First. note that the gnomon as described so fartouches the dial face <strong>in</strong> only one po<strong>in</strong>t. It may beeasier to construct and more stable <strong>in</strong> practice todivide the gnomon <strong>in</strong>to two parts separated by aspace designed to lend stability. The hour scalemust be similarly separated, just as is the casewhen a traditional dial is separated at noon for athick gnomon (see Figure 3).Second, note that it is a good idea to give thegnomon a significant thickness. In this way, thegnomon's shadow will have a straight l<strong>in</strong>esegment <strong>in</strong>stead of a s<strong>in</strong>gle po<strong>in</strong>t on the hour l<strong>in</strong>e;this makes it much easier to determ<strong>in</strong>e exactlywhich part of the shadow is to be used to tell time(see Figure 3). A straight l<strong>in</strong>e shadow will falldirectly on the straight hour l<strong>in</strong>e.F<strong>in</strong>ally, for those who prefer a vertical dial, notethat this exact same gnomon can be used toproduce a vertical direct east or west dial, s<strong>in</strong>cesuch a dial is noth<strong>in</strong>g more than a polar dialdisplaced 90° <strong>in</strong> longitude (6 hours <strong>in</strong> time). Thecycloid will touch the dial face and lie <strong>in</strong> theequatorial plane as it does here. The hour l<strong>in</strong>eswill be equi-spaced and parallel to the celestialaxis, with 6:00 (am or pm) replac<strong>in</strong>g the orig<strong>in</strong>alnoon l<strong>in</strong>e, and noon now at the po<strong>in</strong>t where dialface and gnomon meet. Only one half of thegnomon is needed s<strong>in</strong>ce direct east and westdials function only <strong>in</strong> the am or pm, respectively.Fred Sawyer8 Sachem Drive, Glastonbury CT 06033frederick. sawyer. es. 72@aya.yale.edutII<strong>Sundials</strong> In <strong>Iran</strong>Mohammad Bagheri (Tehran, <strong>Iran</strong>)Design<strong>in</strong>g sundials has a long history <strong>in</strong> <strong>Iran</strong>. Inan astronomical book entitled Zij-e Shahriyar("Astronomical tables of the K<strong>in</strong>g"), composed <strong>in</strong>pre-Islamic <strong>Iran</strong> possibly <strong>in</strong> 555 C.E., there was achapter on a method for graduat<strong>in</strong>g sundials.This book was translated from Pahlavi (Le. MiddlePersian) <strong>in</strong>to Arabic around 790 C.E. The orig<strong>in</strong>altext and the Arabic translation are not extant.However, the em<strong>in</strong>ent <strong>Iran</strong>ian scholar al-Biruni(973-1051) has quoted this chapter from Zij-eShahriyar <strong>in</strong> his Arabic work on shadows.1The earliest extant treatise on sundials written byan <strong>Iran</strong>ian scholar is that by Muhammad ibn'Musa al-Kwarizmi (ca. 870 - ca. 950), entitled'Amal a/-saat fi basit al-rukhama ("Construction ofhour [l<strong>in</strong>es] on the plane of a sundial"). Thesundial described <strong>in</strong> this treatise consisted of ahorizontal marble board and a gnomon. AIKwarizmi wrote this treatise <strong>in</strong> Baghdad.2Horizontal and vertical sundials are mentionedamong the astronomical <strong>in</strong>struments that acerta<strong>in</strong> Jamal ai-D<strong>in</strong> Bukhari took with him fromMaragha (an <strong>Iran</strong>ian center of astronomicalactivity <strong>in</strong> the 13th century to Ch<strong>in</strong>a.3Ghiyath ai-D<strong>in</strong> Jamshid al-Kashi, a famous<strong>Iran</strong>ian mathematician and astronomer of the 15thcentury, was also skillful <strong>in</strong> design<strong>in</strong>g sundials.He left his native city Kashan (<strong>Iran</strong>) forSamarkand upon the <strong>in</strong>vitation of Ulugh Beg,Tamerlane's grandson, <strong>in</strong> whose court there was1 Abu al-Rayhan Muhammad ibn Ahmad al-Biruni, Ifrad almaqalfi amr al-zilal ("'The exhaustive treatise on shadows"),tr. & comm. By E.S. Kennedy, 2 vols., Institute for the Historyof Arabic Science, University of Aleppo, Aleppo, 1976, 1:199,2:125.An analemmatic dial by Karan Rashad at theEducation Office <strong>in</strong> Tehran2 B.A. Rosenfeld, "<strong>Sundials</strong> <strong>in</strong> Islam:, <strong>in</strong> Encyclopedia of thehistory of science, technology, and medic<strong>in</strong>e <strong>in</strong> non-Westerncultures, ed. H. Sel<strong>in</strong>, 1997, pp.921-922.3 W. Hartner, "The astronomical <strong>in</strong>struments of Cha-ma-Iut<strong>in</strong>g,their identification, and their relation to the <strong>in</strong>strumentsof the observatory of Maragha", Isis, 1950,41:184-194.CJbe Compendium - CVolumej 9Yumber 4 CVecember 199(3 epage 24
