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Chiang Mai J. Sci. 2018; 45(6) 2491

Chiang Mai J. Sci. 2018; 45(6) : 2491-2508 http://epg.science.cmu.ac.th/ejournal/ Contributed Paper

Suvarnabhumi-Gregorian Rule to Determine Whether Thai Lunar 2012 is a Leap- Year Cherdsak Saelee* [a], Mullika Tawonatiwas [b] and Smai Yodintra1 [a] Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200, . [b] Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand. * Author for correspondence; e-mail: [email protected] 1 Deceased date:

Received: 26 October 2016 Accepted: 20 March 2017

ABSTRACT Following a widespread disagreement on whether the Thai year 2012 is a leap-month year, qualitative and quantitative analyses were conducted to determine where the inaccuracy lies. Through in-depth studies of the , we discovered an ancient rule used by the Suvarnabhumi civilization to determine leap-month lunar . By observing natural occurrences, the Suvarnabhumi people were able to develop a calendar that synchronized with the . This calendar is believed to have been the origin of the current Thai lunar calendar, as the two share similar characteristics. We restore the Suvarnabhumi rule and adapt it to the internationally recognized and accepted and name the resulting adaptation the “Suvarnabhumi-Gregorian” rule. We then apply the rule to reveal that the year 2012 is not a leap-month lunar year. The rule provides a more accurate way to predict leap-month lunar years while maintaining the same characteristics as the Thai lunar calendar, which should make it a welcome alternative for both academic scholars and practitioners of traditional Thai .

Keywords: Thai lunar calendar, leap-month lunar year

1. INTRODUCTION The Thai (, lunar calendar: Magha Puja , which is on BE, or Phuttha Sakarat) typically provide both full- 3rd month; Visakha Puja Day (the solar (Suriyakhati) and lunar (Chanthrakhati) holiest day of all Buddhist days marking the calendars. The former is the globally-used birth, enlightenment and death of the Gregorian calendar, while the latter is the Thai ), which is on full-moon lunar calendar based on Culasakaraj. All Thai 6th month; Loy Krathong Festival, which is and festivals are set on full-moon 12th month. Furthermore, local according to the Thai lunar calendar. The farmers rely on the Thai lunar calendar for following examples are well known ones their rice cultivation. Thus, it is important and how they are referred to in the Thai that the Thai lunar calendar must be accurately 2492 Chiang Mai J. Sci. 2018; 45(6)

represented, especially as to when it is a Therefore, the accumulated difference leap-month year. We will first describe in this between the two over a period of 200 years section about astronomical aspects related to is 200 × 0.014161 = 2.8322 days. a lunar calendar. Then we will review the history of the Thai lunar calendar. We, finally, Synodic month or is the point out why there exists a conflict whether period of a complete revolution of the Moon the year 2012 is a leap-month lunar year and around the Earth with respect to the propose our astronomical rule to correct ( to full moon or to the calendar. new moon). Its averaged length is 29.530588 days. However, the length of any one synodic 1.1 Astronomical Aspects month can be vary from 29.26 to 29.80 days Important astronomical aspects described due to perturbing effects of the Sun on the here will be regarded throughout the Moon’s eccentric orbit [3]. The period of 12 arguments in this paper. lunar is called a “lunar year.” A period of one lunar year is 354.367056 (also solar, equinoctial, days. natural, or ) is the time required The difference between the solar year for the Sun (or apparently, the Earth) to pass and the lunar year is 365.242199 − 354.367056 from the vernal equinox (the Sun crosses the = 10.875143 days per year, i.e., 10.875143 × 3 Equator, which occurs in ) back to the = 32.625429 days per three years (which is vernal equinox. Four important moments of greater than one lunar month). the Sun’s annual passage through the sky are the two equinoxes (vernal and autumnal) The system of dividing time into and the two solstices (summer and winter). convenient periods of days, months and years The equinoxes are days on which the Sun rises is called the “Calendars.” Due to the fact that due east and sets due west. The summer the astronomical years have a fraction solstice (“north solstice”) is the day on which (instead of a whole number) of days, all the Sun rises and sets at its northernmost derived calendars will eventually be out of points on the horizon, whereas the winter sync over a period of accumulated cycle. solstice (“south solstice”) is the day on which Adding extra days or months to the cycle the Sun rises and sets at its southernmost can preserve synchronization with the solar points on the horizon. year, a method known as intercalation. To date The length of the mean tropical year is the Gregorian calendar is the closest 365.242199 days [1]. approximation to the solar year and is internationally used calendar. A common or star year is the period year for the Gregorian calendar has 365 days. of time during which the Earth makes a An intercalary year or a “” has complete revolution around the Sun with 366 days by adding one day to the month of respect to a specific star. February for the year that is divisible by The sidereal year equals 365.25636 days 4 but years divisible by 100 are not leap years for the J2000.0 [2]. unless they are also divisible by 400. Thus, the difference between the In other words, centurial years that are not sidereal year and the mean tropical year is divisible by 400 (e.g., the year 1700, 1800 365.25636 − 365.242199 = 0.014161 days. and 1900) are not leap years [4]. Similarly, Chiang Mai J. Sci. 2018; 45(6) 2493

