The Burmese & Arakanese Calendars/Chapter 5
101. The Burmese Calendar is essentially a religious one. "The reason given in Maha Wagga why the Wa, or Buddhist Lent, was instituted by Buddha appears to be to prevent the Bhikkus from going on their travels during the rainy season, so that they might not crush the green herbs, hurt the vegetable life, and destroy the lives of many small insects. And the Wa (Vassa), or the retreat, was prescribed to be entered upon in the rainy season for three months." (The Arakanese Calendar, by Htoon Chan; Introduction, page i). Lent begins on the first waning of Wazo or Second Wazo.
102. The direction that the Labyi of Wazo or Second Wazo should fall on a day on which the moon's longitude is at least 266° 40′ is almost exactly equivalent to a direction that the month in which solar new year's day falls should always be the month of Tagu. This is the Hindu rule, viz., the month in which the sun enters Mesha must be called Chaitra.
103. Whether that Hindu rule has any religious significance I know not, but it is evident that however suitable the year of the Surya Siddhanta may be for Hindus, it is not suitable for Buddhists. The rule that the months of Lent, viz., Wazo, Wagaung, Tawthalin and Thadingyut, shall fall in the rainy season cannot be permanently carried out by observing any year except the tropical year.
104. The tropical year (ayana hnit) was known to the author or authors of Thandeikta, but they make no use of it except to calculate the lengths of days and nights. The equinox is said to have coincided with Thingyan Kya about 207 years before Poppasaw's epoch, i.e., about 411 A. D. which is pretty near the truth. The precession is stated to be 54″ per annum, which is not correct. The real rate of precession is about 50″ per annum.
105. The Thandeikta solar year is
365 days 6 hours 12 minutes and 36.56 seconds = 365.2587564814 days.
This is proved by modern science to be incorrect. The mean sidereal year is, according to Guillemin
365 days 6 hours 9 min. and 10.75 secs. = 365.25638 days,
according to Sewell and Dikshit
365 days 6 hours 9 min. and 9.29 secs. = 365.25635 days.
365 days 5 hours 48 min. and 46.15 secs. = 365.2422789 days and
365 days 5 hours 48 min. and 46.054 sec. = 365.2421995 days,
365 days 5 hours 48 min. and 45.37 secs. = 365.2421917 days.
107. It is manifest then that the Burmese first point of Meiktha is not a fixed point among the stars, although it is intended to represent a fixed point. It is moving forward, away from its original place among the stars. It is diverging at a still faster rate (about 59″ per annum) from the point which the mean sun occupies at the equinox, for the precession of the equinoxes is retrograde. Through the accumulation of this error Thingyan Kya is now about 24 days after the vernal equinox.
108. The luni-solar year necessarily consists sometimes of twelve, sometimes of thirteen, months. The Thandeikta rules are designed to make the average luni-solar year equal to the Thandeikta solar year, that is, about 22 minutes longer than the real tropical year.
109. The Metonic cycle, used by Makaranta, makes the average luni-solar year 365.24675 days. This is greater than the tropical year, but less than the Makaranta solar year. In other words
| 19 Makaranta solar years | = 6939.91625 days |
| 235 lunations | = 6939.688415 ays„ |
| 19 tropical years | = 6939.602123 ays„ |
The average Makaranta luni-solar year, therefore, is drifting forward round the seasons, but at a slower rate than the Thandeikta average luni-solar year, which is drifting at the same rate as the Thandeikta solar year.
110. The application of the rules of Thandeikta has lessened the divergence between the Burmese solar and average luni-solar years, but at the expense of accelerating the divergence between the average luni-solar year and the real tropical year. Thandeikta grasped at the shadow (the Burmese solar year not being a real year of any kind) and lost the substance, namely the tropical year which is all-important. It accelerated the pace at which Lent was altering its place in the seasons under the Makaranta system. Lent is already beginning to creep out of the rainy season into the cold season.
