An Ancient Rule for Making Portable Altitude Sundials from an ‘Unedited’ Medieval Text of the Tenth Century

These were temporary or seasonal hours that were used in the Greco-Roman epoch and into the Middle Ages. The day was divided into twelve parts from sunrise to sunset, and likewise the night from sunset to sunrise. The sixth hour of the day was noon, and the sixth hour of the night was midnight. The length of the day hour therefore differed from day to day, being shorter in summer and longer in winter.

“seo sunne astihðo pricmEelum on pam dagmEele”, “Hawa, la cleric, hu seo sunne pricmælum stihðo on pam dagmæle”, Crawford S. J. , Byrthfert's manual (A.D. 1011) (London, 1929), 114–15. See also Baker Peter S. Lapidge Michael , Byrhtferth's Enchiridion (London, 1995).

On the contradictory work of Herwagen (Hervagius) see Jones Charles W. , Bedae pseudoepigrapha: Scientific writings falsely attributed to Bede (New York, 1939), 14–18; reprinted in Jones Charles W. , Bedae, the schools and the computus (Aldershot, 1994). On the false attribution of the Glossae to Byrhtferth, see Jones Charles W. , “The Byrhtferth Glosses”, Medium aevum, vii (1938), 1938–97, and Jones , Bedae pseudoepigrapha, 21 et seq.

“Puntus a pungendo est dictus, eo quod quibusdam punctionibus certae designationis in horologii designetur. Horologium, id est, series horarum de puncto scilicet in punctum”, Byrhtferth , Glossae et scholia , in Venerabilis Beda , De temporum ratione, in Migne Jacques Paul (ed.), Patrologia Latina (217 vols, Paris, 1844–55; hereafter: PL), xc, col. 304.

Contractus Hermannus , De utilitatibus astrolabii libri duo, Liber secundus, caput primum, Demonstratio componendi cum convertibili sciothero horologeci viatorum instrumenti, PL, cxliii, cols 405–8B.

Herwagen Johann Venerabilis Beda , Opera Bedae Venerabilis presbitery, Anglosaxonis: Viri in divinis atque humanis literis exercitatissimi: Omnia in octo tomos distincta…, i (Basel, 1563), cols 464–8.

Venerabilis Beda , Libellus de mensura horologii, PL, xc, cols 951–6.

It is possible that Hervagius has misinterpreted the text of the manuscript in his possession and that Libellus de mensura horologii is really the title of the first text.

The earliest sketches of this type of horologium are from the eighth and ninth centuries; see Schaldach Karlheinz , “Gli ‘schemi delle ombre’ nel Medio Evo latino”, Gnomonica Italiana, xvi (2008), 9–16.

In this case too the earliest text of the Concordia duodecim mensium dates back to the eighth century (see Morini Carla , “Horologium e Daegmael nei manoscritti Anglosassoni di computo”, Aevum, lxxiii (1999), 273–93, p. 286) and even before (Isidorus of Seville, De natura rerum, chap. 5, “De concordia mensium”), but we can recognize the roots of it in more ancient times.

This diagram appears together usually with other rotae in the manuscripts coming from Fleury. According to Jones, op. cit. (ref. 3), the earliest scheme of this type is found in the Ms. Paris BN, Lat. 5543, fols 134v–141r.

This text, together with (6), can be read, with slight differences, in many manuscripts and works; see Thorndike Lynn , History of magic and experimental science, i (New York, 1923), chap. 29 and appendix 2. The earliest manuscript in which this text can be read, it seems, is Ms. Berlin Staadtbibliotek Phill. 1869, fol. 12r (ninth cent.). See Jones , op. cit. (ref. 3), 88. Thorndike , History of magic, says that the earliest is the ninth-century century ms. Paris, B.N. nouv. acq. 1616, fol. 12r. It is, however, also a well known theme in Antiquity and therefore not purely medieval.

See Schaldach , op. cit. (ref. 9).

On ‘shadow schemes’, see Schaldach , op. cit. (ref. 9).

Jones , op. cit. (ref. 3), 15.

Ms. Berlin Staadtbibliotek Phill. 1833, recently consulted by me, quoted by Jones, op. cit. (ref. 3), by Arno Borst, The ordering of time: From the ancient computus to the modern computer (Cambridge, 1993), and also by Morini, “Horologium” (ref. 10) as the probable source of the sketch of the ‘shadow scheme’ (3) and of the Concordia xii mensium (4), does not contain texts 1, 6 and 7 of the Libellus. Although both Jones and Morini write that the manuscript practically presents text 4 with the same title as in the Libellus, in reality it is not this way: In the manuscript that table is divided in two parts, each entitled Concordia sex mensium.

Jones , op. cit. (ref. 3), 87.

Although I have found no others, I did work hard to find them. In their collection of incipits, Thorndike and Kibre list only A and B, but do not recognize B as a fragment of A ( Thorndike Lynn Kibre Pearl , A catalogue of incipits of mediaeval scientific writings in Latin (London and Cambridge, MA, 1963)). I call attention here to A, B and C for the first time.

