In this paper we attempt to determine the foundation date of the Katholikon of Daphni, on the base of its astronomical orientation and by applying the general astrogeodetic method elaborated by one of us (G. Pantazis) in this case. As results from our investigation, the Katholikon, which is sacred to the Virgin Mary, was very likely founded on the day of the celebration of the Dormition of the Virgin in 1153, i.e. in August 15, 1153 (±8years). If it is so, both the church and its famous mosaic decoration date circa half a century later than it is generally accepted by the archaeologists.

KEYWORDS: Geometric documentation, astronomical observations, azimuth, Perceptible horizon, diurnal path of the Sun. 64 G. PPANTAZIS - M.PAPATHANASSIOU ON THE DATE OF THE KATHOLIKON OF DAPHNI MONASTERY 65

THE DAPHNI MONASTIC while its upper parts and the towers, built squinches and eight pillars (i.e. a regular METHODOLOGY COMPLEX HISTORICAL DATA with common stones and in a different style octagonal plan). This type of dome, which In order to determine the date of the of stonework, are part of restoration works allowed space that might be used for a foundation of the Katholikon, we should and completion of the surrounding wall in larger chamber – the diameter of domes on firstly calculate its exact orientation by the Byzantine times. According to the pendentives being generally smaller- was following steps: archaeological evidence, the Byzantine much admired in Greece in the eleventh ñ Geometric documentation of the surrounding wall was a square with a side of century (Grabar 1966). Katholikon and digital drawing of its one hundred meters. Its main entrance was The Katholikon of Daphni has one out of plan. at the West Side and not at the east one as it the three important mosaic decorations in ñ Astronomical observations for the is today. Greece, the other two being the church of determination of the astronomical Archaeological evidence shows further Hosios (the Blessed) Lucas in Phokis and azimuth of any direction. that in the seventh century at the center of that of the New Monastery in the island of ñ Geometric determination of the main this enclosure an Early Christian ‘Basilica’ Chios. Although we know nothing about axis of the monument and its was built possibly as the ‘Katholikon’, i.e. either date or their origin, according to A. astronomical azimuth. Fig. 1: The Daphni monastic complex the main church, of the early Byzantine Grabar the theoretical place occupied by ñ Geometric determination of the profile monastery (Kambouroglou 1920). This Daphni in the history of Byzantine painting of the perceptible horizon, as seen from The famous Daphni monastic complex Basilica is not saved but in the eleventh can be found thanks to stylistic similarities a specific position inside the monument. between various details. Namely, in Daphni (Fig. 1) is situated in the middle distance century a new church was built almost at ñ Reconstruction of the apparent diurnal the same place. This latter is the finest we discover the future style of the (c. 10km) between Athens and Eleusis, and path of the Sun as seen from the Byzantine monastic church of the district of Comnenian period in the second stage of its on the left side of the ancient ≤sacred road≤ monument, in specific dates. Athens. formation. So it is reasonable to date the In the following paragraphs we explain to Eleusis. It is built on the place of an The domical method of construction mosaics of Daphni to the end of the eleventh each one of the above mentioned steps. ancient sanctuary dedicated to Apollo, later governs the plan of Byzantine churches, century, as suggested by G. Millet (Grabar also to Athena, Demeter and Kore, which are all distinguished by a central 1966, 127). GEOMETRIC DOCUMENTATION according to Pausanias (Description of square nave, covered with a dome on On the northern side of the Katholikon First of all by using the GPS system the Greece, Attica, ch.37, 6-7). In Pausanias’ pendentives. Short arms on each side form a was a long building, the Refectory of the geographic coordinates (Ê= latitude, time (c. 150) there was a surrounding wall Greek cross, and the filling in of the angles monastery, almost always the next most Ï=longitude) of the place of the monument splendid building in a monastery after the enclosing at least one temple and one gallery brings the plan nearly to a square. In early (Ê = 38Æ 00 46 N, Ï = 23Æ 38 10 E) Katholikon. Here the monks eat together ’ ” ’ ” (or another building with columns), as examples the dome is supported by semi- were measured. Both are necessary for the and this meal taken in common and served domes. In later examples, the churches are calculation of the astronomical azimuth and there are many drums of columns and immediately after the main religious much smaller and the dome is raised upon a the reconstruction of the apparent diurnal capitals doric and ionic. The ancient service, is regarded as its continuation. high drum with, occasionally, additional path of the Sun as seen at the place. sanctuary survived at least during two and Earthquakes in 1886, 1889 and 1894 smaller domes rising at a lower level. At the Further a polygonometric network half centuries after Pausanias, i.e. until the produced great damages in the narthex of west end is usually a narthex, or entrance consisting of 31 points had been established edicts against pagan religion issued by the Katholikon, as whole parts of it porch, which forms an entrance vestibule, inside and outside the monument (Figure emperor Theodosius I and his successors. frequently crowned with domes. At the east collapsed. The works of restoration under the supervision of the French architect 2) (Project ‘Development of modern Some prechristian remains have been end, opposite the entrance, is the apse for Topographic and digital Photogrammetric used in the buildings of the monastic the altar in the sanctuary, which is screened Troump included the reconstruction of the narthex, of the north west chapel and of the methods for the geometric documentation complex. On the other hand, rectangular off by the characteristic ‘iconostas’ (screen walls of the upper floor, as well as that of the and the total architectural digital drawing of stone blocks of the ancient surrounding wall of icons, i.e. pictures), with its three doors, dome according to the initial plan. The last Byzantine monuments, Application at the have been used in the Byzantine fortress and there were also lateral ritual chapels earthquake of September 1999 produced Daphni Holy Monastery’, NTUA 1999). wall. (Banister 1961). more serious damages and until now is Its ‘elements’ (namely the distances The best saved side of the latter is its The Katholikon of Daphni is a slender going on works for the restoration of the between selected points and the angles lower part along the National Road, which is construction bathed in light because of its formed by these line segments) were the same northern side of the ancient wall, building and especially for the conservation large dome on a squat barrel, supported by of its famous mosaics. measured by using the total station TC 0 0 4 2 1 2 66 G. PPANTAZIS - M.PAPATHANASSIOU ON THE DATE OF THE KATHOLIKON OF DAPHNI MONASTERY 67

