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IE BURMESE AND ARAKANESE CALENDARS.

A. M. B. JEWIX

V

THE

BURMESE & ARAKANESE CALENDARS.

CALENDARS

BY

A. M. B. IRWIN, c.s.i..

i\

INDIAN CIVIL SERVICE.

Rangoon :

PRINTED AT THE HANTHAWADDY PRINTING WORKS,

46, SULE PAGODA ROAD.

1909.

PREFACE.

IN 1901 I published " The Burmese Calendar." It was written in Ireland,

and in the preface I admitted that I had not had access to the best sources of

information. I can claim that the book was not inaccurate, but it was in-

complete. I have since made the acquaintance of the chief Ponnas in Mandalay,

and have learned a good deal more on the subject of the calendar, chiefly

from U Wizaya of Mandalay and Saya Maung Maung of Kemmendine, to

whom my acknowledgments are due. I therefore contemplated issuing a second

edition, but when I applied myself to the task of revision I found it was desirable

to re-write a good deal of the book, and to enlarge its scope by including the

Arakanese Calendar. The title of the book is therefore changed.

My object has been to make the book intelligible and useful to both

Europeans and Burmans. This must be my excuse if some paragraphs seem to

one class or another of readers to enter too much into elementary details.

I have endeavoured firstly to describe the Burmese and Arakanese Calendars

as they are. Secondly, I have shown that an erroneous estimate of the length

of the year has introduced errors which have defeated the intentions of the

designers of the calendar, and I have made suggestions for reform. Thirdly, I

have compiled tables by which English dates may be translated into Burmese

dates and vice versa.

Table I for past years and Tables II and III for future years embrace a

period of 262 years. For any day within this period the Burmese date equivalent

to the given English date, or vice versa, may readily be ascertained by the use

of Table IX, combined with Table I or II or III as the case may be. The

method is described in the notes on Table IX at page 39.

CORRIGENDA.

Since going to press the following errors have been discovered.

Page 7. Paragraph 35. For 365-2687564814, read 365-2587564814.

Page 8. Paragraph 39. Line 7. To the figures 29-530583 add iouf

more places of decimals, viz., 2147. The figures will read, 29-5305832147.

Same page and paragraph. Line 8. For 5*846, read 58-46.

Page 16. Paragraph 59. For + read

25 25

Page 25. Footnote. For 450 read 479.

Page 72. Columns 5 and 6. The figures 97 i should be ^one line lower

down, opposite the Burmese year 1291.

The figures 100 3 should be one line lower down, opposite the Burmese

year 1307.

The figures 98 4 should be one line lower down, opposite [the Burmese

1337.

I must also admit that in paragraphs 81 and 82 the expression " reduce to

days " is not quite correct or appropriate, and may make the paragraphs some-

what obscure. The subject is very briefly and incompletely dealt with in Than-

deikta.

Also in paragraph 89 I omitted to give a rule for finding the Thokdadein.

tft

It is very simple. The rule in Thandeikta is T = 30^ -f- n Y.

2

In the particular case considered m = 4, and n = 14. .-. T = 132 Y.

A. M. B. I.

TABLE OF CONTENTS.

PAGE.

CHAPTER I. INTRODUCTION i

II. DEFINITIONS 4

77 I

III. GENERAL DESCRIPTION OF THE CALENDAR . 7

IV. METHODS OF CALCULATION 15

V. DEFECTS, AND SUGGESTIONS FOR REFORM . 26

VI. NOTES ON THE TABLES 37

TABLES.

I. Elements of the Burmese Calendar for 172 years, from A. D.

1739 to 1910, B. E. noi to 1272 42

II. Elements of the Burmese Calendar calculated by Thandeikta

for 92 future years, from A. D. 1909 to 2000, B. E. 1271

to 1362 52

III. Elements of the Burmese Calendar for 92 future years, from

A. D. 1909 to 2000, B. E. 1271 to 1362, as proposed to be

regulated by de Cheseaux's cycle of 1040 years, commenc-

ing from B. E. 1281 -58

IV. Elements of the Arakanese Calendar for 262 years, from A. D.

1739 to 2000, B. E. noi to 1362 61

V. Arakanese Wazo Labyi week-day for 2000 years, from A. D.

639 to 2638, B. E. i to 2000 68

VI. Thokdadein, Week-day and Moon's longitude at the end of

the I4th didi of Second Wazo, in watat years, from B. E.

1215 to 1362, calculated by Thandeikta 72

VII. Comparison of epacts, as found by European and by Maka-

ranta methods 74

VIII. Comparison of mean new moon and Burmese Civil Lagw6,

every month for 29 years 76

IX. English dates corresponding to the first day of each Burmese

month 84

X. Week-day of any given day in each Burmese month ... 90

THE

BURMESE & ARAKANESE CALENDARS.

CHAPTER I.

INTRODUCTION.

1. Of natural measures of time, denoted by revolutions and rotations of

the heavenly bodies, the best-known and most important are the year, the

lunation or synodic month, and the day. The principal artificial measures are

the solar month (one-twelfth of a year), the week, the hour, the minute, and the

second.

2. For a description of the different measures of the year and month

(tropical, sidereal and anomalistic years, synodic, sidereal, anomalistic, tropical

and nodical months) the reader is referred to text books of astronomy. Such a

description would be too lengthy to insert here.

3. The tropical year, lunation and day vary slightly in length, but none of

them is ever an even multiple or sub-multiple of another. Therefore the problem

of constructing a calendar to measure time by these three units is a very com-

plex one. In Europe, Julius Caesar simplified it enormously by abandoning the

lunation altogether, and dividing the year into twelve artificial solar months

without any remainder. This was not done in Asia, where lunations are still

used.

4. Other methods of simplifying the problem are

(a) To reckon by mean or average years and lunations, instead of

by the actual revolutions of the earth and moon, the periods

of which vary slightly.

(b) To postpone fractions of a day, and reckon each lunar month

and each year as commencing at midnight, the accumulated

fractions being added to the month or year periodically

when they amount to one day.