111. The Indian and Burmese books ascertain the epact (moon's age at the moment when the solar year ends) in two ways. The yet-lun (with its fraction ) is the epact expressed in didi. The adimath thetha is the epact expressed, by Makaranta in 228ths of a lunation or 235ths of a solar month, by Thandeikta in 911ths of a lunation or 939ths of a solar month. If both forms of the epact are correctly calculated they must agree. By Makaranta the adimath thetha is not correct, because the ratio assumed between the lengths of a mean solar month and a mean lunation, 235 : 228, is only a rough approximation; its error is the error of the Metonic cycle. In the first cycle of Poppasaw's era both forms of the epact pyoed in the same year, except in the 8th year when the adimath thetha was slightly in arrear. In the 12th century the error had accumulated so much that adimath pyo was behind yet-lun pyo every time. Thus
| Yet-lun pyo | 1101 | 1104 | 1107 | 1109 | 1112 | 1115 | 1117 |
| Adimath pyo | 1102 | 1105 | 1108 | 1111 | 1113 | 1116 | 1119 |
In five cases the adimath pyo was one year behind, in the other two cases it was two years behind. Later in the century the error was greater, thus
| Yet-lun pyo | 1177 | 1180 | 1182 | 1185 | 1188 | 1191 | 1193 |
| Adimath pyo | 1178 | 1181 | 1184 | 1187 | 1189 | 1192 | 1195 |
In three cases the adimath pyo was two years behind. Thandeikta corrected adimath thetha and made it agree with yet lun.
112. To make the month in which Ata Ne occurs Tagu, and the month in which the full moon is in Athanli Wazo or Second Wazo, the watat year should be, not yet-lun pyo year as stated in Thandeikta, but the year before yet-lun pyo, or approximately every year in which yet lun exceeds 19. This was so at the beginning of the era. After 12 centuries we find 6 watat occurring in yet-lun pyo year and the seventh in the year after yet-lun pyo (year 5—expired—of cycles, 61, 62 and 63, viz., 1145, 1164 and 1183). In cycle 64 this last error was corrected at Amarapura by placing the watat in year 4 (1201) instead of year 5 (1202). The subsequent corrections of the Metonic cycle, namely the changes
| from 2 to 1 in 1217 |
| from„ 13 to„ 12 in„ 1228 |
| from„ 10 to„ 9 in„ 1263 |
have placed watat in the year before yet-lun pyo, but only when the yet-lun amounts to 27, 28 or 29. It seems to have been considered that to revert fully to the original rule, and place watat always in the year before yet-lun pyo, would be too drastic a measure, as it would place the beginning of Lent on the average five days later in the season than it is now. It is already fifteen days later in the season than it was in Poppsasaw's time.
113. From these facts it is clear that
(a) The error of the Burmese solar year is constantly moving the nekkat Athanli later and later in the seasons,
(b) The present practice of fixing watat by yet-lun pyo or yet-lon 27, 28 or 29, while it puts the Labyi of Second Wazo in Athanli in watat years, leaves the Labyi of Wazo short of Athanli in many common years,
(c) If the Athanli rule were fully observed it would immediately move the average Lent five days later than it is at present,
(d) If Lent is to be maintained permanently in, or even near, its proper place in the seasons, the solar year of the Surya Siddhanta must be abandoned, and the tropical year substituted for it.
114. Any calendar, if it is to have the maximum of practical utility and convenience, must be easily ascertainable for many years in advance. The best method hitherto devised to attain this end is to make use of cycles. The most notable example of this is the adjustment of days to years in the European calendar, which was first started by Julius Caesar, and afterwards improved by Pope Gregory XIII. The Julian cycle was 4 years, the Gregorian cycle is 4000 years. Every year which is a multiple of 4 is a leap year, except that every year which is a multiple of 100 but not of 400 is a common year, and 4000 and every multiple of 4000 is a common year. The Gregorian calendar is practically a perfect index of the seasons.
115. The Metonic cycle of 19 years is used by Christian churches to determine Lent and Easter, but the error of the cycle necessitates a complex system of adjustment of the golden numbers every century. Raja Mathan applied the Metonic cycle without any adjustment, and its error has produced in twelve centuries a marked divergence between the solar and average luni-solar years.
116. If reform of the Burmese calendar be undertaken, and the tropical year be adopted, the cycle method of regulating the calendar can be adopted, with practically no error, for there is one perfect luni-solar cycle, namely the cycle of 1040 years, which was discovered by the French astronomer de Cheseaux. 1040 tropical years equal 12863 lunations. This was absolutely correct without any error a few centuries ago. It is not so now because the length of the mean tropical year is decreasing at the rate of about one second in 200 years, while there is no appreciable change in the length of the mean lunation ; but the error is so small that it will not amount to one day in 10,000 years.
117. This fact may be easily verified. Three estimates of the length of the mean tropical year, according to modern science, are given in paragraph 106. If these three be multiplied by 1040, the results are respectively
| 379851.969976 | days | |
| 379851.88748 | days„ | |
| and | 379851.879358 | days„ |
| Ball | 29.530589 | days |
| Young | 29.530588 | days„ |
| Surya Siddhanta | 29.530587946 | days„ |
If these three be multiplied by 12863, the results are respectively
| 379851.966307 | days | |
| 379851.953444 | days„ | |
| and | 379851.952749398 | days„ |
Comparing the greatest estimate of 12863 mean lunations and the smallest estimate of 1040 mean tropical years,
| 12863 mean lunations | = | 379851.966307 | days |
| 1040 mean tropical years | = | 379851.879368 | days„ |
| the difference is only | .086939 | days„ |
In 10,000 years the difference would amount to about 20 hours. This is a maximum estimate.