intercalation cycle every two or three years is chickens from their wild progenitors, all applied to a lunar (lunisolar) calendar in order domestic chickens have the same ancestor to synchronize the lunar year to the solar year. (about 7,000 years ago) originating from Fang A lunar year that adds one extra month (Northern city of Chiang Mai, Thailand) [14]. will have 13 months, which is called a Thus, it is not surprising that the , Thai, “leap-month year.” A lunar year that adds , and all have a sport with one extra day to a month will be called a cockfighting as one of their traditions [15]. “leap-day year.” These connections suggest that the Maya may originate from the Suvarnabhumi region before 1.2 Background on Thai Lunar Calendar migrating to Mesoamerican cultural area. The Thai lunar calendar is believed to have its origins in the “Suvarnabhumi” lunar 1.2.1 Suvarnabhumi lunar calendar calendar [5]. Suvarnabhumi refers to a region The Suvarnabhumi lunar calendar is merely including (formerly Burma), a name suggested by Yodintra [5] in order to Cambodia, Laos, Xishuangbanna (in the south collectively refer to all lunar calendars of Yunnan Province, southwest China), developed by different nomadic groups (with Central Thailand, Northern Thailand, names like Tai, Khmer, Mon, Jean, Muser, Northeastern Thailand and Vietnam [6]. Laos, Shan and Lua) in the Suvarnabhumi This region is also known as the Rice Bowl of region. Each nomadic group developed its the world because it is believed that the first own calendar with a common rule as to match agricultural civilization was established here a lunar cycle to natural surroundings in approximately 15,000-10,000 years ago [7-9]. each area. The Suvarnabhumi lunar calendar Evidences such as rice husk and pottery described here, therefore, reflects the natural artifacts were discovered in Northern Thailand occurrence within Thailand which we have and Northeastern Thailand indicating the gathered from the elders. first attempts at rice cultivation [10-11]. In One regular year of the Suvarnabhumi order to precisely keep track of the seasons lunar calendar consists of 12 lunar months. for agricultural purposes, the Suvarnabhumi Each lunar month has 15 days of waxing lunar calendar must have been developed at moon in the first half of the month. that same time. The second half has either 14 days (for odd Interestingly, there are some ties between month) or 15 days (for even month) of the Suvarnabhumi and the Maya civilization. waning moon. As a result, the 1st, 3rd, 5th, 7th, The Maya civilization developed within the 9th, and 11th month have 29 days each, whereas Mesoamerican cultural area, which gave rise the 2nd, 4th, 6th, 8th, 10th, and 12th month have to a series of cultural developments that 30 days each [16]. The full moon day is the included complex societies, agriculture, cities, last day (15th) of waxing moon and is called monumental architecture, writing, and “Wan Pen.” The last day (14th or 15th) of calendrical systems [12]. The Maya developed waning moon is called “Wan Dub” meaning the calendar by recording lunar and solar a “dark moon day.” When signs from cycles, eclipses and movements of planets nature⎯i.e., blossoming of certain trees, arrival [13]. In addition, the Maya and Cambodia of transitional rain, and moon appearance counting systems are alike, i.e., both counted related to sunrise⎯occur at odd times, the 6 as 5|1; 7 as 5|2; and 8 as 5|3. According to Suvarnabhumi farmers will add one extra DNA research study on the domestication of 8th month (30-day month). The year that 2494 Chiang Mai J. Sci. 2018; 45(6)

has a “Double-8th month” is called an appearance. The lunar year that adds one day “Adhikamat year” (a leap-month year). is called an “Adhikavara year” (a leap-day This adjustment will synchronize the calendar year). An Adhikamat year and an Adhikavara with the seasons and retain a nominal length year will never be the same year [17-18]. of twelve months. Every two or three years, the ancient farmers had to adjust their 1.2.2 Culasakaraj calendar calendar to the Adhikamat year. They became The Culasakaraj calendar or the Makaranta experts in predicting an Adhikamat year using reckoning calendar is adapted from the the Suvarnabhumi land as their observational Suvarnabhumi calendar with the Double- field. 8th month for an Adhikamat year and the They even developed a rule which has 30-day 7th month for an Adhikavara year. been passed down through generations and The Burmese era, known in Thai by the name known to today’s elders as “13 Dub Bungkub Culasakaraj era (CS), was announced by 13 Pen” (13-dark moon impending 13-full King Popa Saw Yahan who usurped the throne moon) detailed in Section 2.3.3. An indicator of Pagan from the Burmese on resulting from this rule is that whenever the March 25, 638 AD (Gregorian date). The day dark moon of the 1st month appears before marks the beginning of as the Sun the south solstice (December 22); the year enters the first point of and is regarded will be an Adhikamat year. Since a full moon the start of Culasakaraj (0 CS) [19]. He is obviously observed, they can use the full matched the Suvarnabhumi calendar to the moon of the 12th month that appears before Indian sidereal calendar because he believed November 9 as the indicator of an Adhikamat that the Indian sidereal calendar which has year to come. the average year length of 365.25875 days Not only did the ancient people of (292,207 ÷ 800) was the most accurate Suvarnabhumi know when to add a month, calendar at the time as it reflected the actual they also recognized the need to add a day. moon in the sky. Therefore, the Culasakaraj Due to the fact that they alternated the hollow calendar is based upon the Suvarnabhumi month (29-day odd-month) and the full calendar matching with 800-year Indian month (30-day even-month), their full sidereal calendar (i.e., from 0 CS to 800 CS) and dark moons sometimes were misaligned in order to locate an Adhikavara year. He also with the actual phases of the Moon. acquired the rule based on the Indian sidereal The Suvarnabhumi full moon, i.e., the 15th calendar to predict an Adhikamat year instead waxing moon, often appears before the actual of using the nature observation method, one. In observing the Suvarnabhumi full moon which he found troublesome. days, they noticed that when the Sun was The Culasakaraj calendar considers setting, the Moon had already risen in the “Tithi” on the New Year of CS to identify East for 1-2 hours. If they observed that an Adhikamat year. The Tithi is the angle of the Suvarnabhumi full moon (or dark moon) the Moon with respect to the Sun considering appears more than one day before the actual the Earth as a vertex. There are 30 Tithis in one and if that year is not an Adhikamat year, total. Tithi 0 represents the Sun and the Moon then they will add one extra day to the 7th in alignment on the same side; hence it is a month (from 29 days to become 30 days) in dark moon day. Tithi 15 represents the Sun order to coincide the calendar with the and the Moon in alignment but on the Chiang Mai J. Sci. 2018; 45(6) 2495