240 240 This system, with the appropriate software, N S4 allows the determination of the D A S26 S2 astronomical azimuth of a direction in short S fieldwork time and with high accuracy 220 S3 S9 (Lambrou 2003). S24 S10 S17 S12 S18 S29 Three sets of measurements were carried S13 S5 S22 S19 S23 S14 out. The table 1 gives the calculated values S28 S30 S11 S20 200 S16 S1 S27 S15 S31 of the astronomical azimuth of each set and S21 S6 S8 S25 the corresponding uncertainties. The mean value of the astronomical azimuth is determined by using weights and 180 S7 180 0 0 0 0 0 6 8 0 4 2 1 1 2 1 2 assuming that the standard deviation of the unit weight is ÛÔ = ±0.3”. Fig. 2: The polygonometric network To the final determined uncertainty must also be added: 1600, the accuracy of which in measuring 1. The influence of the difference ‰Ê between the astronomical and the angles is ±3” and in measuring distances is ± 3mm ± 3ppm. geodetic latitude used for the All the detail points of the building were determination of the astronomical carefully measured by using a reflectorless azimuth. Taking into account that the total station with a laser pointer, in order to difference ‰Ê at the place of the mark the position of each point with great monument is about ±10”, this increases precision. The accuracy of the the uncertainty by an amount of ±0”.1. determination of the coordinates X, Y of each point of the monument is ± 3mm so Fig. 3:The plan of the Katholikon of Daphni monastic complex that we can draw the monument’s digital plan in a scale 1:50. All characteristic geometric elements of the Katholikon of Daphni monastic complex are displayed in ñ Point 9 defines the middle of the altar. the following digital plan (Fig. 3). DETERMINATION OF THE MAIN ñ Finally, point 10 defines the middle of Table 1: The value of the astronomical azimuth. AXIS OF THE MONUMENT. the narrow window at the central apse. DETERMINATION OF THE The Katholikon of the Daphni complex ASTRONOMICAL AZIMUTH 2. The influence of the difference ‰Ï is a symmetric building in respect to its The astronomical azimuth of the side of between the astronomical and the main longitudinal axis. The basic points of the polygonometric network, which is geodetic longitude used for the this axis are determined by the digital plan defined by the points S1 and S3, has been determination of the astronomical of the monument, after its documentation. determined by means of astrogeodetic azimuth. Taking into account that the These points are the following (Fig. 4): observations of the Pole Star (Polaris, difference ‰Ï at the place of the ñ Points 1 and 2 define the middle of the aUMi), using the hour angle method. monument is about ±20”, this increases west entrance. These observations have been done with the uncertainty by an amount of ñ Points 3,4,5,6 and 7 define the middle of . -3 a system of a high precision digital total ±0.”2 10 (Lambrou 2003). the distances between five pairs of station, Leica TDM 5000 connected to a The final value of the astronomical columns.

