¹ In Thailand, where numerals are used in preference to names, the extra month is numbered as 8 in the Central (Ayuthia/Bangkok) region and numbered as 10 in the Northern (Lan Na) region. In Lan Na and Sipsongpanna, however, an alternative mode can be found. This follows the Burmese style and calls the extra month number 9. The same month is intended in all three modes of reference.

Strict application of the 7 in 19 and 11 in 57 principle will generate slightly less than 6 lunar days too many in 800 years (292213 lunar in 292207 solar days) — a rate almost half of that by which the sun's position accumulates error from the system's failure to take account of Precession of the Equinoxes. This slippage between the sign Aries and the constellation Aries increments by 1° in about 72 years. The western sun arrives at 0° on or about 21 March: the Southeast Asian date for this event is currently on or about 13 April. Since the ability to calculate the times of new and full moons, lunar and solar eclipses, etc., is not impaired by either anomaly, the system has not contrived a correction for them.

² Faraut, F. G., Astronomie cambodgienne (Saigon, 1910);Google ScholarChua, Thong, Pattihin Darasasat for years BS 2440–2519 in 4 vols.Google Scholar; Irwin, A.M.B., The Burmese and Arakanese Calendars (Rangoon, 1909)Google Scholar. For Sipsongpanna I use Zhang Gongjin and Chen Jiujin, “Investigating Dai Calendars” (Beijing, 2 vols., 1981, 1984) (“Chinese Astronomical History Collection”); for Northern Thailand, 100-year Calendar, Lanna Thai (Chiang Rai Teachers' College, 1984).

I also use some unpublished manuscript material, and my own Southeast Asian Ephemeris: Solar and Planetary Positions, ad 638–2000 (Cornell University, 1989)Google Scholar.

The limitation here, of course, is that information is available only for relatively modern times. But the conclusion that the record would be worse for the earlier period if only one had the evidence, can be countered. The performance of the Thai horas working in 1500 ad is substantially more impressive than those operating in 1900 ad.

³ For the data, see Eade, p. 160; Faraut, p. 147; Irwin, p. 47; and Gongjin, vol. 2, p. 272. Some calendars and almanacs give what they call the “set” (remainder) for a given year. This value is found modulo 19, so that if the placement of adhikamas years is known, the set value immediately indicates whether or not the year has an extra month.

The distribution of adhikamas years is shown more fully in the Table at the end of this article.

⁴ Irwin, p. 3 (my italics).

⁵ The avoman increases by 11 units a day to a maximum of 692, and the kammacubala increases by 800 a day. It follows that when an inscription gives the kammacubala of date, division of it by 800 will reveal how many days have elapsed in the year and what the base value is for that year.

⁶ Faraut expounds the adhikawan rule on p. 67. On page 115, on the other hand, he claims that adhikamasa years have a frequency of 4 in 11. This is not so: there is no question but that the rate is 7 in 19.

Prince Pethsarath's article on the Lao Calendar [The Kingdom of Laos, ed. de Berval, R. (Saigon, 1959), p. 102]Google Scholar omits to mention that the kammacubala is also involved in the calculation of adhikawan.

A plain instance of the rule's being ignored or flouted comes, for instance, with Thong Chua's Ephemeris for 1922 ad. The head-line for that year gives the avoman as 21 (i.e., as less than 138) and the kammacubala as 239 (i.e., as greater than 207), but Jyestha (under June 1922) is not given an extra day.

⁷ Very occasionally one does find that 12 extra days are inserted, presumably through faulty reckoning. One would expect to find that this excess was cancelled by adding only 10 days to the next cycle — or else that the cycle was being defined at a different point.

While there is no evidence by which to determine the matter, one would suppose that the horas calculated each new year afresh, or else only short runs. It seems unlikely that a map for more than one cycle would be laid out in one operation. When the Chotmaihethon for June 1732 has to record that “this year and the next two have an extra day” [in Prachum Phongsawadan, vol. 8 (Bangkok, 1808/repr. 1964), p. 113]Google Scholar things have got badly out of hand.

⁸ The procedure is called “hsitan” by Zhang Gongjin (p. 251).

⁹ It seems reasonable to suppose that the last two places of the incomplete run would be occupied by 13 and 18.

¹⁰ Clear statements of what defines Lunar New Year are hard to come by. It is generally known the the New Year period varies in length, and the reason is as follows: at the time of New Year the True Sun is ahead of the Mean Sun by slightly varying amounts. The New Year period begins with mahasongkran when the True Sun reaches 0°; it ends with taleungsok, when the Mean Sun reaches 0°. The exact moment is reflected in the kammacubala value for the year. Suppose the value happened to be 200. Its 800-complement is 600, which means that taleungsok took place at 600/800 * 24 hours, i.e., at 6 p.m. on western reckoning; or at 600/800 * 60 = 45 nadi by Southeast Asian reckoning.

¹¹ In the following table “computer” refers to the program written by this author, based on Faraut's data. Its inclusion is justified by the fact that Faraut's results are sometimes less reliable than his outline of the method.

¹² In Sinlapakorn, 13. 4 (BS 2512): 77–79.

¹³ Irwin, pp. 42ff. He also reckons CS 1141, for instance, as set 1 (note 3, above), but rather confusingly calls CS 1140 set 0. In one sense it is, but it makes more sense to reckon it as set 19, in order to make it clear that CS 1441 is the start of a cycle. The 100-year Calendar and Sipsongpanna (Zhang Gongjin), on the other hand, would reckon CS 1141 as set 2. In order to make the material directly comparable, I have modified this latter mode.

The method of counting in the historical record is often ambiguous: the first rcek/naksatra (lunar mansion), for instance, is sometimes reckoned as 0 (Chiang Rai 33, Lamphun 12) and sometimes as 1 (Lamphun 21; Lamphun 24).

In the Burmese record, on the other hand, Saturn (whose number is 7) is sometimes represented by 0 in horoscope diagrams. I suspect the reason for this is as follows: the weekday is frequently represented by a planetary numeral, where day 2=Monday, 3=Tuesday, etc. The relevant weekday can be found from the horakhun modulo 7, where 0=7=Saturn=Saturday. The association between the planet and the day of the week, it seems, became so strong that the relation could be reversed and 0 for the weekday could do duty as 7 for the planet. This was at a time when the discovery of Uranus (nowadays represented by 0) was centuries away.

¹⁴ The total has to be reckoned as eight, not as four, because of the in-built difference between the Burmese and the rest.

¹⁵ The Introduction to my Ephemeris (note 2) gives an indication of what may be done along these lines.