118. The best way to apply the cycle of 1040 years is to use it to make corrections in the Metonic cycle at regular intervals. The problem is to find at what intervals the correction should be made.
119. The number of watat in 1040 years is found by subtracting the solar from the lunar months.
12863 − 12480 = 383.
Now multiply the two kinds of cycles together.
19 × 1040 = 19760.
The number of watat in 19760 years is
| By Meto | 7 | × | 1040 | = | 7280 |
| By de Cheseaux | 383 | × | 19 | = | 7277 |
| Difference | 3 | ||||
The Metonic cycle must be so modified as to cut out 3 watat in 19760 years.
120. The intervals between watat run in a series thus 3 3 3 2 3 3 2 and so on, over again. In each Metonic cycle there are two two-year intervals, one of which follows three three-year intervals, and the other follows two three-year intervals. Every correction must be made by converting into a three-year interval one of those two-year intervals which follow two three-year intervals
Thus
| 1 | . | 1 | . | . | 1 | . | . | 1 | . | 1 | . | . | 1 | . | . | 1 | . | . | ||
| 1 | . | 1 | . | . | 1 | . | . | 1 | . | . | 1 | . | 1 | . | . | 1 | . | . | ||
| 1 | . | 1 | . | . | 1 | . | . | 1 | . | 1 | . | . | 1 | . | . | 1 | . | . | ||
| 1 | . | 1 | . | . | 1 | . | . | 1 | . | . | 1 | . | 1 | . | . | 1 | . | . | ||
| 1 | . | 1 | . | . | 1 | . | . | 1 | . | 1 | . | . | 1 | . | . | 1 | . | . | 1 | |
| 1 | . | . | 1 | . | 1 | . | . | 1 | . | . | 1 | . | 1 | . | . | 1 | . | . | 1 |
121. The average interval between one watat and the next is, by Meto, 197 years. Therefore to reduce the number of watat in any given period by one, the number of forward shifts required is 197 × 7 = 19. The number of shifts required to cut out three watat in 19760 years is 19 × 3 = 57. The interval between one shift and the next is 19760 ÷ 57 = 346.6 years. It is unnecessary to pursue this branch of the inquiry any further. The result at which we have arrived is that if the tropical year be adopted as the solar year in Burma, the positions of the watat in the current cycle, namely
| 1 | 4 | 7 | 9 | 12 | 15 | 18 |
should be maintained without any alteration for 18 cycles more, that is, until the year 1623 B. E. (A. D. 2261).
122. It remains to find a rule for insertion of intercalary days. 1040 years contain 12863 months, of which 12480 are ordinary and 383 intercalated. All the intercalated months have 30 days each. Half the ordinary months have only 29 days each. Therefore without intercalary days the 12863 months would have 12863 × 30 − 6240 days = 379650 days. Subtract this number from the highest and lowest figures for the number of days in de Cheseaux's cycle, given in paragraph 117.
| 379851.966 |
| 379650 |
| 201.966 |
| 379851.879 |
| 379650 |
| 201.879 |
Taking an average, 201.922 intercalary days are required in 1040 years, or 403.845 in 2080 years. If watat were alternately wagyitat and wangètat throughout the whole period of 2080 years there would be 383 wagyitat, leaving a deficit of 20.845 days. This is almost exactly one day in 100 years. Therefore the required number would be made up by intercalary days in two successive watat once in fifty years, all other watat being alternately wagyitat and wangètat. The number of watat in any consecutive fifty years is sometimes 19 and sometimes 18. The rule therefore might be that all watat shall be alternately wagyitat and wangètat, except that (a) the first watat in every fifty years shall be a wagyitat, and (b) if the last watat in any fifty years be a wangètat, then both the first and second watat in the following fifty years shall be wagyitat.
123. If the tropical year be adopted as the solar year of Burma, and the watat continue to be placed as in the current Metonic cycle, there are some preliminary adjustments to be considered. In the first place, in order that the month in which the solar year begins may always be Tagu, and that the Labyi which marks the beginning of Lent may always occur when the moon is in Athanli, it is necessary that Thingyan Tet should be put about 712 days earlier in the season than it is at present. The sun's position at Thingyan Tet marks the zero of longitude; if that zero be moved westwards Athanli will move westwards to an equal extent, and will thus adjust itself to the moon's position at Wazo Labyi as it is in the current cycle.