(c) To add the accumulated fractions of months and days not

exactly when they amount to integers, but at regularly recur-

ring intervals, on the principle of averages and by the aid of

cycles which are more or less accurate common multiples of

days, lunations and years.

These methods have been adopted to varying extents at different times and

in different parts of Asia, as will be seen later,

2 The Burmese and Arakanese Calendars.

5. The Burmese calendar is essentially a Buddhist one, but the methods

of computing it are derived from Hindu books. A few words about the Hindu

calendar are therefore necessary.

6. In paragraph 17 of "The Indian Calendar," by Sewell and Dikshit, is

a list of some of the best-known Hindu works on astronomy. The length of the

year is differently estimated in different works. The principal ones which seem

to have been used in Burma are the Original Surya Siddhanta and the present

Surya Si Idhanta. The length of the year as given in these two is respectively :

Original ... 365 days, 6 hours, 12 minutes, 36 seconds.

Present ... 365 days, 6 hours, 12 minutes, 36'56 seconds.

7. Sewell and Uikshit show (at paragraphs 47 and 52) that the Hindus

formerly reckoned by mean months and years, but at present by apparent

months, while both mean and apparent years are used indifferent parts of India.

The change from mean to apparent reckoning is supposed to have commenced

about A. D. 1040, as it is enjoined in a passage in the Siddhanta Sekhara by

the celebrated astronomer Sripati, written in or about that year.

8. The Hindus insert an intercalary month at any time of year, as soon

as the accumulated fractions amount to one month. In Burma, as we shall see,

this is not so. The intercalary month is always inserted at the same time of year,

in Burma proper after the summer solstice, in Arakan after the vernal equinox.

ERAS.

9. Burmese astronomers use the Hindu Kali Yug, which commenced in

3102 B. c. (Sewell and Dikshit, page 16).

(iautama Buddha's grandfather, King Einzana, is said to have started a

new era in 691 B. c.

The Religious Era dates from 543 B. c., the year in which Gautama is

supposed to have attained Nirvana.

In A. D. 78-9 King Thamondarit of Prome is said to have started another,

identical with the Indian Saka era.

In A. D. 638-9 the era now in common use was started simultaneously, in

Burma by King Poppasaw of Pagan and in Arakan by King Thareyarenu of

Dinyawadi dynasty. The same era is current in Chittagong under the name of

Magi-San. (Sewell and Dikshit, paragraph 71 and table III).

10. So far as I am aware, no record is extant of any calendars as actually

observed either in Burma or in Arakan earlier than the year ITOO of Poppasaw's

era (A. D. 1738). Mr. Htoon Chan, B. A., B. L., of Akyab, in his book The

Arakanese Calendar, published in 1905, gives the elements of the luni-solar

calendar of Arakan for 2,000 years of the current era (A. D. 639 to 2638), but

he states that these were compiled during the reign of King Na-ra-a-pa-ya

Introduction. 3

(A. D. 1742 to 1761), and it is not clear whether the details given for earlier

years represent what was actually observed or not.

IT. The Arakanese follow the rules of Makaranta, in which fractions are

reduced to their lowest terms, and very small remainders are neglected. Inter-

calary months are regulated by the Metonic cycle of 19 years, the use of which

was propounded in the loth book of Raja-Mathan, a Hindu astronomer.

12. The Makaranta is probably derived from the original Surya Siddhanta,

because it defines the length of the year as 365 days, 15 nayi, 31 bizana and

30 kaya (365 days, 6 hours, 12 minutes and 36 seconds), and because it uses

mean reckoning. It is probable that the Burmese followed the same rules from

Poppasaw's time down to iroo B. E. (A. D. 1738).

13. The book which is used now in Burma is Thandeikta, the origin of

which is involved in some obscurity. According to one account it was written

about noo B. E., according to another about 1200. At any rate the change

from Makaranta to Thandeikta reckoning was not effected all at once. From

noo to 1200 the intercalary months are still regulated by the Metonic cycle, as

in Arakan, but the intercalary days are not placed in the same years as in

Arakan, and it is not clear by what rule they were fixed. During that century

the growing discrepancy between the civil solar and luni -solar Years attracted

attention. Much controversy ensued, the party of reform being led by a princess

who was afterwards the chief Queen of King Mindon. The first departure from

the rule of the Metonic cycle was made by putting an intercalary month in 1201

instead of in 1202, but the rules of Thandeikta do not appear to have been fully

introduced untill 1215.

14. Thandeikta is based chiefly, if not entirely, on the present Surya

Siddhanta, but applies its rules only to a limited extent. According to one

account the present Surya Siddhanta was not known in Burma until one

Bhavani Din, a learned pandit of Benares, brought it to Amarapura in 1148

B. E. (A. D. 1786), and about fifty years later it was translated into Burmese.

Thandeikta does not adopt the system of apparent reckoning ; mean years and

mean months are still used. The practice of placing the intercalary month

always next after Wazo and the intercalary day always at the end of Nayon,

and only in a year which has an intercalary month, is still adhered to. But

the new Surya Siddhanta was followed in small alterations of the length of the

year and the month, and the Metonic cycle was abandoned, and intercalary

months so fixed as to prevent further divergence between the solar and luni-

solar years.

The Burmese and Arakanese Calendars.

CHAPTER II.

DEFINITIONS.

15. Yet is a day including the night. Ne (the sun) means the day as

distinguished from the night. A T //a means night. But in astronomy Ne means

a day of the week. The days of the week are denoted by numbers, thus,

1 Sunday.

2 Monday.

3 Tuesday.

4 \Yednesday.

5 Thursday.

6 Friday.

o Saturday.

16. The day is artificially divided as follows :

I yet

= 60 nayi

i nayi

= 4 pat

= 60 bizana.

i pat

= 15 bizana

i bizana

= 6 pyan

= 60 kaya.

i pyan

= lo kaya

I kaya

= 12 kana

= 60 anukaya.

I kana

= 4 nay a

= 5 anukaya.

But only the

following measures

are commonly used in astronomy :

i yet

= 60 nayi

Hindu, ghatika.

i nayi

= 60 bizana

pala.

i bizana

= 60 kaya

,, vipala.

i kaya

= 60 anukaya

,, prativipala

Therefore

i nayi

= 24 minutes

- *4 hour.

i bizana

= 24 seconds

= *4 minute.

