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.THE ASTRAL CLOCK IN ARDEKÂN

By: Homayoon San'ati-zadeh

Abstract: Besides the usual solar calendar, another calendar is common in Ardakaan in the province of Yazd. This calendar could be a vestige of the Yazdgirdian calendar. In this calendar the year is divided into 12 months of 30 days each, and the last five days of Esfand (Dec 22 - Mar 21) is known as 'Pandjeh-ye Mustaragheh'. Days are divided into 8 parts each of which is called a 'tassooj'. Each 'tassooj' is divided into 24 parts (7.30 minutes) called 'saboo'. This calendar has important differences with other local and old calendars in use on the Iranian plateau.

1 - INTRODUCTION
The geographical and historical conditions of the Iranian plateau together have made this land, a museum of old and primitive calendars. Each river, spring, or qanaat, has had an operation cycle which served as a practical automatic noiseless clock in the locality. The traditions and the customs for allocating water and for irrigation are in fact a reflection of the customs and traditions of time-keeping at the time the irrigation network was being established.

The influence of the 'Behizaki' 1440-year cycle of the Avestan system of chronology [1], perhaps can be seen in every irrigation system where the water is divided into 1440 portions or into multiples of it. For example, the complicated and elaborate irrigation system of 'Baagh-e Sar-Aassiab', located on the suburbs of Kerman, which has most probably survived from the Sasanian times, involves dividing water into 2880 portions. It mostly resembles a water bank rather than a simple irrigation arrangement ('nasagh'). The important difference between the concepts of 'distorted hour'[2] and 'proportionate hour' [3], is simply reflected in the differences between the irrigation traditions of Naayin and the 'Qanaat-e Ghastaan' village in Kerman. In both places the day is divided into two day-time and night-time 'taaq's. Each 'taaq' is then divided into 72 parts which is called 'sorqeh' in Nayin, and 'jor'eh' or 'jorreh' in Qanaat-e Ghastaan. In Naayin the tradition was to reduce the number of the 'sorqeh's in the night-time 'taaq' and add to those of the day-time 'taaq' as days grew longer. In the longest days of the year the day-time 'taaq' consisted of 83 'sorqeh's and the night-time 'taaq' consisted of 61 'sorqeh's. But in Qanaat-e Ghastaan, each 'jor'eh' is further divided into 3 'tashteh' and the number of 'jor'eh's in the day-time 'taaq' and night-time 'taaq' always remain constant. Rather, the number of the 'tashteh's in each 'jor'eh' changes in winter and summer. On the first day of summer, the longest day of year, each 'jor'eh' is 3.5 'tashteh's during the day, and 2.5 'tashteh's during the night. Of the multitude of traditions, customs, tools and devices used for chronometry and for allocating water, in various corners of the Iranian plateau, what has been the custom in Yazd's Ardakaan, is the most interesting one. It's a pity that this system is being forgotten and is falling out of use.

2 - THE LOCAL CALENDAR OF ARDAKAAN
In Ardakaan, besides the usual solar calendar and lunar calendars reckoned from Hegira, there is a third calendar. In this calendar each year is divided into twelve thirty-day months. Then there is the well-known five-day period at the end of Esfand, known as 'pandjeh-ye mustaragheh'(literally 'the stolen five days' or rather 'the lost five days'). The solar calendar reckoned from Hegira, decreed in 1925 as the official national calendar by the Parliament, is called the "government calendar" by the Ardakaanis and is only used in official correspondence and documentation. For the local daily use, they still use the so-called "local" calendar. When, for example, the local people talk about Mehr 10th, they mean Mehr 4th (September 26th) in the government calendar. One can imagine that the common calendar in Ardakaan is a vestige of the 'Djalali' or 'Malekshahi' calendar that was created during the reign of Sultan Djalal-al-Din Malek-Shah-e Saljuqi, probably at the instigation of Khaadjeh Nezaam-al-Mulk, by a group of astronomers and mathematicians of the period, including Omar Khayyaam and Khaadjeh Abdollah Khaazeni. The problem with this assumption is that in the 'Djalali' calendar, provisions were made to account for the fraction of day which needs to be added to the 365 days to make a whole year (approximately 6 hours). But so far as the author of this article has researched, there are no leap arrangements in the local Ardakaan calendar.