124. There is no apparent reason why Thingyan Tet should not always be put at midnight. Under the Burmese system the civil month always begins at midnight though the lunation does not. It would be only consonant with this practice to make the civil solar year begin at midnight. It has been shown that the European calendar is a practically perfect index of the seasons. It would be obviously convenient if the Burmese solar year always began at midnight of the same day of the European calendar, say midnight of 7th—8th April. Early in the 12th century B. E. it varied between the 11th and 12th April. It is now 15th April.
125. If any reform of the calendar be undertaken it would be worth while to correct the error of the calendar month. Table VIII shows how this error has grown in twelve centuries. In the 29 years from 1235 to 1263 B. E. the Lagwè was the day on which mean new moon occurred only eight times, namely in
| March | 1873 |
| May | 1873 |
| August | 1874 |
| October | 1874 |
| August | 1883 |
| October | 1883 |
| November | 1883 |
| January | 1884 |
In 171 months Lagwè was one day too early. In 172 months it was two days too early. In 9 months it was three days too early, namely in
| February | 1880 |
| April | 1880 |
| October | 1890 |
| December | 1890 |
| February | 1891 |
| April | 1891 |
| February | 1896 |
| April | 1896 |
| April | 1901 |
| Watat | Thandeikta | Proposed |
| 1272 | gyi | gyi |
| 1274 | ngè | ngè |
| 1277 | ngè | gyi |
| 1280 | gyi | ngè |
| 1282 | ngè | gyi |
126. If the tropical year be adopted, and the two initial corrections suggested in the last three paragraphs be made, viz. the solar year to commence at midnight of 7th—8th April every year and one extra yet-ngin to be inserted between 1270 and 1283, then the reformed calendar might conveniently commence from the first day of the tropical solar year 1281, 8th April 1919. The rules for compiling this calendar for a number of years are very simple.
127. (1) Divide Thagaj'it by 19. If the remainder be
| 1 | 4 | 7 | 9 | 12 | 15 | or | 18 |
the year has an intercalary month. This rule holds good until the year 1623 B. E.
(2). After B. E. 1623 the watat years in the Metonic cycle change as follows:—
| 9 changes to 10 in B. E. 1625 |
| 1 changes„ to„ 2 in„ B. E.„ 1978 |
| 12 changes„ to„ 13 in„ B. E.„ 2331 |
| 4 changes„ to„ 5 in„ B. E.„ 2684 |
| 15 changes„ to„ 16 in„ B. E.„ 3037 |
| 7 changes„ to„ 8 in„ B. E.„ 3390 |
(3). Mark all the watat for a number of years as above. Then divide them into periods of fifty years, commencing from 1281, thus,
| 1281 | — | 1330 |
| 1331 | — | 1380 |
| 1381 | — | 1430 |
and so on. Watat years are alternately wagyitat and wangètat, except that
(a) in each period of 50 years the first watat is wagyitat, and
(b) when the last watat of any 50 years is wangètat, then both the first and second watat of the next following 50 years are wagyitat.
For Wazo, if the preceding year was a common year, add 4. If the preceding year was a watat of either kind, add 6.
For any other month, if the present year is a common year, add 4, If the present year is a wangètat, add 6. If the present year is a wagyitat, add 0.
Whenever the sum exceeds 6, subtract 7.
(5). To find the week-day of Thingyan Tet. Divide Thagayit by 4. If the remainder is 2, add 2, if not add 1, to the week-day of Thingyan Tet of the last preceding year. If the sum exceeds 6, subtract 7. This rule holds good until B. E. 1461.
128. The results obtained from Thandeikta may be compared with those obtained from the system of averages based on de Cheseaux's cycle, for 82 years beginning in B. E. 1281, by examining tables II and III. In 58 years out of the 82 the luni-solar year by both systems begins on the same day. In the other 24 years the luni-solar year in table III begins one day later than in table II. If the tables had been prolonged a few years later the divergence of the two systems would have become conspicuous. We have seen that Thandeikta puts a watat in the year before yet-lun pyo when yet-lun amounts to 27, 28 or 29 (paragraph 100), and in order to effect this four of the seven watat years of the Metonic cycle have been altered (paragraph 112). The next alteration to be made by Thandeikta will be the transfer of watat from year 18 to year 17 of the cycle. This is to take place when yet-lun of year 17 exceeds 26. The yet-lun and its fraction (awaman) of year 17 are as follows:—
| B. E. | Yet-lun. | Awaman. |
| 1233 | 24 | 569 |
| 1252 | 25 | 96 |
| 1271 | 25 | 316 |
| 1290 | 25 | 535 |
| 1309 | 26 | 62 |
| 1328 | 26 | 281 |
| 1347 | 26 | 501 |
| 1366 | 27 | 30 |
So that in B. E. 1366 Thandeikta would create the first serious divergence from the system of averages, and would thrust lent further than ever out of its original place in the tropical year, by transferring the watat from year 18 to year 17 of the Metonic cycle.