I kaya

= '4 second.

i anukaya

'006 second.

And

i hour = 2*5 nayi.

i minute = 2*5 bizana.

i second 2*5 kaya.

Definitions. 5

17. For ordinary use the English divisions of a day have practically oust-

ed the Burmese ones, at least in the towns, and the word " nayi" has come to

mean " hour." The words "minute" and " second" have been engrafted into

the Burmese language.

18. La (moon) is a mean lunation, i.e. the average period from new moon

to new moon. Sandra Matha also means a lunation; Thuriya Matha means a

solar month = -L of a year.

19. Ltbyi is full moon. Laywc is new moon.

20. Ala Yet or Ata Ne is the solar New Year's Day, or the day on which

the mean sun enters the sign Meiktha (Aries).

21. Haragon (Hind. Ahargana) or Thaw ana, is the total number of days

elapsed from the beginning of the era, or from any other fixed point which may

be taken as a starting point for calculations, to a given day.

22. Kyammat is an aggregate of units, each of which is the Sooth part of a

day ( = 108 seconds = 270 kaya). This arbitrary unit is obviously a rude

and imperfect substitute for decimal fractions.

23. Didi (Hind. Tithi) is the 3oth part of a mean lunation, or the aver-

age time in which the mean moon increases her longitudinal distance from the

mean sun by 12 degrees.

24. Kaya is the difference between total days and total didi in any given

period. It must not be confounded with kaya, the measure of time, '4 of a

second (paragraph 16).

25. Awaman is the remainder in the arithmetical operation of reduction

of days to didi or vice versa. In other words awaman is the numerator of a

fraction of kaya.

26. Yet I tin is the epact or moon's age at midnight of solar new year's day,

expressed in whole didi.

27. Adimath (Hind, adhika masd) means both an intercalated month

and the total intercalated months from the beginning of the era or any other

fixed point to a given point of time. Adimath thetha means the epact of the

total intercalated months, or fraction of a month, which accumulates year by

year up to one month.

28. La lun is the number of whole months by which the total solar years

expired during the era exceed the total luni-solar years expired during the era.

When solar new year's day falls in Tagu the la lun is o ; when it falls in Kason

the la lun is i ; and so on. If the solar and luni-solar years were perfectly ad-

justed there would never be any la lun.

6 The Burmese and Arakanese Calendars.

29. Thokdadein at midnight of any given day is the number of days

expired from and excluding Ata Yet.

30. Thar? ay it is the number of the year of the Burmese era. It denotes

expired years, not current years as in Europe. That is to say, the era began at

the commencement of the year o. The first of January 1900 was Burmese 1261

Pyatho waxing 2nd, which means the second day of the month of Pyatho after

the completion of 1261 years of the Burmese era.

31. Ratha or Hnit Kywin is Thagayit minus a constant. In other words,

a fixed number is deducted from thagayit in order to shorten calculations, and

the difference is termed ratha.

32. Wa is the Buddhist lent, which extends from the full moon of Wazo

to the full moon of Thadingyut.

33. Wa-tat (lent repeated) is an expression applied to the Burmese leap

year. Wa-nqc-tat means that the year has an intercalary month without any

intercalary day. Wa-gyi-tat means that it has both intercalary month and

intercalary day.

CHAPTER III.

GENERAL DESCRIPTION OF THE CALENDAR.

34. According to the Surya Siddhanta a maha-yug of

4,320,000 years contains

i>577 J 9 I 7>828 days.

1,603,000,080 didi.

25,082,252 kaya.

51,840,000 solar months.

53433J336 lunar months.

adimath.

The greatest common measure of these numbers is 4. Dividing by 4, we

get

in 1,080,000 years.

394479457 days.

400,750,020 didi.

6,270,563 kaya.

12,960,000 solar months.

i3>35 8 >334 !unar months.

398,334 adimath.

35. The length of a mean year, deduced from the above figures, is

365'26875648i4 days

= 365 yet 15 nayi 31 bizana 31 kaya 24 anukaya.

= 365 days 6 hours 12 minutes 36*56 seconds

The original Surya Siddhanta neglected the fraction of a day beyond five

decimal points, or in other words omitted i kaya 24 anukaya = '36 second.

36. The year as thus defined is about I minute 12 seconds less than the

mean anomalistic year as found by modern science, 3 minutes 27 seconds greater

than the mean sidereal year, and nearly 24 minutes greater than the mean

tropical year.

37. The Burmese zodiac is divided, as in Europe, into 12 signs (" rathi ")

each rathi into 30 degrees (" intha," Hindu "amsa"), each degree into 60

8 The Burmese and Arakanese Calendars

minutes (" leikta ") and each minute into 60 seconds, (" wileikta "). The names

of the signs are :

Burmese '. Hindu. European.

1. Meiktha. Mesha. Aries.

2. Pyeiktha. Vrishabha. Taurus.

3. Medon. Mithuna. Gemini.

4. Karakat. Karka. Cancer.

5. Thein. Simha. Leo.

6. Kan. Kanya. Virgo.

7. Tu. Tula. Libra.

8. Pyeiksa. Vrischika. Scorpio.

9. Danu. Dhanus. Sagittarius.

10. Makara. Makara. Capricornus.

11. Kon. Kumbha. Aquarius.

12. Mein. Mina. Pisces.

38. In Burma the zero of celestial longitude does not move with the pre-

cession of the equinoxes as in Europe. The year theoretically begins at the

moment when the sun enters the sign Meiktha, but as the year is slightly longer

than the mean sidereal year, the first point of Meiktha (the zero of longitude) is

really moving among the stars away from the equinox, faster than the real

precession. The rate of precession of the equinoxes is about 50" per annum ; the

rate at which the first point of Meiktha diverges from the equinox is about 59"

per annum.

39. The length of a mean lunar month, deduced from the figures in para-

graph 34, is 29-530587946 days

= 29 yet 31 nayi 50 bizana 6 kaya 52*58 anukaya.

= 29 days 12 hours 44 minutes 2*7985344 seconds.