It can be assumed that the common Ardakaan calendar is a vestige of the famous 'Yazdgirdian' calendar. According to Mas'oodi:

"The Yazdgirdian year, is the year that was common in the Iranian calendar. It consisted of 12 thirty-day months and five days in 'pandjeh-e mustaragheh'."

The Yazdgirdian calendar is very much similar to the ancient Egyptian calendar. In the Persian Encyclopedia (Mussaaheb's Encyclopedia), it is written:

"Since ancient times the Egyptians celebrated the dawning of Sirius, since its appearance just preceded with the annual rising of the Nile water. The Egyptians based their calendar on this event. The Egyptian year consisted of 365 days, each year had twelve 30-day months and the remaining 5 days were celebrated."

The local Ardakaan calendar, has other relatively major differences with other local calendars and with old calendars of the Iranian plateau. One of these differences is the fact that in contrast to the customary division of day into 24, twelve, or six parts, the Ardakaanis divide the day into 8 parts as follows:

1. 'Awal-e nim-show' (the beginning of midnight)

2. 'Tasoo dam-e sobh' (the early hour of the day)

3. 'Sar-e aaftaab' (sunrise)

4. 'Tasoo baalaa aamadeh' (the hour of noon)

5. 'Pishin zohr' (early afternoon)

6. 'Tasoo show-maandeh' (the hour before nightfall)

7. 'Aaftoo koo-rafteh' (sun behind the mountains)

8. 'Tasoo show-mireh' (the night hour)

Each of the above parts, equal to three hours, is call a 'tasooj'. Each tasooj is further divided to 24 parts, which is called 'saboo' and is equal to 7.5 minutes. The day comprises 192 saboos, divided into two night and day taaqs (each taaq = 96 saboos).

Another difference of the local Ardakaan calendar with other common calendars in the Iranian plateau, as related to irrigation, is that they start counting time from midnight, and this is not to be taken lightly. In this land, it has been customary to start counting the hours from the sunrise or the sunset. But in astronomy, this is not a desirable origin, since the length of the day is variable. In ancient times, the astronomers, and only they, used noon or midnight as the origin for their calculations. The fact that in modern times, midnight is used as the origin of time all over the world, is a recent event and is a result of the development of radio and television and aerial navigation. There is evidence that among the ancient Iranian astronomers, the use of midnight as the origin of time was common. In his book, "Aassar al-Baqieh", Abu-Reyhaan writes:

"Other astronomers have chosen the invisible half of the meridionical circle and begin a day from midnight, as the author of the Shahriaran Shah astronomical tables had chosen to do." [4]

There are many strange stories about the 'Shahriaran Shah' or 'Malek al-Mulook' astronomical tables. The most influential Iranian astronomer after Islam and a forgotten genius, Abu Ma'shar-e Balkhi, is quoted to have said that this astronomical table had been devised before Noah's Storm, and it had been preserved in an elevated and safe place, somewhere near today's Isfahan.

Outside the Iranian plateau, only in China midnight was used as the origin of time in a day. In "Sharh-e Beest Baab" (the exegesis of twenty chapters), Mulla Muzaffar writes about the Chinese calendar:

"... and they use midnight as the beginning of the day as we mentioned before." [5]

3 - ARDAKAAN'S ASTRONOMY AND ASTRONOMERS
From among a hundred and fifty crystal-clear and fully flowing qanaats in Ardakaan and its suburbs, only two or three tiny qanaats are passing away the last days of their lives. The rest have dried up and died. The supervision over the division and the conveyance of water is carried out by a few experienced and expert 'dashtbaan's ('night watches' or literally 'watchers over the land'); all the dashtbaans were famed to be astronomers. Although, like the qanaats, few of these astronomers still survive, the minds and ears of the people of Ardakaan and its suburbs are still familiar with the words "astronomer' and "astronomy". If a stranger asks them about an astronomer or about astronomy, they will not be surprised, instead they will lead him to a certain mosque to look for a certain person when the prayers are held.

The writer of this report was fortunate enough to meet and talk to some of these astronomers, and to be amazed to meet old men who did not know alphabet, but who had measured accurately the longest day and shortest night of the year, and had done this several times during their lives. One of them was Haadj Huseyn Ghaane'i, son of Abu-Taaleb, and another was Haadj Seyyed Ali Khebreh. Haadj Huseyn is a lively and witty old man, eighty-some years old, he is the oldest astronomer of Ardakaan. He has personally experienced the fact that contrary to the common belief, it is not on the first day of Farvardin (March 21st, the first day of the first month of the Iranian calendar) that day and night are of equal lengths. According to his experimentation, it is on the fifth of Farvardin (Farvardin 5th of the local calendar = Farvardin 5th in the governmental calendar) that the lengths are equal.