opposite side; thus it is a full moon day. 1.3 Conflicting Results in Determining An Adhikamat year is then determined, for Adhikamat Year of 2012 example the Culasakaraj New Year’s Day on The inaccuracy in predicting an April 16, if the Tithi on that day is 26, 27, 28, Adhikamat year of the Culasakaraj-based Thai 29, 0, 1, 2, 3, 4, 5 or 6. The prediction of an lunar calendar becomes imminent when the Adhikamat year by this rule is not all correct. two following sources determine the year 2012 We will discuss the problem of using the differently. According to Chunphongthong Indian sidereal calendar as a reference more [20] (the scholar who designed the 5000-year in details in Section 2.1.2. lunar calendar which was published by the National Astronomical Research Institute 1.2.3 Thai lunar calendar of Thailand), when data from the National Between the 11th and the 13th centuries, Aeronautics and Space Administration the Culasakaraj calendar was adopted in the (NASA) were applied, the year 2012 on the Pagan Empire and first came to be used in Thai lunar calendar was shown to be a regular peripheral regions. The adoption of this year. The Astrological Association of calendar had spread to Siamese kingdoms Thailand, published 150 Thai lunar calendars initially from the Lanna Kingdom in the for citizen by Burajaraya [21], along with the mid-13th century, to the Thai official calendar year 2012 stated in the following century, and eventually to the otherwise that it is an Adhikamat year. Ayuddhaya Kingdom in the 16th century [17]. In fact, these conflicting results can be expected Subsequently, Siamese kingdoms retained every 150-200 years because the Thai lunar this calendar as the official calendar under calendar is synchronized to the Indian sidereal the name of Culasakaraj era (CS) until 1889 year, which gradually drifts apart from the AD. Although, the Culasakaraj-based Thai lunar solar year as shown in Section 1.1. calendars have been encountered several In Section 2, we describe why the use of adjustments to coincide with the seasons, Culasakaraj in the Thai lunar calendar is no but the local farmers prefer to use the longer valid. We re-establish the wisdom of Suvarnabhumi calendar for their crop our Suvarnabhumi ancestors and incorporate cultivation. This Culasakaraj-based Thai lunar it into the Gregorian calendar in order to calendar, therefore, is only favored among determine an Adhikamat year. We name the Thai astrologers. The Culasakaraj dates remain resulting combination the Suvarnabhumi- the most commonly used and preferred form Gregorian rule which provides two of entry by the academia for Thai history and advantages: The Thai lunar calendars, like Thai astronomy studies, even after Thailand the Gregorian calendar, will be closely has moved on to Buddhist calendar (BE) synchronized with the seasons; and we can since 1941 AD. As a result, the current Thai maintain the traditions. An Adhikavara year lunar calendar still has an average year length can be assigned using the NASA information. of 365.25875 days. 2496 Chiang Mai J. Sci. 2018; 45(6)

2. MATERIALS AND METHODS 2.1.1 Synchronize Suvarnabhumi year Before we can apply the Suvarnabhumi- with tropical year Gregorian rule to determine the Adhikamat year The Gregorian calendar, an internationally of 2012, we must demonstrate how the accepted calendar for civil and scientific Culasakaraj-based Thai lunar calendar is no purposes, is a that has the closest longer valid; and how continuing to use it approximation of year length to the mean will cause more harm than good. Qualitative tropical year of 365.242199 days. It has a cycle analysis of information will be conducted of 400 years (146,097 days). The average year based on the following questions: length is 146,097 ÷ 400 = 365.2425 days [4]. I. Is it suitable for the Thai lunar calendar One synodic month is 29.530588 days on to be synchronized with the Indian average. The length of the lunar month is not sidereal calendar? an even fraction of the length of the tropical II. Is there any drawback in using a year year. As a result, a purely lunar calendar will length of 365.25875 as in Culasakaraj quickly drift away from the seasons [22]. calendar in the Thai lunar calendar? Throughout history, the Suvarnabhumi III. Why does the Thai lunar calendar add people used their calendar to help them plan a leap month to the 8th month? for rice cultivation by observing astronomical IV. How accurate when using data of new phenomena cycles. One Suvarnabhumi lunar moon and full moon from NASA to year has 354 days. They regularly noticed set an Adhikavara year? that the rising of the Moon did not precisely V. What advantages to employ the match with their calendar and also shorter Suvarnabhumi-Gregorian rule for an than a solar year, i.e., 11 days shorter of Adhikamat year? the 365-day solar year. Therefore, in approximately three years there is a difference Once the above questions are answered, of more than one synodic month between we will establish the four Suvarnabhumi- the lunar and the solar year. In this case, Gregorian conditions as a rule to determine an every two or three-year intervals, the ancient Adhikamat year, which combine rules from Suvarnabhumi added a thirteenth intercalary the Thai astrologer group and the scholar month (a leap month of 30 days) to the lunar group. year to form the 11-year-cycle (3332: as the 3rd, 6th, 9th, and 11th year each has 13 months) 2.1 Synchronization of Thai Lunar and the 8-year-cycle (332: as the 3rd, 6th, and Calendar with Indian Sidereal Calendar 8th year each has 13 months). The years outside The Suvarnabhumi calendar was these cycles are regular years with 12 months synchronized with the seasons corresponding each. Occasionally, previous two cycles form to the length of the tropical year. The a 19-year (3332 332: equivalent Culasakaraj-based Thai lunar calendar to seven leap-month-lunar-years). matched the Suvarnabhumi calendar with the In the 19-year-cycle, the lunar and the sidereal year as used in the Darakhati India solar can be perfectly matched at the length calendar. We will determine and compare of 6,939 or 6,940 days1. Since an Adhikamat the accumulating drift in 800 years when year has 384 days, whereas a regular year has synchronize the Suvarnabhumi year with the 354 days, after adding seven leap months to tropical year in Section 2.1.1 and with the this cycle (which is found to be 6,936 days 2), Indian sidereal year in Section 2.1.2. it is still three or four days shorter than the 1 19 solar years = 19 x 365.242199 = 6,939.601781 days 235 lunar months = 235 x 29.530588 = 6,939.68836 days 2 (12 regular years x 354) + (7 Adhikamat years x 384) Chiang Mai J. Sci. 2018; 45(6) 2497

