T HE

ME E A RA KA N E S E C ALE N D R BUR S A S .

B U RM ESE A RAKAN

CALE N D ARS

BY

. . 1 . A . . I C 3 x . M B IRW N ,

D CIV IL S E R V ICE I N IAN .

R angoon

PRIN T E D HANT HAWAD DY I \VO R KS AT T H E PR NTI N G ,

6 S U L E G A R OAD . 4 , PA O D

PR E FAC E .

IN 1 0 1 ublished 9 I p The B urmese 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 i n

. Pon n a s complete I have since made the acq uaintance of the chief in M andalay , and have learned a good deal more on the subject of the calendar , chiefly

U Wiza a from y of Mandalay and Saya Maung M aung 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

re- to 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 E uropeans 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 B urmese and Arakanese Calendars as they are . Secondly , I have shown that an erroneous estimate of the len gth 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 B urmese dates and vice versa . Table I for past years and Tables I I and I I I for future years embrace a period of 2 62 years . For any day within this period the B urmese date equivalent

m a to the given English date , or vice versa , y readily be ascertained by the use

. of Table IX , combined with Table I or I I or I I I as the case may be The method is described i n the notes on Table IX at page 39 .

C O RRIG E N DA .

Since going to press the following errors have been discovered .

Page 7 . Paragraph 35 . For read

8 . Page Paragraph 39 . Line 7 . To the figures 2 9 5 30 5 83 add fouf m . 2 1 . 2 8 ore places of decimals , viz , 47 The figures will read , 9 5 305 32 1 47 .

. 8 8 6 S ame page and paragraph Line . For 5 4 , read 1 1 6 — -3 Page . Paragraph 5 9 . For read 25 25

2 . Page 5 Footnote . For 45 0 read 479 .

2 . 6 Page 7 Columns 5 and . The figures 9 7 1 should be Lone line lower d 1 own , opposite the B urmese year 2 9 1 .

1 00 The figures 3 should be one line lower down , opposite the B urmese 1 0 ;year 3 7 . 8 The figures 9 4 should be one line lower down , opposite [the Burmese 1 y ear 337 .

I m ust also admit that i n paragraphs 8 1 and 8 2 the expression reduce to

r days is not quite correct or appropriate , and may make the parag aphs some ‘ fl VVhat obscure . The subject is very brie y and incompletely dealt with in Than

deikta .

8 Th kd n Also in paragraph 9 I om itted to give a rule for finding the o adei .

. Tha ndeikta 0m n Y I t is very si mple The rule in is T 3 ,

z 77: n 1 2 Y . - In the particular case considered 4 , and T 3

A . M . B . I .

TA BLE O F CO NTENTS .

U CHAPTE R I . I NTRO D CTIO N D E FIN IT IO N S I I . E E E S C PT T H E L E I I I . G N RA L D RI ION O F CA N DAR E H S O F C U L I V . M T OD CA L ATIO N FE C S U G G E S S E F M V . D E T , AN D S TIO N FOR R OR E S T H E L E S V I . N OT ON TAB

T AB LES .

1 2 A . . Elements of the B urmese Calendar for 7 years , from D

1 1 0 . E . 1 1 0 1 1 2 1 739 to 9 , B to 2 7

Elements of the B urmese Calendar calculated by Tha nde ikta

2 . D . 1 0 2 000 . E . 1 2 1 for 9 future years , from A 9 9 to , B 7 to 1 362

E O f C 2 lements the B urmese alendar for 9 future years , from

. . 1 0 2 0 0 0 . E . 1 2 1 1 62 A D 9 9 to , B 7 to 3 , as proposed to be

’ Chese a u x s c 1 0 0 com m n regulated by de ycle of 4 years , e c

E 1 8 1 ing from B . . 2

2 62 D Elements of the Arakanese Calendar for years , from A . .

1 2 00 0 . E . 1 1 0 1 1 6 739 to , B to 3 2

L ab i - 2 000 Arakanese Wazo y week day for years , from A. D .

2 6 8 . E . 1 000 639 to 3 , B to 2

’ a de in - T hokd , Week day and Moon s longitude at the end of

1 . E . the 4th didi of Second Wazo , i n watat years , from B

1 62 T ha nde ikta 1 2 1 5 to 3 , calculated by

Comparison of epacts , as found by European and by M aka ranta methods

L a wé V I I I . Comparison of mean new moon and Burmese Civil g , every month for 29 years English dates corresponding to the first day of each B urmese month Week-day of any given day in each B urmese month

T HE

BURME S E 81 ARA KA N ES E C A LE N DA RS .

PT E R I C H A .

I N T R O D U C T I O N .

1 . O f Of natural measures time , denoted by revolutions and rotations of - t he heavenly bodies , the best known and most i mportant are the year , the l unation or synodic month , and the day . The principal artificial measures are

- O f the the solar month (one twelfth a year) , the week , the hour , the minute , and second . i 2 . For a descr ption of the di fferent 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 con s tructing a calendar to measure time by these three units is a very com

E ae plex one . I n urope , j ulius C sar simplified it enormously by abandoning the l unation 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 Simpl ifying the problem are

a T O ( ) reckon by mean or average years and lunations , instead of b y the actual revolutions of the earth and moon , the periods

of wh ich vary slightly .

b 0 ( ) T 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 w hen they amount to one day . (6 ) To add the accumulated fractions of months and days not

c w exa tly hen they amount to integers , but at regularly recur

O u ring intervals , the principle of averages and by the aid of cycles w hich are more or less accurate common multiples of

s s . days , lunation and year

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

different parts of Asia , as will be seen later . a e a r 2 T he Bu rm e se a n d A r ka n e s C l e nd a s .

is s 5 . The B urmese calendar e sentially a B uddhist one , but the methods of computing it are derived from H ind u books . A few word s about the Hindu calendar are therefore necessary . “

6 . 1 D ikshi I n paragraph 7 of The I ndian Calendar , by Sewell and t, is - a list of some of the best known H indu works on astronomy . The length of the f vear is di fferently estimated in di ferent works . The principal ones which seem to have been used in B urma are the O riginal Surya Siddhanta and the present d Sur v a Si dhanta . The length of the year as given in these two is respectively O 6 6 1 2 6 riginal 3 5 days , hours , minutes , 3 seconds . 6 6 1 2 6 6 Present 3 5 days , hours , m inutes , 3 5 seconds .

D ks i 7 . S ewell and i h t show (at paragraphs 47 and 5 2) that the H indu s formerly reckoned by mean months and years , but at present by apparent

months , while both mean and apparent years are used in different parts of India . The change from mean to apparent reckoning is supposed to have commenced

. . 1 0 0 kh r about A D 4 , as it is enjoined in a passage in the Siddhanta S e a a by the celebrated astronomer Sripati , written in or about that year .

8 . s The H indus in ert an intercalary month at any time of year , as soon

as the acc umulated fractions amount to one month . I n B urma , 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 .

E R A S .

Yu 9 . B urmese astronomers use the H indu Kali g, which commenced in

1 C D ikshit 0 2 . . 3 B (Sewell and , page

’ E i nza n a Gautam a B uddha s grandfather , King , is said to have started a new era in 69 1 B . C .

E ra B . C . The Religious dates from 543 , the year in which Gautama is supposed to have attained N irvana .

8 - K T ha m onda r it O f I n A . D . 7 9 ing Prome is said to have started another , identical with the I ndian Saka era . 6 8- . D . I n A 3 9 the era now in common use was started simultaneously , in B urma by King Po p p a s aw of Pagan and in Arakan by King T ha reyare n u of

D iny a wadi dynasty . The same era is current in Chittagong under the name of

- Dikshit 1 . M agi San . (Sewell and , paragraph 7 and table I I I)

1 0 . 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 1 1 00 of Pop p a s aw s B A H oon . . . L . . . t A era (A D . M r Chan , B , , of kyab , in his book The 1 0 O f - Arakanese Calendar , published in 9 5 , gives the elements the luni solar

D . 6 calendar of Arakan for years of the current era (A. 39 to but he states th at these were compiled during the reign of King N a -ra -a -pa -ya I tro tio n duc n . 3

A. ( D . 1 742 to and it is not clear whether the details given for earlier years represent what was actually Observed or not .

1 1 . M a ka ra n ta The Arakanese follow the rules of , in which fractions are

w n reduced to their lo est terms , and very small remainders are eglected . Inter 1 calary months are regulated by the Metonic cycle of 9 years , the use of which l o th - was propounded in the book of Raj a M athan , a H indu astronomer .

1 2 . M a ka ra nta The is probably derived from the original Surya Siddhanta , b t 6 1 1 ecause it defines the leng h of the year as 3 5 days , 5 nayi , 3 bizana and

30 ( 6 6 1 2 6 s kaya 3 5 days , hours , minutes and 3 econds) , and because it uses mean reckoning . I t is probable that the B urmese followed the same rules from

’ Po a saw s 1 1 00 . E . . p p time down to B (A D .

1 . n ow Thandeik a 3 The book which is used in B urma is t , the origin of

c which is involved in some obs urity . According to one account it was written

1 1 00 . E . 1 0 0 . about B , according to another about 2 At any rate the change

Ma karan ta T h n from to a de ikta reckoning was not effected all at once . From 1 1 00 1 2 0 0 to the i ntercalary months are still regulated by the Metonic cycle , as A i n rakan , but the intercalary days are not placed i n the same years as in

c . Arakan , and it is not lear by what rule they were fixed D uring that century the growing discrepancy between the civil solar and luni -solar Years attracted

. Of b y attention Much controversy ensued , the party reform being led a princess who was afterwards the chief Q ueen of King Mindon . The first departure from the rule of the Metonic cycle was made by putting an intercalary month in 1 2 0 1

1 20 2 Th n ik fu llv instead of in , but the rules of a de ta do not appear to have been introduced untill 1 2 1 5 .

1 . Tha ndeikta fl 4 is based chie y , if not entirely , on the present Surya

a . Siddhanta , but pplies its rules only to a limited extent According to one account the present Surya Siddh anta wa s not known in B urma until one 1 1 8 B havani D in , a learned pandit of Benares , brought it to Amarapura in 4

E . . . B . (A D . and about fifty years later it was translated into B urmese Tha nde ikta 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 N ayon , and only in a year which has an intercalary month , is still adhered to . B ut the new Surya Siddhanta was followed in small alterations of the length of the

c year and the month , and the M etoni cycle was abandoned , and intercalary months s o fixed as to prevent further divergence between the s olar and luni s olar years . C e ar . 4 T he Bu rm e se a nd Ara ka n e se al nd s

C HA PT E R H .