For the writer, the interest shown by the local water master ('miraab') and astronomer in making an accurate determination of the length of night, was very intriguing. The surprise subsided when I understood that in the dry desert climate, water lasts one third longer at night than at day, and the hard-working Ardakaani farmer prefers to have water delivered to him at night. The instrument for measuring time for the purpose of allocating water, like many other villages of the Iranian plateau, is a very rudimentary and simple water clock which is known by the various names 'tasht'(a basin), 'saboo'(a cup), 'jor'eh' (a sip), 'sorgheh', 'tasooj'(an hour), and 'pangaan' (a copper bowl).

"Saboo-kashi" (measuring by saboo) or "waiting by saboo" is the act of putting a metal cup which has a known volume and a copper-welded hole at its bottom, on a bowl full of water. The 'saboo' is fully submerged in a certain amount of time (say seven minutes and a half). This method of measuring time has been common almost everywhere in Iran, as well as among the peasants in the villages of China. In every village, the water masters and the dashtbaans usually performed this task in a certain place where all those interested could gather.

Apparently, in Yazd's Ardakaan and its suburbs, the local people insisted on supervising the operation of the dashtbaans and the water masters, and the latter did not like to go to the appointed place for saboo-kashi, therefore, they had devised methods for knowing about the water allocation situation and whose turn it was to receive water, through the measurement of the length of shadows during the day and the sequence in which the stars appeared in the sky during the night.

The result is that we find some local version of constellations which are different from the ones related to the solar calendar and the zodiac, and also different from those related to the stations of the Moon.

From the first day of Sagittarius (November 22nd), the dashtbaan has complete control over the water. From Esfand 9th to Esfand 12th (End of February to March 3rd), water is free. From midnight Esfand 12th (March 3rd) the accounting begins on the following basis:

Each of these stars rise half a saboo earlier each night."

This the heavenly astral clock of Yazd's Ardakaan, which until before the qanaats dried up and wrist watches became popular, was used by everyone in Ardakaan and the surrounding villages; a magnificent, immense, bright, and scintillating clock, slow and mild, with no need for batteries, electricity, or winding up.

Every tourist who is fortunate enough to see this clock, after overcoming the initial amazement at such a useful and intelligent scheme, will have many questions to ask, including:

-How does this clock work? What is its mechanism? How was its
clockwork assembled?
-When was it built, in which century or period?
-Is it the only such means of chronometry in the Iranian
plateau?
-Does or did such a clock exist outside the Iranian plateau,
in other parts of the world with old civilizations such as
Egypt, Mesopotamia, Indian, and China?

To the extent that it is possible, we will try to answer these questions in the rest of this article.

4 - THE OPERATION AND THE STRUCTURE OF ARDAKAAN'S ASTRAL CLOCK
To prepare the mind for picturing the structure of the clock and for how it operates, first one should note that:

(a) The clock is made of stars and it cannot be seen during the day.
(b) Its face consists of the eastern horizon.

Therefore, unambiguous and precise definitions of 'night' and 'east' are needed. A concise definition of 'night' would be as follows:

Night is the shadow of the planet Earth.

Due to Earth's rotation, every 24 hours we alternately observe the bright day and the dark night. When we move towards the illuminated side of the planet, we imagine that the sun is dawning and the day is arriving. And, when we move towards the dark side of the planet we imagine the sun is setting and night is approaching. What we consider to be 'sunrise' and 'sunset' are results of mental habits. And a concise definition of 'East' could be the following:

East is the common direction of Earth's rotation and orbital motion.

Considering the above definitions, the person watching the horizon at night, is like a traveller flying in an airplane at night at an altitude of 30 to 40 thousand feet, and looking outside through the airplane's window. The difference is that he is now riding the planet Earth. In the same way that the airplane traveller sees the lights of the cities and the villages in the dark background of the earth, the traveller riding on the planet Earth will observe the heavenly cities and villages (the stars and the other planets) as the Earth moves in its orbit around the Sun.

If the airplane repeats its path, as the Earth does, and maintains a constant speed, as the Earth, from the sequence in which the city and village lights appear, the traveller can deduce how much of the path has been covered or what time of night it is. Any pilot or traveller who has covered this predetermined path several times during the night, can feel and understand these concepts.