Makaranta, probably following the original Surya Siddhanta, takes the mean

lunation at _^ 2 x 30 days

= 2 9'5305 8 3 days.

= 29 yet 31 nayi 50 bizana 5 kaya 5*846 anukaya.

= 29 days 12 hours 44 minutes 2*38975 seconds.

General Description of the Calendar. 9

40. The mean lunation being a small fraction over 295 days, the Burmese

ordinary months contain 29 and 30 days alternately. Their names are : :

DAYS.

1. Tagu ... ... ... 29

2. Kason ... ... ... 30

3. Nayon ... ... ... 29

4. Wazo ... ... ... 30

5. Wagaung ... ... 29

6. Tawthalin ... ... ... 30

7. Thadingyut ... ... ... 29

8. Tazaungmon ... ... ... 30

9. Nadaw ... ... ... 29

10. Pyatho ... ... ... 30

n. Tabodwe * ... ... ... 29

12. Tabaung ... ... ... 30

Total ... 354

41. The remainder of the luni-solar year is made up by inserting an inter-

calary month at intervals. Approximately seven intercalary months are required

in nineteen years. Makaranta inserts exactly seven months every nineteen

years. Thandeikta makes corrections for the small fractions remaining in

the cycle of Meto. The intercalary month always has 30 days. In Arakan

it is inserted between Tagu and Kason, and is called Second Tagu. In

Burma proper it is inserted between Wazo and Wagaung, and is called Second

Wazo.

43. It is obvious that the intercalary month not only corrects the length of

the year, but also corrects the accumulating error of the month to the extent of

half a day, In other words, it causes the first day of every alternate succeeding

month to fall one day later than it would fall if the intercalary month had not

been inserted. The average length of the month is further corrected by adding

a day to Nayon at irregular intervals a little more than seven times in two

cycles, 38 years. The intercalary day is never inserted except in a year which

has an intercalary month.

43. The days of the month are reckoned in two series, waxing and

waning. The isth of the waxing is the civil full moon day (" labyi ") The

civil new moon day is the last day of the month (i4th or i5th waning, as the

case may be), and is called "lagwe" (moon disappears). It is frequently in

advance of the real new moon, as will be seen later.

2

10

The Burmese and Arakanese Calendars.

44. Though Tagu is nominally the first month in the year, it is sometimes

the last. The Thagayit number is applied to the solar year, consequently every

year except watat year has n ambiguous days, bearing identical month names

and day numbers, at its beginning and at its end. The latter are distinguished

by the word "hnaung" prefixed. Thus B. E. 1257 Tagu waning loth was

April i8th, 1895, and B. E. 1257 Hnaung Tagu waning loth was April 6th,

1896. Again, I4th April 1898 from midnight to 1-51-36 p. M. was B. E. 1259

Hnaung Tagu waning gth. The same day from 1-51-36 P.M. to midnight was

B. E. 1260 Tagu waning gth.

45. Besides the 12 signs of the zodiac, the ecliptic is also divided into

27 nekkats (Hind, nakshatra), representing the 27 days of the sidereal month.

The Pali names of the nekkats are almost identical with the Sanskrit names of

the nakshatras.

46. The actual length of the mean sidereal month is 27*321661 days. The

fraction gave rise in India to three different systems of reckoning the amount of

celestial longitude covered by each nakshatra. The following list of nekkats

is taken from Thandeikta: Athawani commences at longitude 350. The spaces

in this list differ greatly from both the Indian systems of unequal spaces. The

most modern system in India is that of equal spaces, 13 20' being assigned

to each nekkat.

No. Burmese name. Hindu name. Extent, i n t ?

1. Athawani

2. Barani ,

3. Krattiga

4. Rawhani

5. Migathi

6. Adara

7. Ponnapokshu

8. Poksha

9. Athaleiktha

10. Maga

11. Prokpa Palgonni

12. Oktra Palgonni

13. Hathada

14. Seiktra

15. Thwati

16. Withaka

17. Anurada

18. Zeta

19. Mulathan

Asvini

18

8

Bharani

10

18

Krittika

16

34

Rohini

12

46

Mrigasiras

J 4

60

Ardra

5

65

Punarvasu

27

92

Pushya

14

106

Aslesha

12

118

Magha

II

129

Purva Phalguni ...

16

145

Uttara Phalguni ...

9

154

Hasta

10

164

Chitra

i5

179

Svati

13

192

Visakha

21

213

Anuradha

II

224

Jyeshtha

5

229

Mula

13

242

General Description of the Calendar. 11

No. Burmese name. Hindu name. Extent. , *>'

20. Prokpa Than ... Purva Ashadha ... 15 257

21. Oktra Than ... Uttara Ashadha ... 5 262

22. Tharavvan ... Sravana ... 13 275

23. Danatheikda ... Dhanishtha ... 12 287

24. Thattabeiksha ... Satataraka ... 26 313

25. Prokpa Parabaik ... Purva Bhadrapada 10 323

26. Oktra Parabaik ... Uttara Bhadrapada 16 339

27. Rewati ... Revati ... n 350

47. The days of the week are named after the sun, moon, and five planets,

as in India and Europe, and are generally indicated by numbers.

Day. Burma. India.

1. Sunday ... Taninganwe Ne

2. Monday ... Taninla Ne

3. Tuesday ... Inga Ne ... Angaraka

4. Wednesday ... Buddahu Ne ... Budha

5. Thursday ... Kyathabade Ne ... Vachaspati

6. Friday ... Thaukkya Ne ... Sukra

o. Saturday ... Sane Ne ... Sani

48. The Burmese astronomical day begins at midnight, the civil day at

sunrise.

49. The following is a translation of one month of the Burmese Thandeikta

calendar for forty years, published by Saya Wizaya of Mandalay. The longi-

tudes of the sun, moon and planets are given in signs, degrees and minutes.

Rahu is the moon's ascending node, and is regarded as a dark planet which

causes eclipses.

12

The Burmese and Arakanese Calendars.

English year

and month.

1502 January

English day.

9

10

1

II 12

13

M

15

16

17

18

19

23

21

22

23

Burmese year

and month.

1263 Pyatho waxing.

Burmese day.