D E F I N I T I O N S .

Y N e s 1 . et is 5 a day including the night . (the sun) mean the day as N e N . distinguished from the night . ya means night B ut in astronomy means a day of the week . The days of the week are denoted by n u mbers , thus ,

1 Sunday . 2 M onday .

3 Tuesday .

4 Wednesday.

5 Thurs day .

6 Friday .

0 Saturday .

1 6 . The day is artificially divided as follows 1 yet 60 nayi

1 nayi 4 pat 6 0 bizan a . 1 pat 1 5 biz ana

1 bizana 6 pyan 60 kaya . 1 pyan 1 O kaya

n k 1 kaya 1 2 kana 60 a u aya . 1 k kana 4 n aya 5 a n u a y a . B ut only the following measures are commonly used in astronomy

1 60 ha ti ka yet nayi H indu , g . 1 6 nayi 0 bizana pala . l 1 bizana 60 kaya v ip a a . 1 kaya 60 a nu kay a p ra tiv ip a la Therefore e fi itio D n ns . 5

1 7 . For ordinary use the English divisions of a day have practic ally oust ” a t s ha s ed the B urmese ones , lea t in the towns , and the word nayi come to ” ” ” i mean hour . The words minute and second have been engrafted nto

the Burmese language .

8 . L a Le n w 1 . e (moon) is a mean lunation , the average period from moon

’ S a ndra M a lz Thun a M a t/1 a to new moon . t a also means a l unation ; y means a

: solar month 72. of a year .

L a b 1 . i o . L a wé 9 y is full mo n g is newmoon .

A Y A ’ 20 . la et m N e Y or is the solar New ear s D ay , or the day on which the mean sun enters the sign Meiktha (Aries) .

H a m n Alta r na T/ a na o . a z wa 2 1 . g (H ind g ) or is the total number of days elapsed from the beginning of the era , or from any other fixed point wh ich may

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

K 80 th . a m m a t 0 2 2 y is an aggregate of units , each of which is the part of a

is o bv io u s lv day 1 0 8 seconds 2 70 kaya) . This arbitrary unit a rude

and imperfect substitute for decimal fractions .

Didi Tit/Ii 2 . . 3 (H ind ) is the 3oth part of a mean lunation , or the aver age time i n which the mean moon increases her longitudinal distance from the

mean sun by 1 2 degrees .

K a a s 24 . y is the difference between total day and total didi in any given ‘ O f period . It must not be confounded with kaya , the measure time , 4 of a second (paragraph

A wa m a n O f 2 5 . is the remainder in the ari thmetical operation reduction

w a wa m a n i s of day s to didi or vice versa . I n other ords the numerator of a

fraction of kaya .

‘ ’ Y In n o f s o l r 2 6 . et a is the epact or moon s age at midnight new year s day , w expressed in hole didi .

’ A zm a lz cllzika m a d t . a m s 2 7 . (Hind ) mean both an intercalated month and the total intercalated months from the beginning of the era or any other

O f Adi m a t/z [be t/Ia fixed point to a given point time . means the epact of the

s c total intercalated month , or fra tion of a month , which accumulates yea r by

year up to one month .

L a In n i 2 8 . s the n umber of w hole months by which the tota l solar yea rs

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

’ \Vhen solar n e w year s day falls in Tagu the la lun is 0 ; when i t falls in Kaso n

- the la lun is 1 and so on . I f the solar and luni solar years were perfectly ad

j usted there would never be any la lun . e a a r 6 T he Bu rm e se a nd A ra ka n es C l e nd s .

’ T/zokda a ei n 2 9 . at midnight of any given day is the n umber of days expired from and excluding Ata Yet .

Tha a i t . 30 . g y is the n umber of the year of the B urmese era I t denotes expired years , not current years as in Europe . That is to say , the era began at

1 00 1 2 6 1 the commencement of the year 0 . The first of j anuary 9 was B urmese

P a tho w 2 nd O f P a tho y axing , which means the second day the month of y after the completion Of 1 2 6 1 years of the B urmese era .

’ R t/l H wt K wi n h a i 1 . a a a t w 3 or y is T g y minus a constant . I n other ords ,

tha a it d a fixed number is deducted from g y in or er to shorten calculations , and

r a t/2a the di fference is termed . IV ' 2 . a s \ 3 is the B uddhi t lent , which extends from the full moon of Vazo

Th i n to the full moon of ad gy u t .

I'Va - t 33 . ta (len t repeated) is an expression applied to the B urmese leap

Wa -n é- a year . g t l means that the year has an intercalary month withou t a n y

lVa - i l intercalary day . g l i a t means that it has both intercalary month and intercalary day .

8 T he Bu rm e se a n d A ra ka n e se C a l e nd a rs

leikta 60 wile ikta m inutes and each minute into seconds , The names of the signs are

38 . I n 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

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

O f Me i h than the mean sidereal year , the first point kt a (the zero of longitude) is really moving among the stars away from the equinox , faster than the real

. 0 precession The rate_ of precession of the equinoxes is about 5 per ann um ; the rate at which the first point of Meiktha diverges from the equinox i s about 5 9 per annum .

39 . The length of a mean l unar month , ded uced from the figures in para graph 34, is days

2 1 0 6 a n u ka 9 yet 3 nayi 5 bizana kaya y a .

2 1 2 2 8 9 days hours 44 minutes 7 9 5344 seconds .

M aka ra nta , probably following the original Surya Siddhanta , takes the mean 6 9 2 l unation a t fig x 30 days

2 0 8 9 53 5 3 days .

2 1 0 a n u ka 9 yet 3 nayi 5 bizana 5 kaya y a .

2 1 2 9 days hours 44 minutes seconds . Genera D scri io n o the a e ar l e pt f C l nd . 9

° The mean lunation being a small fraction over 2 9 3days , the B urmese

a re months contain 2 9 and 30 days alternately . Their names

DAYS . 2 9 30 2 9 30 2 9 30

30 2 9 30 2 9 30

‘ ‘ : 41 . The rem ainder Of the luni solar year is made up by inserting an inter

” calary month at intervals . Approximately seven intercalary months are required ' ‘ In n i n e n a a r n et e yea rs . M k a ta inserts exactly s even months every nineteen _ h years . T a nde ikta makes corrections for the small fractions remaining in

. a 0 the cycle of Meto The intercalary month lways has 3 days . In Arakan

i ‘ be twee n o it is inserted Tagu and Kason , and is called Sec nd Tagu . In

W Wa a un Burma proper it is inserted between azo and g g, and is called Second

Wazo .

42 . It is obvious that the intercalary month not only corrects thelength of o the year , but als corrects the accumulating error of the month to the e xtent O f

O f l u half a day . I n other words , it causes the first day every a ternate s cceeding month to fall one day later than it would fall if the intercalary month had not

h them on th been inserted . T e average length of is further corrected by adding ‘ — a day to N ayon at irregular intervals a little more than seven times in two

8 . cycles , 3 years The intercalary day is never inserted except in a year which has an intercalary month .

O f‘ x 43 . The days the month are reckoned in two series , wa ing and 1 th waning . The s of the waxing is the civil full moon day The 1 th 1 civil new moon day is the last day of the month ( 4 or st h waning , as the “ ” la wé . in case may be) , and is called g (moon disappears) It is frequently

' e s . advance of the real new moon , as will b een later

2 i n O The r e e and rakane e a e ar L Bu m s A s C l nd s .

~

. e 44 Though Tagu is nominally the first month in the year , it is sometim s

. T ha a it m e r e e the last The g y nu b is appli d to the solar y ar , consequently every

ta t 1 1 year except wa year has ambiguous days , bearing identical month names

e and day numb rs , at its beginning and at its end . The latter are distinguished

f ‘ ” hn a u n . B B 1 2 1 by the word g prefixed Thus . . 5 7 Tagu waning oth was

A 8 B . 1 2 n n h A 6th 1 th 1 8 . E H a u 1 0t pril , 95 , and 5 7 g Tagu waning was pril , ‘ 8 8 - - M E 1 2 A 1 1 1 6 . . . 1 8 6 1 . 9 . Again , 4th pril 9 from midnight to 5 3 P was B 5 9 - - th . M . H na u ng Tagu wa ning 9 The same day from 1 5 1 36 P . to midnight was

B th . E . 1 60 . 2 Tagu waning 9

1 2 d 45 . Besides the signs of the zo iac , the ecliptic is also divided into

’ na kshatra 2 . 2 7 nekkats (H ind . ) , representing the 7 days of the sidereal month

The Pali names of . the nekkats a re almost identical with the Sanskrit names of h the naks atras .

“ ° a a 2 2 1 66 1 . 46 . The actu l length Of the me n sidereal month is 7 3 days The fraction gave ri se i n I ndia to three different systems Of reckoning the amount of

l n i ude n aksh t celestial o g f covered by each a ra . The following list of nekkats is taken from Than deikta : Athawa n i commences at longitude The spaces ff in this list di er greatly from both the I ndian systems of unequal spaces . The

° m a a 1 e most odern system in I ndi is that Of equ l spaces , 3 b ing assigned to each nekkat .

Long . Of e . . . NO . B urm se name H indu name Extent last pt .

Athawa ni Barani Krattiga

R awhani

Migathi Adara Pon n apokshu

Poksha

Athaleiktha Maga Prokp a Pa lgo n ni O ktra Palgon n i

H a thada

Se ikt ra

Thwa ti

Withaka A murada Z eta Mula than i io of th a Gen eral D escr pt n e Ca le nd r.

Long of Burmese name . Hindu name . Extent . l as t p t .

k a Asha a 1 2 2 0 . Pro p Than Purva dh 5 57

k ra Ashadha 262 2 1 . O t Than Uttara 5

T ha ra wa n 1 2 2 2 . Sravana 3 75

D a n a the ikda Dhan ishtha 1 2 2 8 23 . 7

hattabe iksha S a tata raka 2 6 1 2 4 . T 3 3

2 Prok a Pa raba ik Bhadra ada 1 0 2 5 . p Purva p 3 3

ktra Para ba ik Bhadra ada 1 6 2 6 . O Uttara p 339 2 i i 1 1 0 7 . Rewat R ev a t 35

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

e . as in I ndia and Europ , and are generally indicated by numbers

D ay . B urma . I ndia .