129. Tables II and III exhibit a marked difference in respect of the solar year. In table II Thingyan Tet is frequently in Kason. In table III it occurs on 1st waxing of Kason once in each Metonic cycle and no more. In all other years it is in Tagu. If Tagu happened to be a month of 30 days it would always be in Tagu.
130. The official calendar-makers to the late Burmese Government were a race of Hindu astrologers, the descendants of Brahmans said to have come to Mandalay from Manipur, and known in Burma as Ponnas. Since the annexation of Upper Burma the British Local Government has assumed the function of officially promulgating the essential elements of the calendar every year by notification in the Burma Gazette. The details are obtained from the Ponnas at Mandalay, as they were by the Native Government, and are submitted for approval to the Head of the Buddhist religious orders before the Government takes action.
131. A glance at the specimen page given in paragraph 49 is sufficient to show that the learned Ponnas expend enormous labour in computing all the details set out in the calendar. But those details consist chiefly of an ephemeris of the longitudes of the sun, moon and planets, which, though they are interesting, and may be essential to the pursuit of the science of astrology, are quite irrelevant to the all-important matter of fixing the number of months and number of days in each year. This is the only matter with which the public in general is concerned. But since the introduction of Thandeikta methods this distinction has been lost sight of, and the determination of watat and yet-ngin has been retarded by waiting on the computation of the ephemeris. Until recently the calendar for each year was notified only in the autumn of the previous year, too late for use in preparing the numerous diaries that are published in Burma, India and England. The compilers of such of these diaries as are intended for use in Burma had to guess the intercalary months and days, or act on the advice of irresponsible astrologers in Rangoon or elsewhere, and the guesses and advice were sometimes wrong. The last few years an improvement has been effected by notifying the calendar nearly two years in advance. But there is no reason why it should not be notified forthwith for hundreds of years, or for ever by means of the rules in para. 127.
132. One reason which makes it desirable to notify the calendar forthwith for a long series of years is that the present practice tends to encourage some amateur astrologers who dispute the correctness of the Ponnas' calendars, and publish pamphlets in which they endeavour to enforce their own views about the insertion of intercalary months and days in certain years. Whether they succeed in gaining many adherents may be debatable, but it obviously tends to create confusion in legal documents and otherwise if such persons get a hearing at all. The important point is that the matter should be settled once for all, by authority, by the promulgation of such simple rules that any educated man may be able to construct a calendar of any year for himself. The author claims that the rules proposed in paragraph 127 fulfil this condition.
133. No doubt it would be possible without the promulgation of any rules to fix the watat and yet-ngin in advance for a long series of years by notification. If it be conceded that Government should do this, it may be asked what is there to choose between adopting Table II which is the result of Thandeikta methods and adopting Table III which is compiled in accordance with the rules proposed for a reformed calendar in paragraph 127. The answer is that so far as results in the near future are concerned there is very little to choose. In 24 years out of 82 the Lagwè is nearer to the real new moon in table III than in table II, and table III makes 18 out of every 19 solar years begin in Tagu, whereas table II makes 22 of the 82 years begin in Kason. But table III has this advantage, that it is based on simple rules by which the whole of it could be reconstructed at any time in an hour or two, given the details for any one year; and the same rules would carry it on for ever; whereas if table II be adopted the rules of Thandeikta will in 1266 B. E. create a serious departure from correct principles by placing lent later than ever in the season, and further errors will be introduced at intervals of 130 years or less. Long and tedious calculations are required to determine the watat and yet-ngin by Thandeikta; these are all abolished by the proposed rules for a reformed calendar.
134. The Arakanese calendar, it is believed, has never been officially notified by Government since the annexation of that part of the Province. There was apparently no need to do so, because the calendar had been fixed for 2000 years at once, and no controversy about the correctness of it seems to have arisen. Lent is falling later in the season than it used to be, but the Arakanese calendar would go on for about 1400 years more before the average lent would get so late as the average lent by Thandeikta is now. Therefore there seems to be no reason why the Arakanese calendar should be interfered with. Its chief defect is the error of the solar year. That could be corrected, if so desired, without any interference with the luni-solar year.