'i

A. M. B. JEWIX

V

THE

BURMESE & ARAKANESE CALENDARS.

CALENDARS

BY

A. M. B. IRWIN, c.s.i..

i\

INDIAN CIVIL SERVICE.

Rangoon :

PRINTED AT THE HANTHAWADDY PRINTING WORKS,

46, SULE PAGODA ROAD.

1909.

PREFACE.

IN 1901 I published " The Burmese Calendar." It was written in Ireland,

and in the preface I admitted that I had not had access to the best sources of

information. I can claim that the book was not inaccurate, but it was in-

complete. I have since made the acquaintance of the chief Ponnas in Mandalay,

and have learned a good deal more on the subject of the calendar, chiefly

from U Wizaya of Mandalay and Saya Maung Maung of Kemmendine, to

whom my acknowledgments are due. I therefore contemplated issuing a second

edition, but when I applied myself to the task of revision I found it was desirable

to re-write a good deal of the book, and to enlarge its scope by including the

Arakanese Calendar. The title of the book is therefore changed.

My object has been to make the book intelligible and useful to both

Europeans and Burmans. This must be my excuse if some paragraphs seem to

one class or another of readers to enter too much into elementary details.

I have endeavoured firstly to describe the Burmese and Arakanese Calendars

as they are. Secondly, I have shown that an erroneous estimate of the length

of the year has introduced errors which have defeated the intentions of the

designers of the calendar, and I have made suggestions for reform. Thirdly, I

have compiled tables by which English dates may be translated into Burmese

dates and vice versa.

Table I for past years and Tables II and III for future years embrace a

period of 262 years. For any day within this period the Burmese date equivalent

to the given English date, or vice versa, may readily be ascertained by the use

of Table IX, combined with Table I or II or III as the case may be. The

method is described in the notes on Table IX at page 39.

CORRIGENDA.

Since going to press the following errors have been discovered.

Page 7. Paragraph 35. For 365-2687564814, read 365-2587564814.

Page 8. Paragraph 39. Line 7. To the figures 29-530583 add iouf

more places of decimals, viz., 2147. The figures will read, 29-5305832147.

Same page and paragraph. Line 8. For 5*846, read 58-46.

Page 16. Paragraph 59. For + read

25 25

Page 25. Footnote. For 450 read 479.

Page 72. Columns 5 and 6. The figures 97 i should be ^one line lower

down, opposite the Burmese year 1291.

The figures 100 3 should be one line lower down, opposite the Burmese

year 1307.

The figures 98 4 should be one line lower down, opposite [the Burmese

1337.

I must also admit that in paragraphs 81 and 82 the expression " reduce to

days " is not quite correct or appropriate, and may make the paragraphs some-

what obscure. The subject is very briefly and incompletely dealt with in Than-

deikta.

Also in paragraph 89 I omitted to give a rule for finding the Thokdadein.

tft

It is very simple. The rule in Thandeikta is T = 30^ -f- n Y.

2

In the particular case considered m = 4, and n = 14. .-. T = 132 Y.

A. M. B. I.

TABLE OF CONTENTS.

PAGE.

CHAPTER I. INTRODUCTION i

II. DEFINITIONS 4

77 I

III. GENERAL DESCRIPTION OF THE CALENDAR . 7

IV. METHODS OF CALCULATION 15

V. DEFECTS, AND SUGGESTIONS FOR REFORM . 26

VI. NOTES ON THE TABLES 37

TABLES.

I. Elements of the Burmese Calendar for 172 years, from A. D.

1739 to 1910, B. E. noi to 1272 42

II. Elements of the Burmese Calendar calculated by Thandeikta

for 92 future years, from A. D. 1909 to 2000, B. E. 1271

to 1362 52

III. Elements of the Burmese Calendar for 92 future years, from

A. D. 1909 to 2000, B. E. 1271 to 1362, as proposed to be

regulated by de Cheseaux's cycle of 1040 years, commenc-

ing from B. E. 1281 -58

IV. Elements of the Arakanese Calendar for 262 years, from A. D.

1739 to 2000, B. E. noi to 1362 61

V. Arakanese Wazo Labyi week-day for 2000 years, from A. D.

639 to 2638, B. E. i to 2000 68

VI. Thokdadein, Week-day and Moon's longitude at the end of

the I4th didi of Second Wazo, in watat years, from B. E.

1215 to 1362, calculated by Thandeikta 72

VII. Comparison of epacts, as found by European and by Maka-

ranta methods 74

VIII. Comparison of mean new moon and Burmese Civil Lagw6,

every month for 29 years 76

IX. English dates corresponding to the first day of each Burmese

month 84

X. Week-day of any given day in each Burmese month ... 90

THE

BURMESE & ARAKANESE CALENDARS.

CHAPTER I.

INTRODUCTION.

1. Of natural measures of time, denoted by revolutions and rotations of

the heavenly bodies, the best-known and most important are the year, the

lunation or synodic month, and the day. The principal artificial measures are

the solar month (one-twelfth of a year), the week, the hour, the minute, and the

second.

2. For a description of the different measures of the year and month

(tropical, sidereal and anomalistic years, synodic, sidereal, anomalistic, tropical

and nodical months) the reader is referred to text books of astronomy. Such a

description would be too lengthy to insert here.

3. The tropical year, lunation and day vary slightly in length, but none of

them is ever an even multiple or sub-multiple of another. Therefore the problem

of constructing a calendar to measure time by these three units is a very com-

plex one. In Europe, Julius Caesar simplified it enormously by abandoning the

lunation altogether, and dividing the year into twelve artificial solar months

without any remainder. This was not done in Asia, where lunations are still

used.

4. Other methods of simplifying the problem are

(a) To reckon by mean or average years and lunations, instead of

by the actual revolutions of the earth and moon, the periods

of which vary slightly.

(b) To postpone fractions of a day, and reckon each lunar month

and each year as commencing at midnight, the accumulated

fractions being added to the month or year periodically

when they amount to one day.

(c) To add the accumulated fractions of months and days not

exactly when they amount to integers, but at regularly recur-

ring intervals, on the principle of averages and by the aid of

cycles which are more or less accurate common multiples of

days, lunations and years.