1 in n . Sunday Ta n ga we Ne 2 .Monday Ta nin la Ne

3 . Tuesday Inga Ne Angaraka

4 . Wednesday B uddahu Ne B udha

5 . Thursday Kya thabade Ne V a chasp ati 6 kk . Friday Tha u ya Ne Sukra

0 . Saturday Sane Ne Sani

8 . b . 4 The B urmese astronomical day egins at midnight , the civil day at

sunrise .

on 49 . The following is a translation of e month of the B urmese Thandeikta Wiza a Of calendar for forty years , published by Saya y Mandalay . The longi

afe n tudes of the sun , moon and planets given in sig s , degrees and minutes .

’ c ar Rahu is the moon s as ending node , and is regarded as a d k planet which

cau ses eclipses . ’ ’ ’ The Burni a aka Ca } e se rid Ar n e se le nda r .

P tho wa in ya x g .

ekkat N .

r Mercu y .

Saturn .

2 4 5 4 i ht th N g , after 4 beat .

Poksha n nam i hokdad i e r 1 Po . e n Y a 2 63 . T ‘ ” a D ri io f al n a r Ge ner l e sc pt n O the C e d .

February

P atho wan n y i g .

“ N

0 W 0 H 0 0 Q I st a Ua e and a Day, after be t. y , aft r be t .

A m a thi T hok ad i Poks ha h w . d e n “ 1 The B r e e and raka e e Ca e ar 4 u m s A n s l nd s .

f ' 5 0 . The di ference in tini e between the entry of the apparent sun and

Me iktha S odh a that of the mean sun into the Sign is called in I ndia y , and in

1 1 Burma Thingyan . The length of this period 8 fixed at 2 yet 0 nayi and

3 bizana ( 2 days 4 hours 1 minute and 1 2 seconds) . There is a fable about the i King of the N ats coming down to reside on earth during the Th ngya n . The w day on hich the Thingyan commences is called Thingyan Kya , and the day on which it ends Thingyan Tet .

1 f r 5 . There have been di ferences of opinion as to whether the sola year

’ hin a n commences at Thingyan Tet or at T gy Kya , but the actual practice for

o many years has been that it commences at Thingyan Tet . This is cons nant with the use of mean years in all calculations .

T he r e e a n d ra a e e a e ar 1 6 Bu m s A k n s C l nd s .

0 k am m a t 1 a n and 3 kaya . is the y of kaya and 24 ukaya second) 1 33

Tha ndeikta Makar n which forms the difference between the and a ta years . By

f 1 1 00 1 B the formula given above the di ference is disregarded from to 2 9 2 . E . I n 1 2 93 the end of the solar year is postponed by one kyam m a t un it (1 0 8 seconds

0 2 k a m m a t 1 0 or 2 7 kaya) . The constant 1 774 y equals 2 2 yet nayi and 39

1 0 L a wé bizana , the time which elapsed from 99 Tabaung g midnight to the

Meiktha 1 1 00th moment when the mean sun entered , when the year expired .

6 akara nta i and 5 . By M the fract on is disregarded , omitted altogether . $3

R= Tha a it e g y , and the total days xpired are 29 2 20 7 } 373 800

u 2 8 0 The constant 373 eq als 7 nayi 5 bizana and 3 kaya , the time whi ch elapsed from Kali Yu g 3738 Tabaung L a gwe midnight to the moment when the mean

’ sun entered Me iktha and the year 0 of Popp a saw s era (Kali Yug 3739) com

n Maka ran ta m R atha z Tha a it — 8 m e ced. By the second ethod , in which g y 79 , the constant is 8759 .

i s H ara on or hawa n a . 5 7 . The g T the quotient of R 2 92 207R 1 .774 2 1 93 8 00

’

1 ha ra on . plus , because the g includes new year s day The remainder is the por

’ 8 00 tion of new year s day which belongs to the old year . m inus the remainder

m m at is the Ata Ne Kya .

a ha n deikta be 58 . The d y of the week , by T , is the remainder of 7

r ha ra on 2 . 2 1 B E . cause Ata Ne in 1 1 00 . was Satu day , and its g was 3 divided

the Ma kara nta 0 . B by 7 gives remainder , which represents Saturday yeither of

} wa s 0 . E . methods the remainder of ; is the day of the week . I n B Ata Ne ‘

8 B E . Ata d hara on 1 . . Sunday , and its g was I n 79 N e was Wednes ay , and its ha ra on 1 1 g was ; remainder 4 .

. Tha n de ikta 5 9 The kaya , or excess of didi over days , is by the quotien t

R— I I H ‘ “ I“ I 76 2 5 69 2

awa m a n The 1 1 : 6 f e a n d the remainder is the . ratio 9 2 is the dif erence b tween

0 : 6 2 n u nity and 7 3 9 , which is an approximatio to. M eth o of a c atio ds C l ul n . 1 7

of the Surya Siddhanta ratio of the length of a day to the length a didi . (Para .

R ° — ‘ 0 1 Wt ll hand i The fraction represents the OOOOO473 day , by a T e kta 55 M akaranta mean lunation exceeds a mean lun ation . (See para . The con

1 1 stant day 5 nayi , 5 bizana and 45 kaya , the time which elapsed from 69 2

e 0 . the moment of mean new moon to midnight of Tabaung L agw 1 99 B B . By Makara nta the kaya is the quotient O f 1 1 H 65 0 69 2

da nayi 28 bizana and ka a , the time which the constant ggg y being 55 , y elapsed from the moment of mean new moon to midnight of T aba u ng L agwe 4g Yu Makara nta 3738 Kali g. By the second method the constant is 69 2

n 60 H ara on . 0 . g kaya total didi Didi divided by 3 gives quotie t ’ Of a Sandra Matha , and remainder yet l un or epact at midnight solar new ye r s 7 — day expressed in whole didi , the fraction of the epact being . 382

- 6 1 . Thand ikt M akaranta e a rules for hnit bo end here . adds the follow 7 L M ‘ gives quotient adim ath and remainder adim ath thetha . 2 35 — . d . . L M . A S M

D ivide solar months by 1 2 . The quotient is the year or Ratha with which the calculations commenced . I f there is no remainder the Ata Ne or Thingyan Tet

1 falls in Tagu . I f the remainder is it falls in Kason . This remainder is the I La nn .

6 Thandeikta . a 2 . The reason why this rule is not in is evident The r tio 7 Thand ikt . is the ratio of the Metonic cycle , which e a does not follow It i s 235 the error of this ratio with reference to the Burmese solar year that causes Ata

a i Ne to fall in Kason instead of Tagu . I f the d m ath were al ways adj usted in

harmony with the solar year there would be no la l un .

- ’ 6 . handeikta bo Po asaw s o 3 I f T hnit were calculated from pp ep ch , with

off 1 1 0 0 n ha ra on out cutting years , the consta t for the g would be 442 instead

. 6 k a m m at 2 of 373 The added 9 y consist of two items , 5 and 44 . 2 5 represents 1 2 anu ka a 8 the accumulated error of kaya and 4 y per year during 4 39 years , 1 B 1 00 . . from the beginning of the Kali Yug to B We have seen (para . 5 5) that k a m m a t 1 . 1 2 = 8 the error a mounts to one y in 93 years 93 x 5 4 2 5 , The 44 kya m m a t represent the difference between Amarapura time and Lanka time which a is used in H indu c lculations .

- 64 . The following table of Thandeikta hnit bo is copied from the

T ha nde ikta Wiz a a a C alendar for forty years , published by Saya y of M ndalay . 1 8 T e r e e and ra a e e Ca e ar h Bu m s A k n s l nd s .

N D E IKT T HAGAYIT 1 2 0 o 1 6 T HA A H N I T BO FOR 3 t 2 9 .

T ha it gay . Methods of Calcul ati on .

YE T B0 .

an 1 2 K . Adim ath, 65 . The total solar months expired m The by Th deikta , is the quotient of R 6 o 2 8 8 . M . 9 475 9 1 1 2 8 : 1 1 Is f and the remainder is Adim a th thetha , The ratio 9 the di ference bet ween unity and which is an approximation to the Surya Siddhanta ratio of the length of a mean solar month to

to the length of a mean lunar month (para . is a correction obtain a

6 0 adim a th thetha closer approximation . The constant 9 is the at the end of

’ the 1 1 00th year of Popp asaw s era . R

66 . M akara nta not only omits the correction but takes a slightly 5 75 1 e i v isa o : 9 2 , rougher approximation of the Surya Siddhanta rat o , , 94 becaus

2 2 28 . This is the ratio of this ratio can be reduced to lower terms , namely 35 2 2 8 solar months . the Metonic cycle ; nineteen years contain 235 lunar months , — M . n 1 D =3o L . + , that is 67 . Total lunar months i handeikta , is the quot ent of to m idnight preceding the day n . Kaya , by T R I I D 1 76 5 3 70 3 The day of the week IS the Ka . and the remainder is awam a n . H D —2 remainder of 7 R D 1v 1de 1 2 . this k am m a t BOOH 774 68 . The y of the whole period is 1 93 t- remainder is kyam m a pon , or by 2 9 2 207 . The quotient is Ratha , and the during the current solar year . the ky am m at of the fraction of a year elapsed er in rem aind - hokdade , and the D ivide kyam m at pon by 800 . The quotient is T

is Ata kyam m at . method of 6 M akaran ta , 9 , by using the Metonic cycle takes a different the i ntercalary months arriving at the total didi , and at the same time ascertains the , and days . The watat years are first found by the Metonic cycle and then r i Waz o of each watat ye a yet-bo for midnight preceding the L aby of Second

are calculated , as follows .

. the 1 . 70 . D ivide the year by 9 The quotient is the expired cycles I f

. e e 2 1 0 1 1 1 8 remainder is , 5 , 7 , , 3, 5 or there is an intercalary month Th s alone are the years with which we are concerned at present . = of the The expired cycles multiplied by 7050 (2 35 x 3o) the total didi 7 1 . i the L a we . To find the d di of completed cycles , ending on the g of Tabaung fo r the a s 1 2 . A 4 remaining years and fraction , first multiply these ye r by dd r a n a a a ar 2 0 T he Bu m ese d A r k n ese C l e n d s .

months of Tagu , Kason , N ayon and First Wazo , and one month for each watat year expired during the cycle , thus I n the first watat year of each cycle add 4 second 5 third 6 fourth 7 fifth 8 sixth 0 seventh 1 0 ‘ h M ultiply the total months by 30 and add 1 4 didi of Second Wazo . Add t is

to total the total didi of the completed cycles . The result is the total didi of the whole period from the beginning of the era to the midnight preceding the L a byi of Second Wazo of the given year .