Construction of the suspended sundial.

Rule to make a sundial.

B: “Inventio pendentis orologil” (“the construction of the suspended sundial”). The title of B is, as far as we know, the only one that reveals the exact nature of the sundial described in the first text of the Libellus.

C: “quod instar”.

C lacks the reference to the cylindrical sundial and we read only: “… videtur formari, per sena latera, in quibus ordo horarum totius anni….”.

I accept here the reading of B (“xii Kal^dis Iuni et iulii”) against that which is certainly wrong of A (“xii Kal. Januarii atque Julii”), which perhaps is a bad interpretation by Hervagius of the written contraction for Juni as Januarii.

In B we read: “… terminus, vel. v. horae confinium….” This value gives the best result in the column related to the months of January-December, but I have left the version of A and C because at the moment it appears in the majority.

I have translated ‘umbilicus’ as ‘gnomon’ according to the teaching of Pliny the Elder (“umbilicus, quem gnomonem vocant”), Natural history, VI, 39, 2; this lesson was approved also by Bede (“Umbilici quem gnomonem appellant”) in De natura rerum, PL, xc, cap. 48, col. 274A; see also De temporum ratione, PL, xc, cap. 33, col. 450 A.

“first section”, that is the order of the hours in the first line. It has to be understood for all the other remaining five ‘sections’.

Sundials of this type were still in use in the nineteenth century, carved in the hilt of the trip stick of the Tibetan monks. An example can be seen in the Science Museum in London: http://www.sciencemuseum.org.uk/images/I059/10325654.aspx (accessed April 2010).

de Solla Price Derek J. , “Review of T. O. Cockayne, ed., Leechdom, wortcunning and starcraft in early England [London 1961]”, Journal for the history of medicine, xvii (1962), 202–3.

We are speaking, obviously, of seasonal hours.

“Quando vis scire in dorso astrolapsus hora, in primis scias quantum sol debeat ascendere in ipsa die qua volueris horas probare, et ipsam ascensionem vel altitudinem solis a primo gradu ortus solis usque ad ultimum partire per vi partes ipsasque partes per signa, et, dum sol pervenerit ad ipsa signa in Alhidada, scias sic horas certas usque ad vi; post vi, retorna descendendo usque ad occasum. Sed tu, lector, si diligenter animadvertere quaeris, tu ipse per praedictam walzacoram, id est planant sphaeram diversa poteris fabricare horologia.” Hermannus Contractus (Gerbertus), De utilitatibus astrolabii libri duo. Liber primus, caput xxi: De inveniendis in dorso astrolabii horis, PL, cxliii, col. 404D.

Contractus Hermannus , De mensura astrolabii liber, PL, cxliii, cols 379–90A.

Hermannus Contractus, De utilitatibus astrolabii libri duo. Liber secundus, caput primum: Demonstratio componendi cum convertibili sciothero horologeci viatorum instrumenti, PL, cxliii, cols 405–8B.

He finds the shadow length by a quarter of a circle, divided into 90° on the border. The gnomon (sciothere) tip ends in the centre and from there rays reach the outer scale of degrees. At the end of the gnomon a vertical line crosses the degree rays giving the shadow length of that hour.

The text is preserved in Ms. Istanbul, Aya Sofya 4830, fol. 129r—v; it is described as a pillar dial construction with a table of vertical shadow lengths. Cf. King David A. , In synchrony with the heavens: Studies in astronomical timekeeping in medieval Islam, i (Leiden and Boston, 2004), part 4, chap. 7, para. 7.4, pp. 585–6.

Wiedemann E. Würschmidt J. , “Über eine arabische kegelförmige Sonnenuhr”, Archiv für die Geschichte der Naturwissenschaften und der Technik, vii (1916), 359–76. See also Livingston J. , “The mukhula, an Islamic conical sundial”, Centaurus, xxvi (1972), 1972–313.

For a complete description see Charette François , Mathematical instrumentation in fourteenth-century Egypt and Syria: The illustrated treatise of Najm al-Dīn al-Mīrī (Leiden, 2003), 145–53.

Arnaldi Mario Schaldach Karlheinz , “A Roman cylinder dial: Witness to a forgotten tradition”, Journal for the history of astronomy, xxviii (1997), 107–17. Recently a second sundial of this kind has been recognized in France which is dated back to the 3rd–4th century; see Christine Hoët-van Cauwenberghe and Éric Binet, with the participation of Thuet Annick , “Cadran solaire sur os à Amiens (Samarobriva)”, Cahiers du centre Gustave Glotz, xix (in press) and in Bulletin des antiquaires de France (also in press). I thank Dr Christine Hoët-van Cauwenberghe of the University of Lille 3, for telling me of the discovery before their article was published.

Ferrari Gianni , “Uno studio sull'orologio romano conosciuto come ‘Prosciutto di Portici’”, Gnomonica Italiana, no. 15 (June 2008), 2–12.