These methods have been adopted to varying extents at different times and

in different parts of Asia, as will be seen later,

2 The Burmese and Arakanese Calendars.

5. The Burmese calendar is essentially a Buddhist one, but the methods

of computing it are derived from Hindu books. A few words about the Hindu

calendar are therefore necessary.

6. In paragraph 17 of "The Indian Calendar," by Sewell and Dikshit, is

a list of some of the best-known Hindu works on astronomy. The length of the

year is differently estimated in different works. The principal ones which seem

to have been used in Burma are the Original Surya Siddhanta and the present

Surya Si Idhanta. The length of the year as given in these two is respectively :

Original ... 365 days, 6 hours, 12 minutes, 36 seconds.

Present ... 365 days, 6 hours, 12 minutes, 36'56 seconds.

7. Sewell and Uikshit show (at paragraphs 47 and 52) that the Hindus

formerly reckoned by mean months and years, but at present by apparent

months, while both mean and apparent years are used indifferent parts of India.

The change from mean to apparent reckoning is supposed to have commenced

about A. D. 1040, as it is enjoined in a passage in the Siddhanta Sekhara by

the celebrated astronomer Sripati, written in or about that year.

8. The Hindus insert an intercalary month at any time of year, as soon

as the accumulated fractions amount to one month. In Burma, as we shall see,

this is not so. The intercalary month is always inserted at the same time of year,

in Burma proper after the summer solstice, in Arakan after the vernal equinox.

ERAS.

9. Burmese astronomers use the Hindu Kali Yug, which commenced in

3102 B. c. (Sewell and Dikshit, page 16).

(iautama Buddha's grandfather, King Einzana, is said to have started a

new era in 691 B. c.

The Religious Era dates from 543 B. c., the year in which Gautama is

supposed to have attained Nirvana.

In A. D. 78-9 King Thamondarit of Prome is said to have started another,

identical with the Indian Saka era.

In A. D. 638-9 the era now in common use was started simultaneously, in

Burma by King Poppasaw of Pagan and in Arakan by King Thareyarenu of

Dinyawadi dynasty. The same era is current in Chittagong under the name of

Magi-San. (Sewell and Dikshit, paragraph 71 and table III).

10. So far as I am aware, no record is extant of any calendars as actually

observed either in Burma or in Arakan earlier than the year ITOO of Poppasaw's

era (A. D. 1738). Mr. Htoon Chan, B. A., B. L., of Akyab, in his book The

Arakanese Calendar, published in 1905, gives the elements of the luni-solar

calendar of Arakan for 2,000 years of the current era (A. D. 639 to 2638), but

he states that these were compiled during the reign of King Na-ra-a-pa-ya

Introduction. 3

(A. D. 1742 to 1761), and it is not clear whether the details given for earlier

years represent what was actually observed or not.

IT. The Arakanese follow the rules of Makaranta, in which fractions are

reduced to their lowest terms, and very small remainders are neglected. Inter-

calary months are regulated by the Metonic cycle of 19 years, the use of which

was propounded in the loth book of Raja-Mathan, a Hindu astronomer.

12. The Makaranta is probably derived from the original Surya Siddhanta,

because it defines the length of the year as 365 days, 15 nayi, 31 bizana and

30 kaya (365 days, 6 hours, 12 minutes and 36 seconds), and because it uses

mean reckoning. It is probable that the Burmese followed the same rules from

Poppasaw's time down to iroo B. E. (A. D. 1738).

13. The book which is used now in Burma is Thandeikta, the origin of

which is involved in some obscurity. According to one account it was written

about noo B. E., according to another about 1200. At any rate the change

from Makaranta to Thandeikta reckoning was not effected all at once. From

noo to 1200 the intercalary months are still regulated by the Metonic cycle, as

in Arakan, but the intercalary days are not placed in the same years as in

Arakan, and it is not clear by what rule they were fixed. During that century

the growing discrepancy between the civil solar and luni -solar Years attracted

attention. Much controversy ensued, the party of reform being led by a princess

who was afterwards the chief Queen of King Mindon. The first departure from

the rule of the Metonic cycle was made by putting an intercalary month in 1201

instead of in 1202, but the rules of Thandeikta do not appear to have been fully

introduced untill 1215.

14. Thandeikta is based chiefly, if not entirely, on the present Surya

Siddhanta, but applies its rules only to a limited extent. According to one

account the present Surya Siddhanta was not known in Burma until one

Bhavani Din, a learned pandit of Benares, brought it to Amarapura in 1148

B. E. (A. D. 1786), and about fifty years later it was translated into Burmese.

Thandeikta does not adopt the system of apparent reckoning ; mean years and

mean months are still used. The practice of placing the intercalary month

always next after Wazo and the intercalary day always at the end of Nayon,

and only in a year which has an intercalary month, is still adhered to. But

the new Surya Siddhanta was followed in small alterations of the length of the

year and the month, and the Metonic cycle was abandoned, and intercalary

months so fixed as to prevent further divergence between the solar and luni-

solar years.

The Burmese and Arakanese Calendars.

CHAPTER II.

DEFINITIONS.

15. Yet is a day including the night. Ne (the sun) means the day as

distinguished from the night. A T //a means night. But in astronomy Ne means

a day of the week. The days of the week are denoted by numbers, thus,

1 Sunday.

2 Monday.

3 Tuesday.

4 \Yednesday.

5 Thursday.

6 Friday.

o Saturday.

16. The day is artificially divided as follows :

I yet

= 60 nayi

i nayi

= 4 pat

= 60 bizana.

i pat

= 15 bizana

i bizana

= 6 pyan

= 60 kaya.

i pyan

= lo kaya

I kaya

= 12 kana

= 60 anukaya.

I kana

= 4 nay a

= 5 anukaya.

But only the

following measures

are commonly used in astronomy :

i yet

= 60 nayi

Hindu, ghatika.

i nayi

= 60 bizana

pala.

i bizana

= 60 kaya

,, vipala.

i kaya

= 60 anukaya

,, prativipala

Therefore

i nayi

= 24 minutes

- *4 hour.

i bizana

= 24 seconds

= *4 minute.