° 2 . T o 7 reduce these didi to days , Kaya is the quotient of

and the remainder is the awam an . H = D ~ K&

Divide H by 7 . The remainder i ndicates the day of the week on which . the

L ab i of y Second Wazo falls .

73 . The intercalary day is determined by the changes in the awam an from

to watat year watat year . These changes can easily be found without calculating

hara on the g in full for each watat year . I n the arithmetical operation expressed by 1 1 D 65 0 o it is obvious that the change in the remainder depends solely on the i ncZeren t of total didi . When the interval from watat to wata t is two years ,

0 the increase of total didi is 2 5 X 30 75 . M ultiply this by 1 1 and divide by

’ 0 1 7 3 ; the remainder is 5 7 . Therefore in every case of two years interval the awa m a n is found by simply adding 5 1 7 to the last preceding a wa m a n and then subtracting 70 3 if the total is 703 or greater . I n like manner in every case of

’ three years interval the awa m a n is found by adding 2 59 and subtracting 703 if the total is 703 or greater .

A awa m a n 74 . still easier method of calculating the for a long period is this : the awa m a n for any watat year is obtained from the awa m a n for the

220 8 corresponding year in the last preceding cycle by adding , or subtracting 4 3 if the preceding one is 483 or greater .

2 75 . The kaya found from the equation in paragraph 7 is subtracted

O f 1 2 awa m an from didi . Hence , when the addition 5 7 or 59 does not raise the

. t hara on 1 awa m a n o 0 , the increase of the g is greater by than when the _ 7 3

0 . A becomes 703 or more , and has to be reduced by subtracting 7 3 little calculation will show that the increase of the ha ragon in 2 5 months is 738 when

0 0 . . 7 3 is subtracted and 739 when 7 3 is not subtracted The corresponding

figures for 37 months are 1 09 2 and 1 093 . M eth o o f a a 2 1 ds C lcul tion .

6 . i 7 Hence the rule . When the a wam an of Second Wazo L aby is less

wa m a n than in the last preceding watat year N ayon has 2 9 days . When the a 0 is greater than in the last preceding watat year N ayon has 3 days .

77 . The day of the week on which the L abyi of Second \Vazo falls in any watat year may be deduced from the last preceding watat year by dividing the

of hara on increase the g by 7 . The result may be expressed thus :

nterv al Da s in n cr e ase of ncre ase of I , y I I d e ars a on . hara n we e a . y . N y go . k y 2 9 738 3 30 739 4 2 9 1 09 2 0 30 1 0 93 1

f wa -n e- 78 . From the 1 st O Tagu to the 1 sth of Second Wazo is in a g tat

- - 1 2 wa . year 3 days , in a gyi tat year 1 33 days Dividing by 7 , we find that in a wa -nge-tat year the 1 st of Tagu falls one day later in the week than the L a byi

- - of Second Wazo ; in a wa gyi tat year they fall on the same day of the week .

- The Table in paragraph 77 , therefore , gives the sequence of luni solar New Y ’ f ear s Days from watat year to watat year , with this di ference , in the case of

’ New Year s Day the column Days in N ayon refers to the former watat year ; in the case of Second Wazo it refers to the latter watat year .

T HAN D E IKTA WATAT

ha ndeikta determ in 79 . T does not give any clear and invariable rule for ing which years shall be watat , and the reason probably is that the Surya Siddhanta does not contemplate the Burma practice of placing the intercalary month always near the summer solstice . The B urmese sayas who framed the

T ha ndeikta rules were thus thrown on their own wits for guidance , and the result is that several different tests are applied .

- of Yu 80 . D ividing the number of days in one fourth a Maha g by the number of adim a th in the same period we find that the average time from one intercalary month to the next should be 990 yet

2 1 an u ka a . 1 9 nayi , 4 bizana , kaya and y Consequently it is laid down in Thande ikta that the period from one intercalary month to the next is 990 yet

and 1 9 nayi .

adim a th the tha 8 1 . T0 apply this principle , one method is to reduce the - to days ; another is to reduce the yet lun to days . I n each case the resulting 0 1 days being subtracted from 99 days and 9 nayi , the difference is the number

’ of days to run from solar new year s day before the a dim a th the tha amounts to

- is a full month , or the yet lun amounts to a full month , as the case may be . I t not expressly stated that an i n te rcalary ' m on th should be inserted if the full 22 The Bu rm e se a nd Araka ne se C al e nd a rs .

ab i numbe r of days expires before the L y of Wazo , but it may be inferred that that is what is meant .

adim ath the tha the 8 2 . The rule for reducing to days is to multiply

- o a dim ath the tha by 1 00 and divide by 9 2 . The rule for reducing yet lu n t days is “r 44 Ky H 33Y 2 1 2 4

- o . 83 . A third rule is that every yet lun py year should be a watat year

- - Ye t l un pyo means that the didi epact , which has been increasing every year by 0 0 about 1 1 , amounts to 3 or more , when 3 is deducted from it , one lunar month

to of is added , and the total lunar months exceed those reckoned the end the f previous year by 1 3 instead o 1 2 .

A L ab i e 84 . fourth rule is that the y on the day following which L nt begins nekkat Athanli m ust fall on a day when the moon is within the , that is , between

' ° h n li longitude 266 40 and At a is a P ali name for the month of Wazo .

I t is not one of the 2 7 lunar nekka ts .

e 85 . N one of these rules seems to have b en consistently followed since B - E . , 1 2 1 5 . The third is con tradictory to the fourth for when the yet lun exceeds h 1 9 the full moon of the third succeeding month never reaches At a nli . This

1 1 . point is further discussed in para . 2 The actual practice since 1 2 1 5 has - been that watat has always occurred either i n yet lun pyo year , or in the year - - 8 to 2 2 2 . o preceding yet lun pyo when the yet lun amounted 7, or 9 I t is t be observed that under this practice although the rule of Athanli is fulfilled in watat

’ years , yet there are m any common years in which the moon s longitude on the

Atha nli - L a byi of Wazo falls short of , namely every year in which the yet lun is

0 1 2 2 2 2 2 2 6 . 2 , 2 , , 3 , 4 , 5 or

AN D IKTA YE T - T H E N G I N .

86 . For determining the places of intercalary days there are three rules

a given i n Tha nde ikt . One is that every year in which the kaya increases by 5 awa m a n (not 6) or in other words every pyo year , should have an intercalary

awa m an day . As thus stated the rule is impossible , for pyo years are frequently - n ot watat years , and yet ngin never occur except in watat years . If the awa

man of watat years alone be considered , the rule is practically the Ma kar a nta 6 rule stated in paragraph 7 , and this has certainly not been followed in B urma

E . proper since 1 1 00 B .

e 8 7 . Another rule is based on the average time which should elapse b tween - one yet ngin and the next . Taking the figures for a quarter Maha Yug in

s paragraph 34 , the total days in B urme e months , if there were no 0 — intercalary days , would be 3 é or days .

a e ar 2 4 T he Bu rm es e a n d A ra k a n ese C l nd s .

1 . 9 . The difference of longitude between sun and moon is found by didi A didi is the time in which the mean moon increases her longitudinal distance

‘ ne w from the mean sun by 1 2 degrees . The didi elapsed from mean moon next before Ata Ne to the midnight indicated by the given Thokdade in equal the sum

- n of yet lun and its fraction pl us T hokdadei reduced to didi . That is to say W 1 1 1 1 T W 69 2

2 . 0 9 H aving foun d the sum of didi , divide by 3 , and reject the quotient , as

s it represents complete l unation , and at every new moon the difference of longi

1 tude between sun and moon is zero . The remainder multiplied by 2 is degrees of longitude .

1 1 T W . a a m a n 9 3 The remainder of is the w of the day . I f it be denoted 69 2 W' d by , then the increase of difference of longitude during the fraction of a didi is , i n minutes , Wd Wd 7 I 73

Red uce it to degrees and minutes by dividing by 60 .

’ 94 . Add together the sun s longitude and the two parts of the difference

e . 2 b tween sun and moon Subtract from the sum 5 minutes . The result is the

’ moon s longitude .

- 95 . Add the week day figure of Ata N e to the Thokdade in of Second ' W L ab i azo y . D ivide the sum by 7 . The remainder indicates the day of the week of Second Wazo L a byi . The sequence of this day from watat to watat ought to agree with the table in paragraph 77 .

’ 6 . Athanli 9 If the moon s longitude as calculated does not lie within , a

- day may be added or subtracted , provided it does not set the week day wrong .

- wa n eta That is to say , if the increase of week day indicates a g t one day may be

wa itat . 1 2 added ; if it indicates a gy one day may be subtracted Thus , in 34

- 1 2 1 T hokdade in 0 the increase of week day since 3 as Obtained from the was ,

’ ° é 2 indicating a wa n g ta t . The moon s longitude as calculated was 54 fall

Thokda de in Atha nli . ing short of O ne day was added to the , m aking the year

- a ita t 1 . 1 2 a w gy , with week day increase The same occurred in 45 , when the

’ ° calc ulated moon s longitude was 2 6 1 I n 1 2 6 1 the calculated longitude was

° - 1 wa itat . O ne 2 76 and increase of week day , indicating a gy day was

’

wa n eta t . deducted , making a g The object of this is not apparent , as the moon s l longitude Often exceeds Athan i . These are the only occasions on which a correction has been applied to the calculated T hokdadein for Second Wazo

1 L abyi since 1 2 5 B . E . M etho of a a i ds C lcul t on . 2 5

~ ’ 9 7 . Table V I shows the week day and moon s longitude of Second Wazo L ab i , E . 1 2 1 y calculated as above described , for all the watat years from B . 7 to 1 6 1 wa i e 3 , and the resulting gy and wang tat . For past years the three corree tions mentioned in the last paragraph have been made . For future years four corrections are made . ’ ° ’ 1 29 1 moon s longitude 2 63 20

° ' 1 307 265 29

° ' I 337 26s 35

° ' 1 348 261 5 0

8 ’ 9 . I n each of these four years the moon s calculated longitude falls short Atha nli h l of , and the addition of one day would bring i t within At an i . Without i correction each of these years would be wangetat . The Thokdade n is therefore increased from 96 Saturday to 97 Sunday 99 Monday to 1 00 Tuesday 9 7 Tuesday to 98 Wednesday 6 and 95 Sunday to 9 Monday respectively , a ita and all four years will be w gy t .

. a 1 2 1 1 0 1 1 99 I n consequence of these alterations the ye rs 93, 3 , 339 and 350

{ 53 0 a cto wa ita t wan état h are 1 f altered from gy to g , the T okdadein of Second i Wazo L aby i n each case remaining unaltered .