solar cycle. In order to match the full moon constellations relative to the equinoxes in the Suvarnabhumi calendar (Thai lunar only becomes apparent over centuries. calendar before 638 AD) with the actual full However, the fact that the sidereal year is moon, the ancient people also added a leap nearly 24 minutes longer than the tropical year, day (known as an Adhikavara year) three or eventually all sidereal-based calendars four times per cycle. Thus, the Suvarnabhumi will slowly drift away from the seasons. calendar always coincides with a solar (tropical) Synchronizing the Suvarnabhumi calendar, year. Continuing the calculation for 800 years, by inserting intercalary months and days on it was found that there is a total of the Metonic cycle, with the 800-year sidereal 292,194 days (= 800 × 365.2425) by yields a total of 292,205 days (≈ 800 × Gregorian calendar covering 294 Adhikamat 365.25636) which includes 295 Adhikamat years and 155 Adhikavara years in the years and 155 Adhikavara years. The total Suvarnabhumi calendar [23]. number of days in the 800-year sidereal are only 11 days longer than that in the 800-year 2.1.2 Synchronize Suvarnabhumi year solar (292,205 − 292,194 = 11), but there is with Darakhati India sidereal year one more Adhikamat year. In other words, “Darakhati India” called by there are at least 30 days that the Thai lunar refers to the that adapted calendar does not coincide with the from the Siddhanta system of ancient seasons. India and merged with a 19-year intercalation Synchronizing the Thai lunar calendar schedule (Metonic cycle) [24]. It is unclear to the sidereal year will gradually shift the from where, when or how the Metonic calendar away from the actual seasons, with system was introduced. However, it is potentially disastrous consequences for believed that this system came from the farmers. This may be the reason why the Suvarnabhumi calendar system. This Burmese Sukhothai Period, when the Culasakaraj calendar calendar, thus, used a “strange” combination was initially introduced, saw many famines. of sidereal years from the Indian calendar with The Sukhothai people had adjusted their the Metonic cycle [25]. King Popa Saw Yahan calendar frequently to coincide with the then synchronized the Suvarnabhumi calendar Suvarnabhumi calendar in order to set the right to this 800-year Darakhati India as he time for rice-planting. It is therefore better believed it was the most accurate one for to synchronize the Thai lunar calendar to holy days, harvest, and so on. the solar year and to avoid the sidereal year As mentioned previously in Section 1.1, calendar altogether. a sidereal year length is equal to 365.25636 days, which is a small amount longer 2.2 Effect of Applying 365.25875-day than the solar year. Before the discovery Year in Thai Lunar Calendar of the precession of the equinoxes by Most Thai astrologers follow the Hipparchus in the Hellenistic period, the Culasakaraj system, which is influenced by difference between the sidereal and the and therefore has to reconcile with the solar year was unobserved by ancient people. 800 Darakhati India years as tabulated in For naked-eye observation, the shift of the comparison in Table 1. 2498 Chiang Mai J. Sci. 2018; 45(6)

Table 1. Comparison on the New Year’s Day between the Culasakaraj calendar and the Darakhati India calendar for 800 years. CS (BE) Gregorian Dates and Times for New Year’s Day (in AD) Culasakaraj calendar Darakhati India calendar 0 (1181) March 25, 638 at 11:11:24 March 25, 638 at 11:11:24 1 (1182) March 25, 639 at 17:24:00 March 25, 639 at 17:20:34 …… …… ……

775 (1956) April 6, 1413 at 23:56:24 April 5, 1413 at 3:32:30

799 (1980) April 7, 1437 at 4:58:48 April 5, 1437 at 7:12:25 800 (1981) April 7, 1438 at 11:11:24 April 5, 1438 at 13:21:35