I kaya

= '4 second.

i anukaya

'006 second.

And

i hour = 2*5 nayi.

i minute = 2*5 bizana.

i second 2*5 kaya.

Definitions. 5

17. For ordinary use the English divisions of a day have practically oust-

ed the Burmese ones, at least in the towns, and the word " nayi" has come to

mean " hour." The words "minute" and " second" have been engrafted into

the Burmese language.

18. La (moon) is a mean lunation, i.e. the average period from new moon

to new moon. Sandra Matha also means a lunation; Thuriya Matha means a

solar month = -L of a year.

19. Ltbyi is full moon. Laywc is new moon.

20. Ala Yet or Ata Ne is the solar New Year's Day, or the day on which

the mean sun enters the sign Meiktha (Aries).

21. Haragon (Hind. Ahargana) or Thaw ana, is the total number of days

elapsed from the beginning of the era, or from any other fixed point which may

be taken as a starting point for calculations, to a given day.

22. Kyammat is an aggregate of units, each of which is the Sooth part of a

day ( = 108 seconds = 270 kaya). This arbitrary unit is obviously a rude

and imperfect substitute for decimal fractions.

23. Didi (Hind. Tithi) is the 3oth part of a mean lunation, or the aver-

age time in which the mean moon increases her longitudinal distance from the

mean sun by 12 degrees.

24. Kaya is the difference between total days and total didi in any given

period. It must not be confounded with kaya, the measure of time, '4 of a

second (paragraph 16).

25. Awaman is the remainder in the arithmetical operation of reduction

of days to didi or vice versa. In other words awaman is the numerator of a

fraction of kaya.

26. Yet I tin is the epact or moon's age at midnight of solar new year's day,

expressed in whole didi.

27. Adimath (Hind, adhika masd) means both an intercalated month

and the total intercalated months from the beginning of the era or any other

fixed point to a given point of time. Adimath thetha means the epact of the

total intercalated months, or fraction of a month, which accumulates year by

year up to one month.

28. La lun is the number of whole months by which the total solar years

expired during the era exceed the total luni-solar years expired during the era.

When solar new year's day falls in Tagu the la lun is o ; when it falls in Kason

the la lun is i ; and so on. If the solar and luni-solar years were perfectly ad-

justed there would never be any la lun.

6 The Burmese and Arakanese Calendars.

29. Thokdadein at midnight of any given day is the number of days

expired from and excluding Ata Yet.

30. Thar? ay it is the number of the year of the Burmese era. It denotes

expired years, not current years as in Europe. That is to say, the era began at

the commencement of the year o. The first of January 1900 was Burmese 1261

Pyatho waxing 2nd, which means the second day of the month of Pyatho after

the completion of 1261 years of the Burmese era.

31. Ratha or Hnit Kywin is Thagayit minus a constant. In other words,

a fixed number is deducted from thagayit in order to shorten calculations, and

the difference is termed ratha.

32. Wa is the Buddhist lent, which extends from the full moon of Wazo

to the full moon of Thadingyut.

33. Wa-tat (lent repeated) is an expression applied to the Burmese leap

year. Wa-nqc-tat means that the year has an intercalary month without any

intercalary day. Wa-gyi-tat means that it has both intercalary month and

intercalary day.

CHAPTER III.

GENERAL DESCRIPTION OF THE CALENDAR.

34. According to the Surya Siddhanta a maha-yug of

4,320,000 years contains

i>577 J 9 I 7>828 days.

1,603,000,080 didi.

25,082,252 kaya.

51,840,000 solar months.

53433J336 lunar months.

adimath.

The greatest common measure of these numbers is 4. Dividing by 4, we

get

in 1,080,000 years.

394479457 days.

400,750,020 didi.

6,270,563 kaya.

12,960,000 solar months.

i3>35 8 >334 !unar months.

398,334 adimath.

35. The length of a mean year, deduced from the above figures, is

365'26875648i4 days

= 365 yet 15 nayi 31 bizana 31 kaya 24 anukaya.

= 365 days 6 hours 12 minutes 36*56 seconds

The original Surya Siddhanta neglected the fraction of a day beyond five

decimal points, or in other words omitted i kaya 24 anukaya = '36 second.

36. The year as thus defined is about I minute 12 seconds less than the

mean anomalistic year as found by modern science, 3 minutes 27 seconds greater

than the mean sidereal year, and nearly 24 minutes greater than the mean

tropical year.

37. The Burmese zodiac is divided, as in Europe, into 12 signs (" rathi ")

each rathi into 30 degrees (" intha," Hindu "amsa"), each degree into 60

8 The Burmese and Arakanese Calendars

minutes (" leikta ") and each minute into 60 seconds, (" wileikta "). The names

of the signs are :

Burmese '. Hindu. European.

1. Meiktha. Mesha. Aries.

2. Pyeiktha. Vrishabha. Taurus.

3. Medon. Mithuna. Gemini.

4. Karakat. Karka. Cancer.

5. Thein. Simha. Leo.

6. Kan. Kanya. Virgo.

7. Tu. Tula. Libra.

8. Pyeiksa. Vrischika. Scorpio.

9. Danu. Dhanus. Sagittarius.

10. Makara. Makara. Capricornus.

11. Kon. Kumbha. Aquarius.

12. Mein. Mina. Pisces.

38. In Burma the zero of celestial longitude does not move with the pre-

cession of the equinoxes as in Europe. The year theoretically begins at the

moment when the sun enters the sign Meiktha, but as the year is slightly longer

than the mean sidereal year, the first point of Meiktha (the zero of longitude) is

really moving among the stars away from the equinox, faster than the real

precession. The rate of precession of the equinoxes is about 50" per annum ; the

rate at which the first point of Meiktha diverges from the equinox is about 59"

per annum.

39. The length of a mean lunar month, deduced from the figures in para-

graph 34, is 29-530587946 days

= 29 yet 31 nayi 50 bizana 6 kaya 52*58 anukaya.

= 29 days 12 hours 44 minutes 2*7985344 seconds.