1 00 a . The conclusion I arrive at is that in c lendars computed under

ha ndeikta - - e T rules watat will continue to be placed in yet lun pyo y ars , but in - - - 2 28 2 - the year before yet lun pyo when yet lun is 7 , or 9 ; and that yet ngin will

’ hokdadein be determined by computation of the moon s longitude by means of T ,

0 four corrections be ing made within the next 9 years , namely those in the years "k 1 1 1 0 1 1 8 V I. 29 , 3 7 , 337 and 34 , shown in Table

nt o n d i n ar 8 1 as e an n t at it adim ath oe s U Kyaw Yan i nterprets the rule m e i e p a . m i g h py d ar t t e re i s a w atat in the curre nt ear s w e the s un is in M e ikth a P eiktha e on or K a a . hil , y , M k , h y Thi i n n r i n w c the e a ct e ce eds e t lun 2 6 awam an is eq u iv a l e n t to sayi ng th at watat occurs a y yea hi h p x y w 0 I v e n ture to t n t at suc a ru e as t s has not e e n fo owe t erto . In 1 2 the e a ct as 1 3 . hi k h h l hi b ll d hi h 44 p

t l n 2 6 a wa m an 0 but t ere was no watat. ye u 45 , h 26 T he r e e and ra a e e Ca e ar Bu m s A k n s l nd s .

C PTE R HA V .

D AN D S UG S O S FO R R O EFE CTS , GE TI N EF RM .

“ 1 0 1 . e The B urmes C alendar is essentially a religious one . The reason

h a Wa given i n M a a Wagg why the , or B uddhist Lent , was instituted by B uddha appe ars to be to prevent the Bhikkus from going on their travels during a so not the rainy se son , that they might crush the green herbs , hurt the v ege f and e o sm all . Wa table life , destroy the liv s many insects And the (Vassa) , or a e to the retre t , was prescrib d be entered upon in the rainy season for three ” . A a Htoon months (The rakanese C lendar , by Ch an ; I ntrod uction page i , ) . Le e of a or nt b gins on the first waning W zo Second Wazo .

L a 1 02 . The direction that the byi of Wazo or Second Wazo should fall

’ ° ' 1 n i on a day on which the m oon s 3 0 g tude is at least 266 40 is almost exactly

’ equivalent to a direction th at the m onthlintwhichfsolar new year s day falls should

a . v i z. al ways be the month of T gu This is the H indu rule , , the mon th in which

the sun enters Mesha must be called Chaitra .

a an n ot 1 03 . Whether th t H indu rule has y religious significance I know , but it is evident that however suitable the year of the S urya Siddhanta may be

. e for Hindus , it is not suitable for Buddhists The rule that the months of L nt , v i Wa au n a wthalin Thadin u t z . , Wazo , g g, T and gy , shall fall in the rainy season cannot be permanently carried out by observing any year except the tropical year .

0 a a was to or a 1 4 . The tropical ye r (ay na hnit) known the author uthors no u se of of of T handeikta , but they make it except to calculate the lengths days

a to hin an K a and nights . The equinox is s id have coincided with T gy y about

’ Po asaw s a o 1 1 . D . a 207 years before pp epoch , b ut 4 A which is pretty ne r the '

to be er a . truth . The precession is stated 54 p nnum , which is not correct The

" 0 e real r ate of precession is about 5 p r an num .

Thandeikta a 1 05 . The sol r year is

6 1 : 6 8 6 81 365 days hours 2 minutes and se conds 3 5 25 75 4 4 days .

o s to e . The a This is proved by m dern cience be Incorr ct me n sidereal year is , accordi ng to G u illem in

= ° 6 6 . . 6 6 8 3 5 days hours 9 min and se cs 3 5 25 3 days , according to Sewell and Dikshit 6 6 = ° and 6 2 6 a . 3 5 days hours 9 min . se cs . 3 5 5 35 d ys D efect and S e tio for Re or s ugg s ns f m . 2 7

‘ 1 06 . a a a The mean tropic l ye r , ccording to several authorities qu oted by S ir o e a the b R b rt B ll for last century , varied etween

6 ° 8 . s = 6 3 5 days 5 hours 4 min and ecs . 3 5 2 42 2 789 days and

6 = ° 8 . and se e . 6 2 2 1 3 5 days 5 hours 4 min 3 5 4 995 days , while Sewell and Dikshit give the length of the mean tropical year for 1 900 as

6 = ° 8 . 6 3 5 days 5 hours 4 min and secs . 3 5 2 42 1 9 1 7 days .

0 1 7. It is manifest then that the B urmese first point of Meiktha is not a

fixed point among the stars , although it is intended to represent a fixed po int . r It is moving fo ward , away from its original place among the stars . I t is diver ” ging at a still faster rate (about 59 per annum) from the point which the mean

of r . sun occupies at the equinox , for the precession the equinoxes is retrog ade Through the accumulation of this error Thingyan Kya is now about 24 days a fter the vernal equinox .

- 1 08 . a a of The luni solar ye r necess rily consists sometimes twelve , some oi h ik times thirteen , months . The T ande ta rules are designed to make the

- to T handeikta average luni solar year equal the solar year , that is , about 2 2 minutes longer than the real tropical year .

- 1 0 . s M akaranta a s a 9 The Metonic cycle , u ed by , m ke the verage lu ni solar

ar 6 2 6 . a a ye 3 5 4 75 days This is greater th n the tropical ye r , but less than the Makaranta a solar ye r . I n other words 1 9 Makaranta sol ar years days 2 35 lun ations 69396 8841 5 1 9 tropical years

k n - a t wa the The average Ma ara ta l uni solar ye r , therefore , is drif ing for rd round

n Thandeikta -s seasons , but at a slower rate tha the average luni olar year , which is dr ifting at the same rate as the Thandeikta solar year .

1 1 of of Thandeikta s ce 0 . The application the rules has les ened the divergen

- e f between the B urmese solar and average luni solar years , but at the exp n se o accelerating the divergence between the average luni -solar year and the real tro

Than e ikta not pical year . d grasped at the shadow (the B urmese solar year being a real year of any kind) and lost the substance , namely the tropical year - a e which is all important . I t acceler ted the pace at which L nt was altering its place in the seasons under the Maka ran ta system . Le nt is alrea dy be ginning to creep ou t of the rainy season into the cold season .

’ oo sc a on s a 1 1 1 . The Indian and B urmese b ks a ertain the ep ct (mo ge at the The - moment when the solar year ends) in two ways . yet lun (with its fraction a—‘—iV—13 i n . The adim a h th h g5 is the epact expressed didi t et a is the epact Makaranta i n 228ths na or 2 of ar expressed , by Of a lu tion 35ths a sol month , by

Thandeikta in 9 1 1 ths of a lun ation or 939ths of a solar month . If both forms 2 8 T he r e e and ra a e e a e ar Bu m s A k n s C l nd s .

karanta of the epact are correctly calculated they must agree . By Ma the adi

thetha not e math is correct , b cause the ratio assumed between the lengths of a 8 mean solar month and a mean lunation , 235 2 2 , is only a rough approximation

’ o asaw s its error is the error of the Metonic cycle . I n the first cycle of P pp era both

of oed 8th forms the epact py in the same year , except in the year when the adi

1 h accu m u~ math thetha was slightly in arrear . I n the 2t century the error had - lated so much th at adim ath pyo was behind yet lun pyo every time . Thus

Yet-lun pyo 1 1 0 1 1 1 04 1 1 07 1 1 09 1 1 1 2 1 1 1 5 1 1 1 7 Adim ath pyo 1 1 02 1 1 05 1 1 08 1 1 1 1 1 1 1 3 1 1 1 6 1 1 1 9

adim ath o I n five cases the py 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 1 1 77 1 1 80 1 1 82 1 1 85 1 1 88 1 1 9 1 1 1 93 Adim ath pyo 1 1 78 1 1 8 1 1 1 84 1 1 87 1 1 89 1 1 9 2 1 1 95

adim ath n i I n three cases the pyo was two years behind . Tha de kta corrected adim ath thetha and made it agree with yet lun .

1 2 . 0 and 1 T make the month in which Ata Ne occurs Tagu , the month in

Athanli which the full moon is in Wazo or Second Wazo , the watat year should

- Thand ikta - be , not yet lun pyo year as stated i n e , but the year before yet lun pyo ,

r e so o approximately very year in which yet l un exceeds 1 9 . This was at the 1 - beginning of the era . After 2 centuries we fi nd 6 watat occurring in yet lun pyo

- — — year and the seventh in the year after yet lun pyo (year 5 expired o f

6 1 62 6 0 1 2 1 1 1 1 6 6 cycles , , and 3, 45 , 4 and I n cycle 4 this las t error was corrected at Amarapura by placing the watat in year 4 (1 20 1 )

t of ins ead of year 5 The subsequent corrections the Metonic cycle , namely the changes

from 2 to 1 in 1 2 1 7

1 1 3 u 2 n 1 2 28 1 0 9 1 263

- - have placed watat in the year before yet lun pyo , but only when the yet lun

2 28 2 . amounts to 7 , or 9 I t seems to have been considered that to revert fully - to the original rule , and place watat always i n the year before yet lun pyo , would be too drastic a measure , as it would place the beginning of Le nt on the

n average five days later in the season than it is ow . I t is already fifteen days

’ n Po sasaw s later in the season tha it was in pp time .

1 1 3 . From these facts it is clear that (a ) The error of the B urmese solar year is constantly moving the

nekkat Athanli a and a r th l ter l te in e seasons , D efect and S e tio for Re or 2 s ugg s ns f m . 9

(b) The present practice of fixing watat by yet-lun pyo or yet -lun 2 28 2 L ab i 7 , or 9 , while it puts the y of Second Wazo in Athan li a i f of in watat years , leaves the L by o Wazo short Athanli a in many common ye rs ,

(c) I f the Athanli rule were fully observed it would immediately e move the average L nt five days later than it is at present , d i ( ) If Lent is to be maintained permanently in , or even near , ts

proper place in the seasons , the solar year of the S urya

su s ti Siddhanta must be abandoned , and the tropic al year b

tu t f ed or it .

1 A f 1 . o 4 ny calendar , if it is to have the maximum practical utility and convenience , must be easily ascertainable for many years in advance . The best f method hitherto devised to attain this end is to make use o cycles . The most notable example of this is the adj ustment of days to years in the European a w calendar , which was first started by j ulius C esar , and after ards improved by

X . 000 Pope Gregory I I I The j ulian cycle was 4 years , the Gregorian cycle is 4 years . Every year which is a multiple of 4 is a leap year , except that every 1 00 00 000 year which is a multiple of but not of 4 is a common year , and 4 and every multiple O f 4000 is a common year . The Gregorian calendar is practically a perfect index of the seasons .