5 - THE DAILY SHIFT OF THE STARS BY HALF A SABOO
What do Haadj Hasan Mirzayi and Mirza Muhammad Kermanian mean when they say that: "Each star rises half a saboo earlier, each night?" They are actually saying: "If at the end of the night of Mehr 4th (Shahrivar 29th in the government calendar = Sept 20th) the star of the constellation Leo appears exactly at six o'clock after midnight on the horizon, on Mehr 5th (Sept 21st), the same star will appear at 5:56:15. And, the next night it will be visible at 5:52:30. The other stars in the above list, follow the same rule. This 3 minute and 45 second - or according to the Ardakaanis, half a 'saboo' - advance in the time of observation, is an objective reason for the Earth's orbital motion, and in fact, it indicates the distance the planet has covered during the past 24 hours. The spaceship Earth is moving at a speed of more than a 100,000 kilometers per hour. The daily advance of the time Leo becomes visible by 3 minutes and 45 seconds is due to the fact that the planet Earth, during the past day and night, has come closer to Leo's angular direction by more than 2.5 million kilometers (24 times 108,000).

Of course, this does not mean that the dashtbaans and the farmers of Ardakaan, know about all this and about Earth's rotation and its orbital motion. They do not, just as most people who use a wrist watch do not know the construction and the operating mechanism of the watch they are wearing on their wrists.

6 - THE HISTORY OF ARDAKAAN'S ASTRAL CLOCK

As far as I know, no direct document or evidence has yet been found as to when this innovation was introduced. Nor did I meet anyone who had anything to say that was directly related to this question. One might proceed in the way a historic monument is dated from the material used in its construction. As an example, one can say - and this is just speculation - that the face of the clock introduced by Ahmad-abaad's astronomers corresponds to September 22nd. How can we conclude this? We see that there is a total of 96 'saboo's, exactly half the number included in a complete day and night. There are only two nights when day and night are of equal lengths. Farvardin 5th and Mehr 5th. How do we know that the face of the clock does not correspond to the Spring? From the fact that Canopus is in the list. An old Persian proverb says: "An apple who does not see Canopus, will have no color." Since, Canopus is one of the stars of the southern hemisphere, on the Iranian plateau it can only be observed in Fall.

If the scientific identity of the stars whose local names were given in the above list, is established, there is a chance that we can find more accurate information about the time and the age of Ardakaan's astral clock.

Perhaps there is one other clue to this question. We can look for the answer to the following question:

7 - IS THERE ANOTHER ASTRAL CLOCK?
If the answer is positive and we know the history of the other clock, we may be led to a solution of our problem.

And the answer is positive. There are many documents that show such an astral clock was in use in ancient Egypt, between the 21st and 16th centuries B.C. These documents consist of the name of stars and constellations which were painted or inscribed upon the water clocks, on the burial boxes of the mummies, and on the gates and the walls of the temples, in ancient Egypt. These tables which the Egyptians originally called "oblique calendars", have exactly the same function as Ardakaan's astral clock, and they are based on the same principle. Neugebauer [6], the famous science historian, has written about these 'oblique hours' in his book, "The Exact Sciences in Ancient Times" [7]:

"The fact is that what we are facing here is not a calendar, rather it is a clock constructed from the stars. The owner of this table could refer to the list to find the time each of the 'dahgaan's (decades) [9] would rise within each of the ten days of the month and determine what time of the night it is. Now we will investigate how such a clock would work " [10]

Neugebauer then explains that if we watch the eastern horizon all night until dawn, we will see that after dawn, the number of stars appearing from east decreases, until the last star seen just before the sunrise will stay in the sky for a short period of only 4 minutes (half a 'saboo'). This is that same heavenly phenomenon about which the poet Daghighi has said:

When the day dawned in the mountains,
The light of the stars disappeared.

It is also the same phenomenon we already mentioned i.e. what in Ardakaan is called "a progress of half a 'saboo'" and whose scientific name among the Iranian astronomers in the Islamic age was "the burning of the star" or "star-burning".

Like Ardakaan's astral clock, the Egyptians' oblique clock could only be used during the night. The Egyptian clock was a caravan of thirty six stars whose appearance at dawn indicated the arrival of one of the thirty six decades within each year. The train was headed by the famous star Sha'raa (Sirius or the Dog-star known in Iran also by the names Shabaahang = Tishtar = Tir) [10], whose first dawning was a short time before the tides of the River Nile, and the constituted the origin of the Egyptian calendar.