Makaranta, probably following the original Surya Siddhanta, takes the mean

lunation at _^ 2 x 30 days

= 2 9'5305 8 3 days.

= 29 yet 31 nayi 50 bizana 5 kaya 5*846 anukaya.

= 29 days 12 hours 44 minutes 2*38975 seconds.

General Description of the Calendar. 9

40. The mean lunation being a small fraction over 295 days, the Burmese

ordinary months contain 29 and 30 days alternately. Their names are : :

DAYS.

1. Tagu ... ... ... 29

2. Kason ... ... ... 30

3. Nayon ... ... ... 29

4. Wazo ... ... ... 30

5. Wagaung ... ... 29

6. Tawthalin ... ... ... 30

7. Thadingyut ... ... ... 29

8. Tazaungmon ... ... ... 30

9. Nadaw ... ... ... 29

10. Pyatho ... ... ... 30

n. Tabodwe * ... ... ... 29

12. Tabaung ... ... ... 30

Total ... 354

41. The remainder of the luni-solar year is made up by inserting an inter-

calary month at intervals. Approximately seven intercalary months are required

in nineteen years. Makaranta inserts exactly seven months every nineteen

years. Thandeikta makes corrections for the small fractions remaining in

the cycle of Meto. The intercalary month always has 30 days. In Arakan

it is inserted between Tagu and Kason, and is called Second Tagu. In

Burma proper it is inserted between Wazo and Wagaung, and is called Second

Wazo.

43. It is obvious that the intercalary month not only corrects the length of

the year, but also corrects the accumulating error of the month to the extent of

half a day, In other words, it causes the first day of every alternate succeeding

month to fall one day later than it would fall if the intercalary month had not

been inserted. The average length of the month is further corrected by adding

a day to Nayon at irregular intervals a little more than seven times in two

cycles, 38 years. The intercalary day is never inserted except in a year which

has an intercalary month.

43. The days of the month are reckoned in two series, waxing and

waning. The isth of the waxing is the civil full moon day (" labyi ") The

civil new moon day is the last day of the month (i4th or i5th waning, as the

case may be), and is called "lagwe" (moon disappears). It is frequently in

advance of the real new moon, as will be seen later.

2

10

The Burmese and Arakanese Calendars.

44. Though Tagu is nominally the first month in the year, it is sometimes

the last. The Thagayit number is applied to the solar year, consequently every

year except watat year has n ambiguous days, bearing identical month names

and day numbers, at its beginning and at its end. The latter are distinguished

by the word "hnaung" prefixed. Thus B. E. 1257 Tagu waning loth was

April i8th, 1895, and B. E. 1257 Hnaung Tagu waning loth was April 6th,

1896. Again, I4th April 1898 from midnight to 1-51-36 p. M. was B. E. 1259

Hnaung Tagu waning gth. The same day from 1-51-36 P.M. to midnight was

B. E. 1260 Tagu waning gth.

45. Besides the 12 signs of the zodiac, the ecliptic is also divided into

27 nekkats (Hind, nakshatra), representing the 27 days of the sidereal month.

The Pali names of the nekkats are almost identical with the Sanskrit names of

the nakshatras.

46. The actual length of the mean sidereal month is 27*321661 days. The

fraction gave rise in India to three different systems of reckoning the amount of

celestial longitude covered by each nakshatra. The following list of nekkats

is taken from Thandeikta: Athawani commences at longitude 350. The spaces

in this list differ greatly from both the Indian systems of unequal spaces. The

most modern system in India is that of equal spaces, 13 20' being assigned

to each nekkat.

No. Burmese name. Hindu name. Extent, i n t ?

1. Athawani

2. Barani ,

3. Krattiga

4. Rawhani

5. Migathi

6. Adara

7. Ponnapokshu

8. Poksha

9. Athaleiktha

10. Maga

11. Prokpa Palgonni

12. Oktra Palgonni

13. Hathada

14. Seiktra

15. Thwati

16. Withaka

17. Anurada

18. Zeta

19. Mulathan

Asvini

18

8

Bharani

10

18

Krittika

16

34

Rohini

12

46

Mrigasiras

J 4

60

Ardra

5

65

Punarvasu

27

92

Pushya

14

106

Aslesha

12

118

Magha

II

129

Purva Phalguni ...

16

145

Uttara Phalguni ...

9

154

Hasta

10

164

Chitra

i5

179

Svati

13

192

Visakha

21

213

Anuradha

II

224

Jyeshtha

5

229

Mula

13

242

General Description of the Calendar. 11

No. Burmese name. Hindu name. Extent. , *>'

20. Prokpa Than ... Purva Ashadha ... 15 257

21. Oktra Than ... Uttara Ashadha ... 5 262

22. Tharavvan ... Sravana ... 13 275

23. Danatheikda ... Dhanishtha ... 12 287

24. Thattabeiksha ... Satataraka ... 26 313

25. Prokpa Parabaik ... Purva Bhadrapada 10 323

26. Oktra Parabaik ... Uttara Bhadrapada 16 339

27. Rewati ... Revati ... n 350

47. The days of the week are named after the sun, moon, and five planets,

as in India and Europe, and are generally indicated by numbers.

Day. Burma. India.

1. Sunday ... Taninganwe Ne

2. Monday ... Taninla Ne

3. Tuesday ... Inga Ne ... Angaraka

4. Wednesday ... Buddahu Ne ... Budha

5. Thursday ... Kyathabade Ne ... Vachaspati

6. Friday ... Thaukkya Ne ... Sukra

o. Saturday ... Sane Ne ... Sani

48. The Burmese astronomical day begins at midnight, the civil day at

sunrise.

49. The following is a translation of one month of the Burmese Thandeikta

calendar for forty years, published by Saya Wizaya of Mandalay. The longi-

tudes of the sun, moon and planets are given in signs, degrees and minutes.

Rahu is the moon's ascending node, and is regarded as a dark planet which

causes eclipses.

12

The Burmese and Arakanese Calendars.

English year

and month.

1502 January

English day.

9

10

1

II 12

13

M

15

16

17

18

19

23

21

22

23

Burmese year

and month.

1263 Pyatho waxing.

Burmese day.

'i

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