1 1 1 5 . The Metonic cycle of 9 years is used by Christian churches to deter

e of mine L nt and Easter , but the error of the cycle necessitates a complex system adj ustment of the golden numbers every century . Raja Mathan applied the

Metonic cycle without any adj ustment , and its error has produced in twelve

a - centuries a marked divergence between the solar and aver ge luni solar years .

1 al 1 6 . I f reform of the B urmese calendar be undertaken , and the tropic

O f year be adopted , the cycle method regulating the calendar can be adopted ,

one - with practically no error , for there is perfect luni solar cycle , namely the

1 0 0 s . cycle of 4 years , which was discovered by the French astronomer de Che eaux

1 040 tropical years equal 1 2863 lunations . This was absolutely correct without

so any error a few centuries ago . It is not now because the length of the mean

e 2 00 tropical year is decreasing at the rate of about one s cond in year s , while there is no appreciable change in the lengt h of the mean lunation ; but the error

is so small that it will not amount to one day in years .

1 1 7 . This fact may be easily verified . Three estimates of the length of the

a a a to mean tropic l ye r , ccording modern science , are given in paragraph 1 06.

1 0 0 are If these three be multiplied by 4 , the results res pectively days 37985 r 88748 and a a a 3 0 The Bu rm ese nd Ar ak n ese C lenda rs .

n to The length of a mean lunatio is , according B all 2 9 530589 d ays Young 2 9 5 30 588 Surya Siddh ant a 2 9 530587946 ee 1 286 are e e If these thr be multiplied by 3, the results resp ctiv ly days 37985 1 0 53444 and

Comparing the greatest estimate of 1 2863 me an lun ations and the sm allest

1 0 0 estimate O f 4 mean tropical years , 1 2 863 mean l unations d ays 1 040 mean tropic al years the difference is only

I n years the difference would amount to about 2 0 hours . This is a maximum estimate .

8 wa to 1 0 0 to to 1 1 . The best y apply the cycle of 4 years is use it make t at corrections in the Metonic cycle at regular intervals . The problem is o find what intervals the correction should be made .

of w a 1 0 0 a a n the so ar 1 1 9 . The number at t in 4 ye rs is found by subtr cti g l from the lun ar months . — 1 2863 1 2480 383 .

N ow multiply the two kinds of cycles together .

1 9 x 1 040 1 9760 . The numbe r of watat in 1 9760 years is By Meto 7 x 1 040 7280 By de Cheseaux 383 x 1 9 7277 D ifference 3

e n c so to out a a 1 60 The M to i cycle must be modified as cut 3 w t t i n 97 ye ars .

1 0 2 . The intervals between watat run in a series thus 3 3 3 2 3 3

nd so on - 2 a . a two two ea , over again I n e ch Metonic cycle there are y r inter al - v s , one of which follows three three year intervals , and the other follows two

- “ three year intervals . Every correction must be m ade by converting into a three year interval one of those two-year intervals which follow two three -year intervals Thu s

r and ra a e e a e ar 32 T he Bu m ese A k n s C l nd s .

1 2 3 . I f the tropical year be adopted as the solar year of B urma , and the

o watat continue t be placed as in the current Metonic cycle , there are some preliminary adj ustments to be considered . I n the first place , i n order that the

L ab i month in which the solar year begins may always be Tagu , and that the y which mar ks the beginning of Lent may always occur when the moon is in

Atha nli hin an , it is necessary that T gy Tet should be put about 7 % 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 Atha nli will move west

’ wards to an equal extent , and will thus adj ust itself to the moon s position at

Wazo L abyi as it is i n the current cycle .

hin an n 1 24 . There is no apparent reason why T gy Tet should ot always be put at midnight . Under the B urmese system the civil month always begins at midnight though the lunation does not . I t would be only conson ant 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 . I t would he obviously convenient if the B urmese solar year always began at midnight of the

Of th— 8 th A same day the E uropean calendar , say midnight of 7 pril . Early in

1 2th B . B . 1 1 th 1 th A the cent ury it varied between the and 2 pril . I t is now

1 5 th April .

1 25 . If any reform of the calendar be undertaken it would be worth w hile to correct the error of the calendar month . Table V I I I shows how this error has

. 2 1 2 1 6 2 . grown in twelve centuries I n the 9 years from 35 to 3 B E . the L agwe was the day on which mean new moon occurred only eight times , namely in M ar ch 1 873 May 1 873 August 1 874 October 1 874 August 1 883 October 1 883 November 1 883 "anuary 1 884

1 I n 1 7 1 months L agwe was one day too early . I n 72 months it was two days

oo e too a t early . I n 9 months it was thre days early , n mely in Febru ary 1 880 April 1 880 October 1 890 December 1 890 February 1 89 1 April 1 89 1 Febru ary 1 896 April 1 896 April 1 90 1 D fo r o e fects a nd S ugge stio n s R e f rm . 33

h The error has increased considerably of late years , and oug t to be corrected to s - ome extent . Thi s can be done most conveniently by placing three yet ngi n

8 E . 1 0 1 . instead of two in the five watat between 2 7 and 2 3 B , thus

\Va ta t T hande ikta Proposed 1 2 7 2 1 2 74 nge 1 2 77 n ge 1 2 80 gyi 1 28 2 n ge

6 1 2 . c If the tropical year be adopted , and the two initial corre tions

viz suggested in the last three paragraphs be made , . the solar year to commence — at midnight of 7th 8th April every year and one extra yet -ngin to be inserted

1 2 0 1 28 between 7 and 3, then the reformed calendar might conveniently commence f 1 2 8 1 8th 1 1 . from the first day of the tropical solar year , April 9 9 The ru es

for compiling this calendar for a number of years are very simple .

P R O P O S ED R U LES FO R A R EFO RM E D B URM ESE CALEN DA R .

i . 1 2 7 . ( 1 ) D ivide T hagay t by 1 9 If the remainder be

1 4 7 9 1 2 1 5 or ' 1 8

the year has an intercalary month . This rule holds good until the yea r.

1 62 3 B . E .

1 6 After B . E . 2 3 the watat years in the Metonic cycle change as follows

0 E . 1 6 2 9 changes to 1 in B . 5 1 2 1 978 1 2 2 331 4 2684 1 5 3037 7 3390

M ark all the watat for a number of years as above . Then divide

s 1 2 8 1 them i nto period of fifty years , commencing from , thus ,

1 28 1 1 330 1 33 1 1 38 0 1 38 1 1 430

wa i tat wa n etat and so on . Watat years are alternately gy and g , except that

’ a 0 e ars the w w a itat ( ) i n each period of 5 y first atat is gy , and 0 w an etat (b) when the last watat of any 5 years is g , then both the first and s econd watat of the next following 5 0 year s are

w agy itat . T he r e a nd A r k e a a ne se . Cale nda rs 34 Bu m s .

- 1 - To find the week day of st waxing of Tagu , or the week day of any w - day in Tagu , Kason or Nayon , from the eek day of the same day of the last

- . preceding luni solar year I f the preceding year was a common year , add 4 . n e 6 a wa tat . I f the preceding ye r was a g , add I f the preceding year was a wa itat 0 gy , add .

For Wazo , if the preceding year was a common year , add 4 . I f the pre

a 6. ceding year was watat of either kind , add

For any other month , if the present year is a com mon year , add 4 . I f the

wa n eta t 6 . w a i tat 0 present year is a g , add I f the present year is a gy , add . 6 Whenever the sum exceeds , subtract 7 .

- . T ha a i To find the week day of Thingyan Tet D ivide g y t by 4 . I f 2 1 - the remainder is 2 , add , i f not add . to the week day of Th ingyan Tet of the

6 . last preceding year . I f the sum exceeds , subtract 7 This rule holds good

E . 6 1 . until B . 1 4

8 1 2 . The results Obtained from Thandeikta may be compared with those

’ h s u x s 8 2 obtained from the system of averages based on de C e e a cycle . for years 8 O f B . B 1 1 8 2 . beginning in . , by examining tables I I and I I I I n 5 years out

- the 8 2 the luni solar year by both systems begins on the same day . In the other 24 years the luni -solar year in table I I I begins one day later than in table

I I . I f the tables had been prolonged a few years later the divergence of the two

T han deikta systems would have become conspicuous . We have seen that puts - - 2 28 2 a watat in the year before yet l un pyo when yet lun amounts to 7 , or 9 (paragraph and i n order to effec t this four of the seven watat years of the Metonic cycle have been altered (paragraph The next alteration to be made by T han de ikta will be the transfer of watat from year 1 8 to year 1 7

s - 6 of the cycle . Thi is to take place when yet l un of year 1 7 exceeds 2 . The yet -lun and its fraction (awa m an) of year 1 7 are as follows

- . B . . Aw m n B Yet lun a a . I 2 33 2 4 5 69 1 2 5 2 2 5 96 1 2 7 1 2 5 3 1 6 1 2 9 0 2 5 5 35 1 309 2 6 62 1 328 2 6 2 8 1 1 347 26 5 0 1 1 366 2 7 30

1 h d ik a E . 66 an e t So that in B . 3 T would create the first serious diver

n ge ce from the system of averages , and would thrust lent further than ever out f 8 of its original place in the tropical year , by trans erring the watat from year 1

1 to ye ar 7 of the Metonic cycle . ‘ De fe t a n d S e tio fo r Refo r c s ugg s ns m . 35

1 2 . 9 Tables I I and I I I ex hibit a marked difference in res pect o f the so lar

. year I n table I I Thingyan Tet is frequently in Kason . I n table I I I it 1 occurs on st waxing of Kason once in each Metonic cycle and no more . I n all other years i t is in Tagu . If Tagu happened to be a month of 30 days it would always be in Tagu .

1 0 - 3 . The official calendar makers to the late B urmese Government were a race of H ind u astrologers , the descendants of B rahmans said to have come to

Pon M andalay from Manipur , and known in B urma as nas . Since the annexa tion of U pper B urma the British Local Government has assumed the function of officially promulgating the essential elements of the calendar every year by

B u r m a Ga ette notification in the z . The details are Obtained from the P o n n a s at Mandalay , as they were by the Native Government , and are submitted for approval to the Head of the Buddhist religious orders before t he Governmen t takes action .