Trimble 4000DL GPS receiver, providing azimuth of the direction S1-S3 and its ñ Point 8 defines the middle of the west accurate UTC time, placed at the point S1 in uncertainty is: side of the altar. At this point the priest Fig. 4: The points of the main longitudinal axis of the church. front of the central apse of the Katholikon. AS1–S3 = 310Æ 7’ 16”.9 ± 0”.2 stands during the Holly Service. 68 G. PPANTAZIS - M.PAPATHANASSIOU ON THE DATE OF THE KATHOLIKON OF DAPHNI MONASTERY 69

The coordinates of the above points in very important role in the investigation of the arbitrary reference system are (table 2): the meaning of the monument’s orientation. This is due to the fact that the apparent positions of the celestial bodies at the time of their rising or setting as seen from the monument depend on the profile of the perceptible horizon in respect to the monument. The profile of the perceptible horizon (skyline) at a specific position on the earth is defined as the projection of the outline of either hills, mountains or buildings situated at the direction of view of an observer Table 2: The coordinates of the points of the main standing at this point against the celestial longitudinal axis. sphere and celestial bodies (Sun, stars). In the case of a monument the direction of view The final longitudinal axis of the coincides with that of its characteristic axis monument is the best fitting line to those (Pantazis 2002). ten points according to the formula In order to determine the profile of a Y = · . X + b + u perceptible horizon, it needs first to Fig. 6: The profile of the east wall. The parameters ·, b, u are calculated by calculate the coordinates of the specific means of the least square method and the position – point, to find a reference direction The results of the measurements are ñ The astronomical coordinates º, § of the astronomical azimuth of this line is and then measure the horizontal and illustrated in a diagram (Fig. 6) where the x monument’s place. determined with the corresponding vertical angles having this point as vertex. – axis shows the azimuth (Az) and the y – ñ The date (any date between 4713 B.C. accuracy: The perceptible horizon of the axis shows the altitude (˘) of each point of and 8000 A.D.). the profile. The dashed line shows the The apparent diurnal path of the Sun, is A = 94Æ 6’ 44” 0’.6 Katholikon of Daphni Monastery is the wall The astronomical azimuth of the built on the east of the church. The study original profile of the east wall of the calculated for August 15 – celebration day of calculated longitudinal axis of the and the analysis of historical sources and enclosure, as seen from the middle of the the ‘Dormition of Virgin Mary’ - during four monument will be used for its orientation. other related documents lead to the altar. hundred years, namely from 900 to 1300 conclusion that the east side of the enclosure The photographic documentation of the A.D., and is illustrated in a diagram where DETERMINATION OF THE saved until now was the same as that of its horizon profile is illustrated in Fig. 5. the x-axis shows the azimuth (Az) and the PROFILE OF THE PERCEPTIBLE north side (Bouras 1998). Consequently The total error in the determination of y-axis the altitude (˘). HORIZON. both had the same height, namely that of the profile of the perceptible horizon is Ûhor The perceptible or conventional horizon the northern wall, ca. 5.00m. = ±1’.2 THE DATE OF THE KATHOLIKON extending in front of a monument plays a OF DAPHNI MONASTERY DETERMINATION OF THE PATH Thus the series of successive diagrams OF THE SUN drawn