tOn July 13, 1998, Paolo Vis<strong>in</strong>t<strong>in</strong>i, a youngastronomer from Ud<strong>in</strong>e (Italy) and a member ofAFAM (Associazione Friulana di Astronomia eMeteorologia) who is <strong>in</strong>terested <strong>in</strong> sundials as ascientific hobby, gave a lecture on sundials at theHistory of Science Institute of Tehran University.The hall was full of enthusiasts for sundials.! IiStone dial <strong>in</strong> al-Zahra University (Tehran) by dialistFatemehAzimlouan active circle of poets, writers, artists, andscientists. He reported on his new environment<strong>in</strong> leUers to his father who lived <strong>in</strong> Kashan. In oneof the letters, he describes his calculation of avertical sundial on a wall of the royal house whichwas neither <strong>in</strong> the East-West nor <strong>in</strong> the NorthSouth direction.4 There are masterpieces ofcomposite astronomical <strong>in</strong>struments such asthose made for f<strong>in</strong>d<strong>in</strong>g the direction of Mecca andthe time of day, made by skilled <strong>Iran</strong>ian craftsmen<strong>in</strong> the Safavid period (16th - early 18th centuries). 5After the <strong>in</strong>troduction of modern clocks <strong>in</strong> <strong>Iran</strong>sundials were abandoned. At present, ther~rema<strong>in</strong> some simple horizontal sundials <strong>in</strong> certa<strong>in</strong>mosques or universities of <strong>Iran</strong>. However, thereis a new trend towards sundial theory andpractice among young <strong>Iran</strong>ian amateurastronomers. A Persian book on sundials byM.A. Ahya'i was published <strong>in</strong> <strong>Iran</strong> <strong>in</strong> 1985. I havedesigned a sundial kit <strong>in</strong> the form of a postcardfor the latitudes of the cities of <strong>Iran</strong>. It was<strong>in</strong>spired by a similar one for higher latitudes that Ibought <strong>in</strong> Deutschmuseum some years ago.A' vertical dial <strong>in</strong> Isfahan, <strong>Iran</strong> with the motto "In thename of the God of the revolv<strong>in</strong>g sphere".At present, the dialists <strong>in</strong> <strong>Iran</strong> rely on two types ofsources, accord<strong>in</strong>g to their <strong>in</strong>terests andmotivations <strong>in</strong> this field: the <strong>Iran</strong>ian tradition ofsundials as found <strong>in</strong> manuscripts, and modernEuropean sources. Further, one may alwayshope to discover an abandoned sundial whentravel<strong>in</strong>g <strong>in</strong> <strong>Iran</strong>. With so much sunsh<strong>in</strong>e <strong>in</strong> ourcountry, we hope to found our <strong>Iran</strong>ian SundialSociety and to set up many more sundials <strong>in</strong> <strong>Iran</strong>.There are many Persian and Arabic treatises onsundials <strong>in</strong> <strong>Iran</strong>ian libraries' manuscriptcollections. Moreover, astrolabes and horaryquadrants, as well as manuscripts about theirdesign, construction and application, are a majorpart of the sundial tradition <strong>in</strong> <strong>Iran</strong>.4 Mohammad Bagheri, "A newly found letter of al-Kashi onscientific life <strong>in</strong> Samarkand", Historia Mathematica, 1997,24:241-256.5 D.A. K<strong>in</strong>g, "Two <strong>Iran</strong>ian world maps for f<strong>in</strong>d<strong>in</strong>g the directionand distance to Mecca", Imago Mundi, 1997,49:62-82.Len Berggren and Mohammad Bagheri at a sundialconference <strong>in</strong> LiegeMohammad BagheriP.D. Box 13145-1785, TEHRAN, <strong>Iran</strong>bagheri@math.sharif.ac.irCJbe Compendium - CZJolume 5 9Yumber 4 CJJecember 199(3 epage 25
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