The dawn of Sirius in the morning and its burning has been described by Naasser Khosrow Ghobaadiani as follows:

Sha'raa is like a cup of ice,
The wheel of the sky wiping the drop clean at dawn,
If not from ice, still, when the sun rises,
They shall find no sign of it, hard as they may try.

Neugebauer and other Egyptologists believe that from the beginning, the astral clock of Egypt was beset with problems. The problem was the skeleton of Egyptian calendar, whereby, as in the Yazdgirdian calendar, the year was divided into 365 complete days, and account was not taken of the additional hours of the solar year. The Egyptologists say that due to this technical problem, the usefulness of the 'oblique hour' did not even last a thousand years. The first examples of the astral clock belong to the Pharaohs of the 9th and 10th dynasties who ruled from 2190 to 2050 B.C. and a later example has been carved in the tomb of Setti I (1317 - 1301 B.C.)

Apparently it was in the late 14th century B.C. when the Egyptian priests and the tomb servants realized the deficiencies of their astral clock and devised new methods for keeping hours at night. In this respect, Neugebauer says:

"In the tombs of Rameses V, Rameses VII, and Rameses IX, we encounter new astronomical texts. We see drawings of certain observations performed for the purpose of keeping hours at nights during the year. For the first and sixteenth days of the month, we see the image of a man sitting cross-legged (the eleventh plate). Above his head, or rather, behind his neck, there is a lattice of axes on which the signs of stars have been drawn. The inscription accompanying the drawing explains how at nights, at the beginning of each hour, which star would be seen 'above the left ear', which 'above the right ear', or 'above the left shoulder' or 'above the right shoulder'." [11]

Amazingly, the writer of this report, has seen with his own eyes and has heard with his own ears old farmers and shepherds from the "Baarez mountains", such as Mashhadi Hemmat-Ali Haadjizaadeh a resident of the Djoghdari village, or Mashhadi Nassrollah Haadjizaadeh, an old shepherd in the Laalehzaar valley of Kerman, using exactly this same method, and these same words and expressions, to determine the hours of night with an accuracy of fifteen minutes.

Before finishing our discussion of the ancient Egyptian clock, it is useful to note that the basis of the Egyptian 'oblique clock' - serving both as a calendar and as a clock, a fact giving rise to the technical problem associated with it - was the division of the year into 36 ten-day periods and one shorter five-day period. In other words the use of a 'decade' instead of a 'week'. There is little doubt that the concept of 'decade', unlike the concept of 'week', did originate within the Iranian plateau. The reason is that even today, the concept of 'decade' is prevalent all over the Iranian plateau and is used by peasants and shepherds. Be it Azerbayjan, Kurdistan, Luristan, and Ishahan, or in Yazd, Kerman, Baluchistan, Qandahar, Kabul, Varzabad valley in Tajikistan, or the Badakhshan province in Pamir Mountains, the peasants and the shepherds all use the terms 'chehellom' (fortieth), 'shastom' (sixtieth), 'haftadom' (seventieth), 'navadom' (ninetieth), 'yeksad-o bistom' (one hundred and twentieth), etc.

The points mentioned about the use and the importance of the decade unit in the farming calculations reminds one of the following sentence in 'Qabus Naameh':

"If you are a peasant, know about time. Everything that you want to farm, do not allow its time to pass. It is better to do something 10 days early rather than ten days late." (Chapter 43).

8 - ARDAKAAN'S ASTRAL CLOCK AND BUNDAHISHN
Another means of finding about the time that Ardakaan's astral clock was established, is the history of the Islamic jargon used for naming stars or constellations used in it; names such as "Parviz's hand", "Parviz" and "Gaz" quoted from Mr. Mirzayi and Mr. Kermanian, or the star named "Bashan" in the listings of Mr. Ali Eqbal and Mr. Hasan Ja'farian, himself a resident of Ardakaan. The expressions "Pish-Parviz" (before Parviz), "Parviz", and "Bashan" have appeared among the 27 stations of the Moon, in the third part of Bundahishn, with the title "About Creating Aloft the Bright Stars". The guess that "Pish Parviz" is the same thing as "the hand of Parviz", is perhaps correct. It is up to the experts to clarify whether "Jodai" ('the Goat' or Capricorn), is the same as the "Buzi-Sar" (Goat's head) in Bundahishn, or whether the expressions "Sar-e Gaz" (Gaz's head), "Khod-e Gaz" (Gaz itself), "Donbaleh-e Gaz" (Gaz's tail) are related to Bundahishn's "Kaht-sar" , "Kaht-miyan", and "Kaht".