The ‘cylinder of Este’ has two gnomons: One for the summer period (the shorter one, of about 21 mm) and one for the winter period (about 27 mm). My choice of the shorter gnomon is made, of course, because the shadow can easily reach the lower hour point at the summer solstice.

The latitude of 45° is that of the ‘cylinder of Este’.

In the text of the De utilitatibus astrolabii this latitude is combined with the seventh climate which is suitable for Britain. “Climatis septimi latitudo 48 gradus et 32 minuta…. Initium septimi ab Oceano orientali … partim Franciam majorem, Britanniam, Scotiam, terram Anglicam …”, Hermannus Contractus, De utilitatibus astrolabii libri duo, PL, cxlii, chaps. 18 and 19, cols 402D–404B.

This is the latitude of Canterbury.

The length of the two gnomons is derived from calculation tests because they are now immovable due to oxidization. Schaldach and I have hypothesized lengths of 27mm and 21mm. Maybe the longer one could be between 25 and 27mm.

Arnaldi Schaldach , op. cit. (ref. 38), Figs 5 and 6, pp. 113–14.

Binns A. L. , on the basis of a passage in the Byrthferth Manual and the tables calculated for twelfth-century Iceland by Oddi, prefers to date the object to the first years of the eleventh century; see Hull A. L. Binns , “Sun navigation in the Viking age, and the Canterbury portable sundial”, Acta archaeologica, xlii (1971), 23–34.

The measurements that we use in this section have been made from the photographs of the original instrument published by Mills Allan , “The Canterbury pendant: A Saxon seasonal-hour altitude dial”, BSS bulletin, xcv/2 (June 1995), 39–44. D. Jordan furnishes different and more approximate measurements: Height 6 cm, width 2.5 cm and the gnomon 2.5 cm (the height could refer to the dial itself without the hanging ring). See Jordan D. King David A. , Überlegungen zur Angelsächsichen Sonnenuhr von Canterbury — Reflections on the Canterbury sundial (Johann Wolgang Goethe-Universität, Institut fur Geschichte der Naturwissenschaften, Preprint series no. 9, 1988), 1–16 and 17–28 respectively.

The flat shape of the Canterbury pendant is not to be considered unique; a very similar instrument, a Syrian sundial of the twelfthth century correctly calculated, has been described by Casanova ( Casanova Paul , “La montre du sultan Nour ad Din (554 de l'Hégire — 1159–1160)”, Syria, iv (1923), 282–99). A third testimony is given in the words of de Solla Price, op. cit. (ref. 29), where he wrote that he has seen a sample “of less elegance” very similar to the pendant of Canterbury in 1962, at the British Museum, but I admit that I have never seen it.

See de Solla Price Derek J. , “Portable sundials in Antiquity…”, Centaurus, xiv (1969), 242–66; de Solla Price, op. cit. (ref. 29); Binns , op. cit. (ref. 46); Jordan King , op. cit. (ref. 47); Mills , op. cit. (ref. 47); Drinkwater Peter I. , “Comment upon the Canterbury pendant”, BSS bulletin, xcv/3 (October 1995), 48.

On the bottom of the plate of the Canterbury pendant there is a hole that penetrates into the body of the instrument. The gnomon is inserted in this when not in use.

Binns , op. cit. (ref. 46).

Mills , op. cit. (ref. 47).

This position seems underlined by the head of dragon/snake that in its action of swallowing the sun in its jaws gives us a classical insight into winter iconography.

These measures do not seem casual; they are almost identical to those of the gnomons of the cylinder of Este.

Charette , op. cit. (ref. 37), 145–53.

We know almost nothing about this author, only that he came from Sicily (al-Siqillī).

‘Stick’ is not the correct translation: It would be better as ‘tongue’. It is meant to be a movable stick.

Wiedemann Würschmidt , op. cit. (ref. 36).

This has been demonstrated also by Livingson, op. cit. (ref. 36).

Schaldach , op. cit. (ref. 9) has well underlined the Hellenistic origin of the ‘shadow schemes’, even if the terminus post quem for the sketch to text no. 3 can now be established as the eighth century.

See ref. 24.

Kellog R. Sullivan M. , “The Tiberius manuscript horologium”, The compendium, iv/2 (June 1997), 1–13.

See Vitruvius , De architectura, I, 6.6; Gromaticus Hygunus , Constitutio limitum, chap. 19; Pliny , Natural history, II, 76.

Although the grave of the Este physician has been dated to the first century, the sundial was probably of the first half of the first century b.c. See Arnaldi Schaldach , op. cit. (ref. 38). The Roman handbooks of gnomonics covered a wide range (unfortunately little has survived) and are attested by Vitruvius, who in chap. 8 of the ninth book of his De architectura writes: “Item ex his generibus viatoria pensilia uti fierent, plures scripta reliquerunt. Ex quorum libris, si qui velit, subiectiones invenire poterit, dummodo sciat analemmatos descriptiones.”.

The measures of the shadow lengths of the other hours of the day seem to be found in simple manuals, such as the Libellus, with simple folk methods.