From Table 1, the 800-year Culasakaraj As previously mentioned, the timing between calendar is about two days longer than the the Moon and the Sun are different. To keep 800-year Darakhati India calendar. As the total the lunar years in sync with the actual seasons, days in 800-year CS (292,207) is two days these people added an extra 30-day month more than that in the Darakhati (292,205), to the 8th month or added an extra day to the resulting in 365.25875 days per CS year. 7th month. Why they had to add a leap month Therefore, the Culasakaraj-based Thai lunar only to the 8th month in an Adhikamat year? year is longer than the sidereal year causing Is it possible or suitable to add to another even more drifts from the solar year. one? For a better understanding, we Furthermore, King Popa Saw Yahan used this compared the dates by converting to the number to calculate the New Year’s Day, Gregorian calendar. The answers to why which moved towards May. In the long term, it has to be the Double-8th month in an the calendars are drifting one day Adhikamat year are discussed in the next approximately every 60 years and 4 months. section. As a result, the CS New Year will move towards the rainy . We might have to 2.3.1 Conditions for continuity of celebrate the Festival in the rain. Suvarnabhumi seasons Consequently, it was suggested that the Thai The intended use of the Suvarnabhumi lunar calendar must avoid using Culasakaraj lunar calendar is to keep track with the seasonal system to be any reference or to adjust an year for their agriculture cultivation, rice in Adhikamat and Adhikavara year. particular. Therefore, the of the Suvarnabhumi lunar calendar coincides with 2.3 Adding a Leap Month to the 8th Month the seasons as follows: The end of the 1st Although the ancient Suvarnabhumi month is in mid-winter; the waning moon people did not have any calendars or adjusting of the 3rd month is the start of summer; instruments that we do today, the ancient the waxing moon of the 5th month is in astronomers used a variety of methods that mid-summer; the waning moon of the 6th can be applied across cultures and time month is the start of the rainy season; the periods. They connected the sky with the cycles waning moon of the 8th month is during heavy of nature for its relationship with agriculture. rainfall (desirable for rice cultivation); the Chiang Mai J. Sci. 2018; 45(6) 2499

waning moon of the 12th month is the start each lunar month falls during the same of winter. The 8th month is the most important Suvarnabhumi season every year, all three month for rice cultivation. Rice seedlings specific lunar dates⎯that can precisely be need to be exposed to the heavy rainfall in observed with the particular angles of sunrise order to be ready for harvesting by the at south solstice (23.5° S), equinox (0°), and mid-11th month. Figure 1 shows dates in the north solstice (23.5° N)⎯must meet Gregorian calendar that are related to the the following conditions as shown in Sun’s declination. In order to ensure that Table 2.

Figure 1. Diagram shows the Sun’s declination and the Suvarnabhumi seasons with corresponding to Gregorian date. The circled number indicates the lunar month, while and represent full moon and new moon, respectively. ( 1 , 4 and 8 referred in Table 2; and 12 , 3 , 6 and 8 referred in Table 3).

Table 2. The Conditions to determine the lunar calendar hold on to the seasons.

Date of lunar calendar Sunrise at Gregorian date Conditions Satisfied Unsatisfied 14th waning moon and new moon, 1st month south solstice After December 22 Before December 23 15th waning moon, 4th month vernal equinox After March 21 Before March 22 15th waxing moon and full moon, 8th month north solstice After July 2 Before July 3

2.3.2 Signs of natural occurrence for at the full moon day of each month as Adhikamat year detailed in Table 3. The data in Table 3 To synchronize the signs of nature in also provide conditional dates to determine Suvarnabhumi seasons with their calendar, an Adhikamat year in the Gregorian they observed various natural events occurring calendar. 2500 Chiang Mai J. Sci. 2018; 45(6)

Table 3. Nature signs of the Suvarnabhumi seasons with Gregorian date conditions.

Full moon Corresponding Nature phenomena with Gregorian date condition of season Regular year Adhikamat year 12th month rainy season - occurs after November 8 - occurs before (a year ends then (a year before) November 9 before) winter or - north-easterly wind, (a year before) (sign #1) northeast cold air from China, - happens in advance of monsoon begins winter season begins - north-easterly wind does not blow yet 3rd month winter ends then - occurs after February 5 - occurs before summer or - mango tree or February 6 (sign #2) pre-monsoon “Mamuang Kalon” - happens in advance season begins (Mangifera caloneura Kurz) of summer flowers in full bloom - mango tree is not in - a rain (of January-March full bloom period) during the - no rain washes the flowering season to flower off wash off the flowers 6th month summer ends - occurs after May 4 - occurs before May 5 then rainy - soapberry (sign #3) (southwest (Sapindus emarginatus Wall) - happens in advance of monsoon) flowers the rainy season season begins - soapberry does not begin flowering 8th month during the peak - occurs after July 2 - occurs before July 3 (first full of rainy season - bungor or “Ta Bek” (sign #4) moon (heavy rainfall) (Lagerstroemia floribunda - happens in advance of after south Jack which is the heavy rainfall solstice) tropical flowering tree) - bungor flower is not flowers in full bloom fully bloom - during heavy rainfall

The Suvarnabhumi people observed these the fields before the full moon of the 7th natural events for their rice cultivation. In month and must finish before the full moon Suvarnabhumi, there are varieties of rice, which of the 8th month. After that there are heavy are based on hydrological characteristics, such rainfalls; the rice plant then grows in flooded as upland rice, lowland rice, dry (off)-season soil during the green season through to rice, wet-season rice [26]. Especially for September (from booting stage in the 9th wet-season rice, the seeding must start in month to heading and flowering stage in the seeding beds before the full moon of the 6th 10th month). The rice turns from emerald to month which have been flooded by rain. darker green and finally to dry gold under the Seedlings later on are transplanted by hand to strong sunray. Between the full moon of the Chiang Mai J. Sci. 2018; 45(6) 2501