1 1 3 . A glance at the specimen page given i n paragraph 49 is sufficient to show that the learned Ponn as expend enormous labour in computing all the de fl tails set out in the calendar . B ut those details consist chie y 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 -i mportan t matter of fixing the n umber of months and n umbe r of days

a in each year . This is the only matter with which the public in gener l is concern

hande ikta ed . B ut s inCe the introduction of T 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 B urma , I ndia and England . The compilers of such of these diaries as are intended for use in B urma had to i guess the intercalary months and days , or act on the adv ce of irresponsible as trologers in Rangoon or elsewhere , and the guesses and advice were sometimes ff wrong . The last few years an improvement has been e ected by notifying the

a calendar nearly two years in advance . But there is no re son why it should not be notified forthwith for hundreds of years , or for ever by means of the rules in

1 para . 27 .

1 32 . One reason which makes it desirable to notify the calendar forthwith for a long series of years is that the pre sent practice tends to enc ourage s ome ’ Pon nas amateur astrologers who dispute the correctness of the calendars , and publish pamphlets in which they endeavour to enforce their own views about the i nsertion of intercalary months and days in certain years . Whether they s u e

' ceed 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

is be all . The important point that the matter should settled once for all , by The B r e e a nd ra ka e e a le a u m s A n s C nd rs .

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

1 2 the rules proposed in paragraph 7 fulfil this condition .

1 33 . N o 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 .

I f i t be conceded that Government should do this , it may be asked what is there

to choose be twee n adopting Table I I which is the result of T handeikta methods a nd adopting Table I I I which is compiled in accordance with the rules proposed

e 1 2 for a reform d calendar in paragraph 7 . The answer is that so far as results

in the near future are concerned there is very little to choose . I n 2 4 years out

8 2 L a we n w of the g is nearer to the real e moon in table I I I than in table I I ,

1 8 1 and table I I I makes out of every 9 solar years begin in Tagu , whereas

8 a l I I ad table I I makes 2 2 of the 2 years be gin in Kason . B ut t b e I has this

it w re vantage , that is based on simple rules by which the hole of it could be

at constructed 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 I I be adopted the

ha n ik 1 E . rules of T de ta will in 266 B . create a serious departure from correct

principles by placi ng lent later than ever in the season , and further errors will be

introduce d at intervals of 1 30 years or less . Long and tedious calculations are required to determine the watat and yet -ngin by Tha ndeikta these are all abolished

by the proposed rules for a reformed calendar .

1 n e ffi 34 . The Araka ese calendar , it is believed , has never b en o cially notified

by Government since the annexation of that part of the Provi nce . There was

a do so 2 0 0 0 app rently no need to , because the calendar had been fixed for years

o nce . a nd at , no controversy about the correctness of it seems to have arisen

e L nt is falling later in th e season than it used to be , but the Arakanese calendar would go o n for about 1 40 0 years more before the average lent would get so late

as the average lent by T handeikta is now . Therefore there seems to be no reason

e e why the Arakanese calendar should be int rf red with . Its chief defect is the

so e rror of the sol ar year . That could be corrected , if desired , without any inter - feren ce with the luni solar year . I C HA PT E R V .

N O TES O N T HE T AB LES .

1 35 . Table I exhibits all the essential elements of the calendar as actually

0 1 0 1 1 0 observed in B urma Proper for the last 1 7 years . The years 9 9 and 9 are added because the calendars of those years have been officially promulgated .

1 6 - 3 . The day of the wee k on which the luni sol ar year begins is s hown in 6 column 5 , and its date by the English calendar in columns and 7. The time of mean new moon obtained from European sources (Guinness ’ s tables) is shown

2 é abau n s in columns to 4 for comparison with the L agw of T g, the la t day of - the expired luni solar year .

1 . 37 The day , hour , minute , and second at which the solar year begins

( hin a n S a nkra n ti 8 1 T gy Tet , or Mean Mesha ) are shown in columns to 4 ,

. hin a n English date , week day and B urmese date The time of T gy Kya , or

S an kra nti 2 apparent M esha , can be found from this by subtracting days , 4 hours ,

1 1 . minute , 2 seconds

1 38 . Columns 1 8 and 1 9 give the watat y ears ; 1 8 show s whether there is an intercalary day or not ; 1 9 s hows the day of j uly on which the full moon Of the i ntercalary month falls . An examinationof column 1 9 is the easiest way of ascertaining whether Le nt is maintain ing its place among the seas on s or moving forward or backward .

' 1 . s C 39 Table I agree with M oyle s alendars , so far as they go , except in

e th 1 8 . B 1 880 . . B . 1 2 the p riod from 9 j une , 77 , to sth j une, Mr Moyle makes 39 - - - - A. . 1 8 B 8 0 a w é ( . . 1 2 2 A. . 1 8 a n . D 77) a wa gyi tat , and B 4 ( D ) g tat All the other authorities I have be en able to consult agree in making 1 2 39 a wa -nge-tat and

1 2 2 w a - - n s 4 a gyi tat . Th is is confirmed by ote of certain new and full moo n s in

Own 1 8 8 . e o I has my diary for 7 For this p ri d , therefore , think M r . M oyle an error of one day .

1 0 s 4 . Table I I is in the ame form , and gives the elements of the B urmese w - calendar compiled by Thandeikta method s for the next 9 2 years . The a tat are - 8 regulated by the yet lun as describe d in paragraph 5 . It is not absolutely

i s certain that this rule will be followed in future . There also some un certainty

- the 1 2 1 1 0 1 1 8 about the yet ngin in years 9 , 3 7 , 337 and 34 , as indicated in

ar s a nd w paragraph s 9 7 to 9 9 . Each of these ye f the next following atat year must

be o n e w a ita t wa n éta t . c , a gy and the other a g The un ertainty is whether the

wa ita t c w an éta t . u the gy will pre ede or follow the g I n the ncertain , years yet rm e a nd ra ka e e Ca e ar 38 T he Bu e s A n s l nd s .

1 0 1 1 1 2 2 ngin are placed as shown in table V I . I n columns and the year 9 is shown as 1 0 8 second s longer than any other year in the table by reason of the correction des cribed in paragraph 5 5 .

1 4 1 . Table I I I is an alternative to table I I . It embodies the suggestions 1 1 6 1 2 made in paragraphs to 7 for removing all doubts , simplifying the regula tion of future calendars ; and keeping lent i n its proper season by using

’ a u x s 1 0 0 . 1 28 1 A. . de Chese cycle of 4 years The cycle would commence in , ( D and in the ten years precedi ng that year one intercalary day more than Tha ndeikta w ould allow is inserted in order to bring the calendar months into nearer conformity with mean and apparent lunations (paragraph The t i mes of mean new moon are omitted as they w ould be a mere repetition of the

e time s s hown in table I I . The hour , minute and s cond of Th ingyan Tet are omitted becau se i t is proposed that Thingyan Tet should in future be fixed at midnight (paragraph I n this table the watat years happen to be the same

1 2 8 - ou t as in table I I (para . ) the yet ngin are placed according to the rule set i n paragraph 1 2 7 .

2 62 1 2 . Table I V exhibits the elements of the Arakanese calendar for 4 . years , in the same form as table I I I except that a special column is retained for the English date of Thi n gyan Tet because that date continues to change slowly in consequence of the error i n the length of the M akara nta solar year (paragraph whereas in table I I I Thingyan Tet is fixed for all time at 8th April and it therefore requires no separate column for the English date .

. H toon . 1 43 . Table V is copied by permission of Mr Chan from his book I t shows the week-day on which the L a byi of Wazo falls in Arakan each year for

wa . 2 00 0 years . I t also shows the watat , in this y When two consecutive years - w i a ta t . have the same week day figure , the later of the two is a gy When the later of two consecutive years has a week -day figure either 1 less or 6 more than

wa-n e- that of the preceding year , the later year is a g tat .

1 44 . Table V I exhibits the results of the calculations by w hich the inter

1 8 . 88 calary days were placed in table I I , column See paragraphs to 1 00 .

’ ’ 1 45 . Table V I I compares the moon s age at midnight of solar New Year s

Makaran a Day , as found from European sources , with the same as found by t

d . 2 metho s Column shows approximately , in days and hours , the European computation for mean new moon , M andalay civil time . Column 3 shows solar

’ ’ New Year s D ay . Column 4 shows the moon s age as calculated from columns 2 ’ and 3 , expressed in days and hours . Column 5 shows the moon s age as cal c u late d M a karan ta by , expressed in didi and fraction . The differences are very

The small . Burmese computations put the mean new moon slightly later than

E uro ea n on e s . the p ‘

TA BLES . ELEMENTS OF T H E B URME SE CALEN DAR FOR 1 72 YEARS

a u wa n I st T g xi g . e an N w n n l e e oo a a a i . M M , M d y T m

March 43

AB T L E I .

. . 1 To 1 1 0 . . 1 1 0 1 To 1 2 2 FROM A D 739 9 , B E 7 .

S ol ar N ew e ar n an T e t Y (Thi gy .)

B ur se m e . TAB LE I

ELEMENTS OF THE BURMESE CALEN DAR FOR 1 72 YEARS

a u wa n 1 st T g xi g .

M ea n N ew M oon an a a e . , M d l y Tim 45 — con tin u ec1 .

1 T o 1 1 0 1 1 0 1 T o 1 2 2 FROM A . D . 739 9 , B . E . 7 .

. S o ar e w e r n n t e n N a a T e . r d l Y (Thi gy ) Expi o y a N Se co nd B ur e se m . a o n W z i L ab i s y . y a

I 4 TABLE I

E LEMENTS OF T HE BURM ESE CALENDAR FOR 1 72 YEARS

a u wa n I st T g xi g .

A . D.

4 8

TABLE I ELEMENTS OF TH E BURM ESE CALENDAR FOR 1 7 2 YEAR S

a u wax m I st T g g . M e a n N ew o on an al a e . M , M d y Tim 49

. . 1 T o 1 1 0 . . 1 1 0 1 T o 1 2 2 . FROM A D 739 9 , B E 7

ear n an T e t S ol ar N ew Y (Thi gy ) . Expi re d

B ur ese m .

Wed. 5 0

TABLE I

ELEMENTS OF THE BURMESE CALEN DAR FOR 1 7 2 YEARS

T a u wax i n s I st g o . M M o on M nd al a i e e an N ew a . , y T m 3 d con ti n ue .

A . D . 1 T O 1 1 0 B . E . I I O I T O 1 FROM 739 9 , 2 7 2 .