for the 15 August shows that the In order to determine the apparent diurnal path of the Sun for the year 1153 diurnal path of a celestial body, as seen from A.D. passes through the point at which the monument’s place, in a given date, we intersect the direction of monument’s main used the Sky map Pro8 software - a digital longitudinal axis defining its astronomical almanac and virtual planetarium (Marriot azimuth and the profile of the percrptible 2001). Our data were the following: horizon (Fig. 7). Moreover, as shown in this ñ The celestial body (the Sun) whose path diagram there is no other day or year in Fig. 5: The photographic panorama of the eastern part of the horizon. must be calculated. which the Sun’s path passes through this 70 G. PPANTAZIS - M.PAPATHANASSIOU ON THE DATE OF THE KATHOLIKON OF DAPHNI MONASTERY 71 point of intersection. Consequently, it The striped area ABCDA in the figure 8 In the case of the Katholikon of Dapnhi accuracy of ±0.6’; consequently it faces becomes obvious that the Sun’s path for the corresponds to the total error of the having as data: South – East. Further we arrive at the th 15 August 1153 A.D. is unique, namely the methodology, which is Ûtotal =±73’. H The digital plan of the monument; conclusion that the Katholikon of only one which passes through this point. The annual change of the apparent H The main longitudinal axis of the Daphni is oriented to the Sun and it th diurnal path of the Sun for August 15 monument (determined by a geometric dates in 1153 A.D. ±8years, which

ACCURACY OF THE DATE from the monument’s place is dSun= 10” method) and the value of its astronomical means that it has been built sometime The final accuracy of the determination Consequently the date uncertainty is: azimuth. between the years 1145 A.D. and 1161 of the foundation date of the church can be H The profile of the perceptible horizon; A.D. calculated if they are known: H The geographic coordinates (latitude Moreover, as in 15 August the diurnal ñ The total error of the methodology. and longitude) of the place of the path of the Sun, the azimuth of the main ñ The annual change of the diurnal path of practically ±8 years monument. longitudinal axis of the monument and the the Sun for a specific date (d sun) H The diurnal path of the Sun drawn for profile of the perceptible horizon meet at According to the formula: the place of the monument in a special the same point, it is confirmed that the

Date uncertainty = ± Û total / dSun CONCLUSIONS date; we find that the accurate value of Katholikon of Daphni Monastery is sacred ñ The error of the methodology depends An accurate determination of the its orientation is 94Æ 6’ 44” with an to the Dormition of Virgin Mary. on: orientation of a monument can be made by ñ The error of the determination of the means of modern digital total stations in astronomical azimuth of the main which a combination of geodetic and longitudinal axis, which is ±0’.6. astronomical methods and procedure are ñ The error of the determination of the used. profile of the perceptible horizon, which It is possible to determine approximately is ±1’.2. the foundation year of the monument (date) The error of the determination of the as well as to identify the saint to whom it diurnal path of the Sun, which is ±2”. was sacred.

Fig. 7: The diagram of the perceptible horizon towards East, the apparent path of the Sun and the main Fig. 8: The total error of the methodology for the orientation of the longitudinal axis. Katholikon 72 G. PPANTAZIS - M.PAPATHANASSIOU

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