11th and the 12th month, it is ready to be according to the NASA is called new moon, harvested. One of the most important factors which we will refer to as “dark moon” for rice cultivation is to have enough water in according to the Suvarnabhumi people. rice fields by observing a heavy rainfall in the In addition to the previous observations, 8th month. Rainy season is the most important the ancient people also noticed for 13 dark nature signs for the farmers. They had noticed moons in one tropical year in between two lunar phases, seasons, and trees as four south solstices, which in turns resulted in the full-moon signs shown in Table 3. It is worth 13 full moons in between two north solstices noting that these signs are simply derived from that followed. This nature rule is known as the three conditions in a regular year given “13-dark moon impending 13-full moon”, in Table 2. The four full-moon signs here and is the most important rule to abide, as triggered the farmers to add an extra 8th the ancient Suvarnabhumi people believed that month in an Adhikamat year. The Buddhist nature had given back the missing month. festivals would be moved to one month later; In practice, there are normally 12 dark moons for example, Visakha Puja Day would be in between two successive south solstices moved to the full moon of the 7th month (from December 23, Y−1 to December 22, instead. The Double-8th month would then fall Y, see bold line in Figure 2), but sometimes on the heavy rain season as desired. there is another observed dark moon of the 1st month within 11 days before the south 2.3.3 13-dark moon impending 13-full solstice (December 12-22, Y) as shown moon graphically in Figure 2. Then, the full moon As the Moon orbits the Earth, its position of the 8th month must be observed within relative to the Earth and Sun changes, and the 11 days after the north solstice and this 8th Moon appears to go through phases. When month is set as a leap month for an Adhikamat the Earth sits between the Moon and Sun, year. Thus, this full moon is referred as the people on Earth see a full moon at night. On 13th full moon of a tropical year starting from the other hand, when the Moon sits between an 11-day-after-north solstice to the next one the Earth and the Sun or when the Moon and (from July 3, Y to July 2, Y+1, see bold dashed Sun are in conjunction, people on Earth will line in Figure 2), which already has 12 full see no moon at night. This moons.

South Solstice Equinox North Solstice Equinox South Solstice Equinox North Solstice Equinox South Soltice 12

10

8

6

4 Lunar Month New moon 2 Full moon 0 9-Nov22-Dec 21-Mar 2-Jul |------Gregorian Year Y ------|------Gregorian Year Y+1 ------| Figure 2. Graphic representation of the event of 13-dark moon impending 13-full moon. Three specific lunar dates referred in Table 2 must occur after those three dates as shown diagonally. The full or new moons that occur before those four dates as shown in the horizontal axis are the Suvarnabhumi-Gregorian conditions (referred in Table 4). 2502 Chiang Mai J. Sci. 2018; 45(6)

The Lua, an ancient Suvarnabhumi tribe, and found that this phenomenon only made use of the Inthakin Pillar (city pillar) occurred on a perfect full moon, while a solar and Chaeng Sri Phum (northeast corner of eclipse occurred only on a perfect new moon. Chiang Mai city wall) as the instruments for A full moon is the lunar phase that occurs adjusting their calendar to synchronize with when the Moon is completely illuminated as the solar year by observing the north solstice. seen from the Earth. It rises in the East almost If they saw a full moon appeared after that the same time that the Sun is setting. within 11 days, this lunar year must add a leap The observers noticed that a full moon month. These ancient astronomers can predict in the sky did not appear as it should because the 13 full moons coming in the next two the Suvarnabhumi lunar calendar has alternating successive north solstices as they already months of 29 days in the odd months and counted a total of 13 dark moons occurred 30 days in the even months, yielding the that year. average lunation length equals to 29.5 days Attempts to retain the appropriate season which is slightly shorter than the mean synodic for rice cultivation at each stage and the fact month by 29.530588 − 29.5 = 0.030588 day. that the most desirable season is the heavy When they found that their calendar’s full rainfall season which falls on the 8th month moon (15th waxing moon) occurred before are the reasons why the focus is on the 8th the actual one by more than one day and that lunar month. More importantly, nature itself year was not an Adhikamat year then they as described in the 13-dark moon impending would add one extra day to a hollow month 13-full moon rule do give back an extra full (29-day month). As mentioned in Section 2.3.2, moon around the 8th month as well. It is thus the Suvarnabhumi people were rice farmers natural and undeniable why the leap month who linked their calendar with the seasons by is the 8th month. Nonetheless, some tribes in adding the leap month to the 8th month. Thus, Suvarnabhumi had chosen other leap month in order to adjust their full moon of the 8th instead of the 8th depending upon which rice month to be coincide with the actual full stage they gave more priority. moon, the extra day of 15th waning moon was added to the 7th month as it is the closest 2.4 Using NASA Data for Calculating of month to the 8th month. The year, which the Adhikavara Year hollow 7th month become a full month of The ancient Suvarnabhumi civilization 30 days, is then called an Adhikavara year. developed in the tropics. Examples of this The complexity of calendars arises civilization include Angkor in Cambodia because astronomical cycles are neither [27]; Wat Pra Yeun in Lamphun [5]; the Inthakin constant nor perfectly commensurable with Pillar and Chaeng Sri Phum in Chiang Mai; and each other. The acceptance of the Gregorian Wat Xieng Thong in Luang Prabang, Laos. calendar as a worldwide standard has spanned These cultures had zenith passages that more than three centuries, however, only occur in the tropics [28]. These ancient astronomical cycles are not absolutely constant, Suvarnabhumi were able to see the Moon and and they are not known exactly. In the long the Sun all year round. Thus, these ancient term, only a purely observational calendar timekeepers were able to differentiate between maintains synchrony with astronomical the actual full moon in the sky and the one on phenomena, even though it exhibits their calendar. Moreover, these people had short-term uncertainty, because the natural witnessed lunar eclipses at least twice a year phenomena are complex and the observations Chiang Mai J. Sci. 2018; 45(6) 2503