This reporter has encountered the name "Gaz" as the name of a star in another place: in the article "Stars in Ardestaan" written by Mr. Ehsaan Hashemi published in the journal, Ayandeh, Nos. 6 & 7, Shahrivar and Mehr of 1364 (Aug 22 - Oct 21 1985). At the end of his highly readable article, under the title of "Khooshh-ye Parvin, Djabbaar (the Orion), Sha'raa-ye Yamaani (the Sirius)" , Mr. Hashemi writes:

"In addition to these, they also know the constellations of "Khoosheh-ye Parvin" (or "Aqd-e Sorayya", the Pleiades), "Djabbaar" (or 'the Hunter', Orion) and the star "Sha'raa-ye Yamaani" (Sirius) which are located near each other in the sky, and they hold certain beliefs about them"

"They also call "Khoosheh-ye Parvin", "Par" (the feather) and "Khoosheh-ye Angoor" (the grape cluster)"

"With the dawn of this group of stars at June 22nd, the weather changes."

"Djabbaar (Orion) is also called 'Gaz va Tarazoo' (Gaz and the Balance), 'Gaz va Gheychi' (Gaz and the Scissors), 'Gaz va Peymaan' (Gaz and the Measuring Cup), 'Seh Ghooti' (Three Tins), and sometimes it is called the Hunter, who holding a balance in his hands, is in pursuit of 'Par' (the Feather) believed to be the hunted animal in flight. The Hunter intends to divide its meat with the help of the balance after he has hunted it down."

and,

"Sha'raa-ye Yamaani (Sirius) which is always distinct because of its brightness, is also sometimes called 'Gaz's Horse' (or 'Gaz's tail') or 'the Tail'."

"These three constellations are mostly used to determine the time of day and as a clock during the night."

Notes:

[1] The 1440 year Behizaki cycle: It is said that during the reign of the Achaemenids, who at the time, ruled over most of the civilized world except for China and Greece, the Iranians had created a complex and elegant calendar by combining several kinds of year and month. Most probably the Iranians had acquired this kind of chronometry from the Egyptians of the age of the Pharaohs and after some reforms and renovations, promulgated it all over their domain including the present-day countries of Central Asia, Afghanistan, Caucuses (= Armenia), and Turkey (Asia Minor). This system of chronometry had survived up to the time of Abu-Reyhaan, in the aforementioned lands.

Among the innovations the Iranians had introduced in this calendar, was the Behizaki 1440 year cycle, formed by having twelve leap months - during the seasonal year. For this reason, every 120 years, celebrations were held all over the Iranian empire and all taxes were annulled during that year. With this procedure, the Iranians succeeded to match the days of the two kinds of year - the 365-day year and the 365-and-1/4-day year - and to use the same names for the days of the month. The 365-day year was called the 'normal' or 'rotating' year, and the 365-and-1/4-day year was called the 'seasonal' or 'Behizaki' year.

[2] The distorted or oblique hour: This chronological unit is obtained by dividing the day and the night into twelve parts each. But starting from the beginning of winter until the beginning of summer, the hours of the night are continually shortened and the hours of the day are elongated. And from the beginning of summer until the beginning of winter, the hours of day are shortened and the hours of night are stretched. This kind of distorted hour was used by the astronomers in ancient times.

[3] Proportionate hour: It is the same kind of hour presently in use, obtained from dividing the length of a full day into 24 equal parts.

[4] 'Aassaar al-Baaghieh' by Abu-Reyhaan Biruni, page 3, translated by Daana Seresht.

[5] The fifteenth chapter "On The Science of the Khataayides".

[6] O. Neugebauer

[7] 'Exact Sciences in Antiquity', Persian translation: Entesharat-e Elmi va Farhangi (The Scientific and Cultural Publications), Tehran, 1996, page 113.

[8] A greek word, similar in sound to the Persian word 'Dahgaan'(decade).

[9] 'Exact Sciences in Antiquity', section 39a.

[10] It is interesting to note that on the Iranian plateau, other names were in use for Sha'raa-ye Yamaani (Sirius): Shabaahang = Kaaroon-Kash Star.

[11] 'Exact Sciences in Antiquity', the Persian translation, page 121.

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