are subject to error. To adjust the Thai lunar 2.5 Suvarnabhumi-Gregorian Rule for calendar using the lunar phases data from Adhikamat Year NASA, we set the 14th waning moon of the Regarding the Gregorian calendar as 7th month every year as a dark moon that the most internationally accepted for must occur before the new moon as defined its synchronization with the seasons, we by NASA data; except for an Adhikamat year, adapt it in accordance with the observations we set the 15th waxing moon of the first 8th discovered by the ancient Suvarnabhumi month instead. This way we will have dark (as listed in Table 2 and 3) and arrive at moons and full moons matches with actual the criteria to determine an Adhikamat ones and they are necessary for utilizing the year. We call these sets of criteria the 13-dark moon impending 13-full moon rule as well. Suvarnabhumi-Gregorian rule. In order to Moreover, using the new moon data determine whether the year is an Adhikamat from NASA and using the same characteristic year, all four conditions as listed in Table 4 with Suvarnabhumi calendar as a reference will must be satisfied in successive orders. be more acceptable for both astrologers and The lunar dates or the lunar phases in Table 4 academic scholars. refer to the actual ones in the sky.

Table 4. Four conditions of the Suvarnabhumi-Gregorian rule. Condition Thai lunar date/ Gregorian date conditions for NASA lunar phase Adhikamat year 1 15th waxing moon, 12th month/ Before November 9 full moon (a year before) 2 14th waning moon, 1st month/ Between December 12 and 22 new moon (a year before) 3 15th waning moon, 4th month/ Before March 22 new moon 4 15th waxing moon, 8th month/ Between June 22 and July 2 full moon

Condition 3 is to mark the 15th waning Thai lunar calendar to determine an Adhikamat moon of the 4th month must occur after the and an Adhikawara year. The calendar does vernal equinox (March 21) as the first new not match the actual seasons because it is moon. The Gregorian calendar also marks this synchronized to the sidereal year rather than equinox as the reference for adjusting their the solar year. It will eventually drift away from calendar every year including a leap year. the natural seasons and no longer serve as a Condition 2 and 4 are the conditions that useful reference for agricultural cultivation. retain the Suvarnabhumi calendar with the The ancient wisdom of Suvarnabhumi is much astronomical seasons. These criteria have more suited for cultivation purposes because cropped the new moon of the 1st month and the region’s people have synchronized their the full moon of the 8th month always occurs calendars with the natural seasons for within 11 days before the south solstice and generations. By combining this ancient after the north solstice, respectively. knowledge with modern knowledge and the We have demonstrated and pointed out globally accepted Gregorian calendar, we drawbacks of using the Culasakaraj-based have a rule for determining an Adhikamat year, 2504 Chiang Mai J. Sci. 2018; 45(6)

which we name the Suvarnabhumi-Gregorian 1) setting 29-day odd month and 30-day even rule. We suggest that the NASA information month, 2) adding a leap month to the 8th is used for determining an Adhikawara year. month and 3) adding a leap day to the 7th month. For the latter group, the calculation is 3. RESULTS AND DISCUSSION based on the new moon and full moon data The Suvarnabhumi-Gregorian rule for sourced from NASA referring to the Adhikamat year provides two advantages: Gregorian calendar. The Thai lunar calendar will be closely synchronized with the solar seasons similar to 3.1 Determine Adhikamat Year in 2012 the Gregorian calendar, and we can hold onto We will demonstrate how to apply the the traditions for Thai astrologers. The rule four Suvarnabhumi-Gregorian conditions harmoniously combines rules from both to determine the year 2012 for Adhikamat. By Thai astrologers and academic scholars. The using the year 2011 and 2012, rules maintained from the former group are those conditions can be examined in Table 5.

Table 5. Identify the year 2012 to the four Suvarnabhumi-Gregorian conditions.

Condition Thai lunar date Gregorian date Satisfy condition NASA lunar phase Date and time (Universal Time) 1 15th waxing moon, 12th month November 10, 2011 No full moon November 10, 2011 at 20.16 (Before November 9?) 2 14th waning moon, 1st month December 24, 2011 No new moon December 25, 2011 at 6.10 (Between December 12-22?) 3 15th waning moon, 4th month March 22, 2012 No new moon March 22, 2012 at 14.37 (Before March 22?) 4 15th waxing moon, 8th month July 3, 2012 No full moon July 3, 2012 at 18.52 (Between June 22-July 2?)

The results show that none of the − Condition 1 is a warning condition if conditions are satisfied. So, it can be concluded the full moon of the 12th month occurs that the year 2012 is not an Adhikamat year. before November 9. This will force the This answer coincides with the academic new moon of the coming 1st month to group and is confirmed by the mango tree be before the mid-winter. Then, the full (referred in Table 3) as the Suvarnabhumi people moon of the 3rd month will occur before have been using signs from nature, sunray, the beginning of summer. This is why and lunar phase to check for an Adhikamat some years the Thai lunar calendar moves year since several thousand years ago. the Magha Puja Day (full moon, 3rd month) to the next one of the 4th month. 3.2 Discussion of Conditions Defining Adhikamat Year − Condition 2 is the condition that fixed The conditions to be an Adhikamat year the Thai lunar calendar with the seasonal can only be fulfilled with evidence of the year (using Gregorian calendar). If event of 13-dark moon impending 13-full moon. the new moon of the 1st month occurs For all four conditions presented, each can be between December 12 and 22 (before discussed as follows: or on the south solstice). It shows that Chiang Mai J. Sci. 2018; 45(6) 2505

the calendar is faster than the seasonal very well. Many times, the full and dark year then it needs to add one more month moon days of the Thai lunar calendar to that lunar year. do not coincide with the actual moon. Condition 2 and 4 can solve this variation − Condition 3 is also a warning condition and keep the Thai lunar calendar aligned if the new moon of the 4th month occurs with, and adjusted to, the tropical year. before March 22 (before or on the vernal Thus, the full and dark moon days of equinox). This will force the waning the Thai lunar calendar will be aligned moon of the 6th month to be before the with the actual lunar phases. These two beginning of the rainy season. This is conditions will confirm when the Thai lunar why some years the Thai lunar calendar calendar needs a leap month added to moves the Visakha Puja Day (full moon, an Adhikamat year. In the long term, 6th month) to the next one of the 7th the average year length of the Thai lunar month. calendar will be equal to the mean tropical year. − Condition 4 is also the condition that 2.) The goal of having Condition 3 is fixed the Thai lunar calendar with the to sync the Thai lunar calendar with seasons. If the full moon of the 8th the solar calendar (being the Gregorian month occurs between June 22 and calendar) by referring to the vernal July 2 (11 days after the north solstice), equinox. If the new moon of the 4th month which will occur before the heavy rains occurs after this equinox then it can start. The calendar needs to add one correct the accumulating error and fix more lunar month to the 8th month and the average year length to be nearly equal that is an Adhikamat year. This is why to the tropical year. some years the Thai lunar calendar 3.) When the full and dark moon days moves the Day (full moon, of the Thai lunar calendar do not coincide 8th month) to the next one which is called with the actual moon up to two days and the Double-8th month (or noted as “88”). Condition 2 and 4 are not satisfied, then the calendar needs a leap day added to By comparing the Thai lunar calendar to that year as an Adhikavara year. the Gregorian calendar, the four conditions of the Suvarnabhumi-Gregorian rule As analysis from the three issues, the Thai describe the relations of the timing that are calendar currently is a Buddhist calendar in easily observable and recognizable for which the months are based on lunar months international researchers. Three important (Culasakaraj or Burmese calendar) and years issues can be gained from this rule. are based on solar year (Gregorian calendar). 1.) Currently, the Thai lunar calendar is One of its primary objectives is to synchronize based upon on Culasakaraj, such calendars the lunar part with the solar part (seasonal). are known as Burmese calendar, which Because of the inaccuracy of the calendric was adapted from the . calculation systems, the average and the As mentioned in Question I and II, its actual full and new moons rarely coincide. average year length is longer than the The lunisolar calendars are slowly drifting tropical (solar) year. The lunar calendar away from the seasons as the time goes by. and the tropical year do not match up The accumulating drift against the seasons 2506 Chiang Mai J. Sci. 2018; 45(6)

means the New Year’s Day (Songkran Day) the Songkran Festival. Otherwise, in the which used to fall on March 22 (; long term, Thai people would be celebrating near the vernal equinox) in 638 AD, but now the Water Festival during the rainy season or falls on April 16 in 2012 AD, and in the long even winter. term, will fall on the rainy season or even winter. There is no known internationally - Referring to Question III : concerted effort to stop this drift. Fortunately, The ancient Suvarnabhumi added one the introduced Suvarnabhumi-Gregorian extra 8th month to an Adhikamat year conditions for checking an Adhikamat year because they wanted to adjust the calendar can stop the drift and use as a guide for for rice cultivation. Growing rice at developing the future Thai lunar calendar appropriate conditions given by the seasons to be perfectly coincided with the seasons. would result in high yield. The 8th month is a heavy rain season which is very 4. CONCLUSIONS important stage for rice vegetation. They In year 2012, there was an argument observed signs from nature, lunar phases between academic scholars and Thai astrology with corresponding to the north and group whether that year is an Adhikamat year. south solstice, and the event of 13-dark Through in-depth studies of the calendric moon impending 13-full moon to determine calculation systems and their history, we find an Adhikamat year. that each group bases its argument in different systems, as discussed through the - Referring to Question IV : five questions. In order to settle the conflict, Using the NASA new moon and full we arrive at the Suvarnabhumi-Gregorian rule. moon data as a reference for checking The rule is a combination of knowledge bases an Adhikavara year, the full and dark from both the astrology practitioners, who moon days on the Thai lunar calendar are accustomed to the Suvarnabhumi calendar, can be adjusted to coincide with the actual and the academics, who are engaged in moon phases. present-day calculations. The summary of our findings through - Referring to Question V : five research questions are as follows: The Suvarnabhumi-Gregorian conditions are - Referring to Question I : established to confirm an Adhikamat The current Thai lunar calendar should year. This astronomical rule is consistent stop utilizing the Culasakaraj. The Culasakaraj with the corrected data of lunar phases is based on a sidereal calendar which from NASA used by academic scholars; slowly drifts from the seasons over furthermore, it remains the Suvarnabhumi times. The Thai lunar calendar should calendar system used by the Thai astrologers. be synchronized with the solar calendar instead like in the internationally accepted The new way to develop the future Thai Gregorian calendar. lunar calendar is suggested as follows:

- Referring to Question II : 1.) A new version of Thai lunar calendar It is confirmed that the Thai lunar is recommended using the Suvarnabhumi- calendar should stop basing their festivals Gregorian conditions for checking an and holy days on the Culasakaraj, especially, Adhikamat and Adhikavara year. It is Chiang Mai J. Sci. 2018; 45(6) 2507

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