S o ar N e w e ar n an T e t E r e d l Y (Thi gy ) . x p i

B u rm ese . We e k ELEMENT S O F T H E B URMESE CALEN DAR CALCULATE D BY TH AN DE IKTA

a n t T gu waxi g I s .

M e an N ew M oon a n a a e . , M d l y Tim

March 53

TA L II B E .

2 . D 1 0 T o 2 0 0 0 . . 1 2 1 T o 1 62 FOR 9 FUTURE YEARS FROM A . 9 9 , B E 7 3 .

N ew e ar n E re S ol ar Y (Thi gya n T et . ) xpi d

e B urm se . TABLE I I

ELEMENTS O F T H E BURMESE CALEN DAR CALCULATED BY T HAN D E IKTA

a u wa n I st T g xi g .

M e an N ew M oon M a n ala e . , d y Tim We e k

5 6

TABLE I I

E LEM E NTS OF T H E B URMESE CALEN D AR CALCULATED BY T HAN DE IR T A

a u wa n I st T g xi g . M e an N ew oo n and al a e M , M y Tim . 5 7

- nued con t. .

U . . 1 0 T 1 To 1 62 . 2 U o 2000 . . 1 2 FOR 9 F T RE YEARS FROM A D 9 9 , B E 7 3

o ar N e w e ar n an T e t S l Y (Thi gy ) .

Kason TAB LE I I I .

. . 1 0 2 0 00 E LEMENTS OF THE BURMESE CALENDAR FOR FUTURE YEARS , FROM A D 9 9 TO , ’ . . 1 2 1 T o 1 62 As D D D E CH E S E AUx s B E 7 3 , PROPOS E TO BE REGULATE BY CYCLE

1 0 0 1 2 8 1 . . OF 4 YEARS , COMMENCING FROM B E

a n I st . n an t d T agu w xi g Thi gy T e . Expi re

A . D . 5 9

— o i TABLE III . c n t m / ed.

D . D . 1 0 T o 2 0 0 0 ELEMENT S OF THE BURMESE CALEN AR FOR FUTURE YEARS , FROM A 9 9 , T 62 As E D ’ . . 1 2 1 o 1 D D E CH E S E AUX S B E 7 3 , PROPOS TO BE REGULATE BY CYCLE

1 0 0 1 2 8 1 E . OF 4 YEARS , COMMENCING FROM B .

a u wa n I st. n a n T e t T g xi g Thi gy . 60 — TABLE I I I conti n ued

H M . . 1 0 T 2 00 0 ELEMENT S OF T E BURMES E CALEN DAR FOR FUTURE YEARS , FRO A D 9 9 o , ’ . . 1 2 1 T o 1 62 As T o H E B E 7 3 , PROPOSED BE REGULATED BY DE C S E Aux S CYCLE

1 0 0 1 2 8 1 . OF 4 YEARS , COMMENCING FROM B E .

Wa n I s t n an T e t a u . i T g xi g Thi gy . Exp red

W e e k 61

TABLE IV .

TH E D 2 62 R . . 1 T o 2 000 ELEMENTS OF ARAKANESE CALEN AR FOR YEA S , FROM A D 739 ,

. . 1 1 0 1 T o 1 2 B E 36 .

o r I st a u S o ar N ew e a r n an T ag u . T g l Y (Thi gy E r e d n I st T e t . wa xi g . ) xpi

D A . . r a a n e se A k . E n gli s h We e k d t D a a e . y . 62

— ' . rontzn u ed TABLE IV .

D 2 62 . . 1 T o 2 000 ELEMENTS OF THE ARAKAN ESE CALEN AR FOR YEARS , FROM A D 739 ,

. 1 0 T o B E . 1 1 1 362 .

a u or I st a u S o ar N e w e ar n an T g . T g l Y (Thi gy re d n st T e t E waxi g I . ) . xpi

. D . n e s A A rak a e . e r Y a .

April . March

64

' I - m z d TAB LE V . ron ti c .

AR AR AN E S E 2 62 1 ELEMEN TS OF TH E CALEN DAR FOR YEARS , FROM A . D . 739 TO

2 00 0 1 0 1 T o 1 62 . , B . E . 1 3

or st u S o lar N e e ar n an T a gu I . T ag w Y (Thi gy T E red w a n I et . xi g st. ) xpi 65

— cont n u d TABLE IV . i e .

H D D 2 oo 2 62 . . 1 To c ELEMENTS OF T E ARAKANESE CALEN AR FOR YEARS , FROM A 739 ,

. 1 0 T o 2 B E . 1 1 1 36 .

a u r I st a u T g o . T g i re d n st Exp waxi g I .

D . . ra an se A A k e . We e k E ngli sh W e e k D ° d ate . D a y . 66

— . co m u a TABLE IV nt e .

R 2 62 . 1 To 2 0 00 ELEMENTS OF TH E ARAKAN E SE CALEN DA FOR YEARS , FROM A D . 739 , 0 1 T o 62 B . E . 1 1 1 3 .

o r 1 5 1 u ol ar N ew e ar n an Tagu . T ag S Y (Thi gy Ex ired w a n I st T et . p xi g . )

D ; N n se A rak a e . 67

— ° TABLE IV . con tzrm cd.

D 2 62 . D . 1 T o EL EMENTS OF T HE ARAKANESE CALEN AR FOR YEARS , FROM A 739

2 00 0 . o 2 . , B . E 1 1 0 1 T 1 36

S o l ar N e w Year (Thi n gya n re wa n t T et Expi d xi g I s . ) ,

D ra a ne se . A . . A k TABLE V .

WAzo L AE YI 2 0 0 ARAKAN ESE WEEK DAY FOR 0 YEARS . 69 — ’ V con tim zea . TABLE .

A z L ABYI RAKANESE WA o WEEK DAY FOR 2 00 0 YEARS . A — ‘ T B LE V com i nu ea .

WAzo L ABYI 2 0 0 0 ARAKAN ESE WEEK DAY FOR YEARS .

TABLE VI .

’ DAD E IN AN D 1 T H T HO K , WEEK DAY , M OON S LON GITUDE AT THE EN D OF THE 4 DIDI OF W 2 WAz o 1 2 1 T o I 6 . E . D SECON D , I N ATAT YEARS , FROM 5 3 , B , CALCULATE BY

T H AN D E IKT A .

D B . E . at at A . . W . 73

' — u TABLE VI con tzn ed.

' ’ THO R DAD E IN AN D D E N D 1 T H D D , WEEK DAY , MOON S LONGITU E AT THE OF TH E 4 I I OF 2 T o 6 2 E D W 1 1 1 . D WAz o . SECON , I N ATAT YEARS , FROM 5 3 , B , CALCULATE BY T AN D I T A H E K .

’ C o rre cte d C o rre cte d M o o n s d n hok de i . e e a on i tud e e fo e T a W k D y . l g b r c orre ct o n i . 74 TABLE VI I .

As D M AKAR AN T A . COMPARISON OF EPACTS , FOUN BY EUROPEAN AN D BY M ETHOD S

’ M oon s Age by

M akaranta .

Y e t L u n . Aw am a n . TA LE I — ti B V I con nu ed. 75

M AKAR AN TA . COMPARI SON OF EPACTS , AS FOUND BY EUROPEAN AND BY METHODS

e an N e w M o n ’ ' M o , M ea n M oo n s Age M oo n s Age l by v a n l i e . da lay C lV l T n d n t M kar a n t a a . m Thi gy a n Mi igh .

T e t .

D . H . Ye t L u Aw m an n . a . 76 E TAB L VI I I .

N E W L AG W E COMPARI SON o M EAN MOON AN D B URMESE CIVI L , EVERY M ONTH 2 Y E AR S FOR 9 .

M o n t . e a e ars h L p Y .

Wazo . 77 T L — ' A . B E VII I con tzn u ed.

S N E W L AG WE COMPARI ON OF M EAN MOON AND BURMES E CIVI L , EVERY MONTH 2 FOR 9 YEARS .

’

B E . M nt . L D . o e a Ye ars A . . l h p .

2 n d a W zo . ' B — zzt zzuccl TA LE VI I I co t .

N E w L AG WE COMPARISON OF M EAN MOON AN D BURMESE CIVIL , EVERY MONTH FOR 2 9 YEARS .

M o n t . e a e rs h L p Y a .

r a a Inte cal ry d y .

1 2 nd 9 35 Wazo . l 9

80 —con tin ued TABLE VI I I .

N e w L AG W E COMPARI SON OF M EAN MOON AND BURMESE CIVIL , EVERY MONTH 2 FOR 9 YEARS .

M nt o . e a e ars h Y . r L p Yea .

April May June July s Augu t 2 nd Wazo . S eptember O ctober Nov ember December January

Feliiu ary March April May June July Augus t September October Novembe r December Ja nuary Feb ruary March A pril May Ju ne Iu ly Augu st Septembe r October November December J anuary Feb rua ry March April May June Iuly August Se ptember O ctober

H 8 1

— co t n u ed TABLE VI II n i .

N E w AN D L AGWE COMPARISON OF MEAN MOON B URMESE CIVIL , EVERY 2 MONTH FOR 9 YEARS .

o n t . ea ars M h L p Ye .

a 2 ndW zo . ' L E I—t on tzn u TAB VII cd.

ME AN N E W AN D L AG WE COMPARISON OF MOON BURMESE CIVI L , EVERY MONTH 2 FOR 9 YEARS .

ont M h . 83

' TABLE I— r VII con tr m ed.

C N E w L AG wE H OMPARISON OF M EAN M OON AND BURMESE CIVI L , EVERY MONT 2 FOR 9 YEARS .

M nt D o . A. . h

a W zo . TA IX T BLE . PAR I .

ENGLISH DATES CORRES PON DING T o TH E

Wa aun wt n g g. T a h ali .

March 1 3 April 1 1 1 4

I S

I 6

1 7

2 J une

Augu st O AR COMM N YE .

FIRST DAY OF EACH BURMESE MONTH .

T hadi n ut . a aun g) T b g .

O ctobe r 1 TA E I RT II B L x . PA .

E N G LI SH DATE S CORRESPON DING T o T H E

a 1 s t W zo .

Au 2 6 M a rch g.

E IX . TAB L PART I I I .

ENGLI SH DAT ES CORRESPONDING T o T HE

n I st Wa zo zu d a o . . Waz o W a n . a u . awt a n N y g g T h li .

M a rch 89

T WAGY ITA YEAR .

DAY FIRST OF EACH BURMESE MONTH .

n Tabau g . x TABLE .

- i O MO . PART . C M N YEAR

WEEK -D AY O F AN Y G IVEN DAY I N EACH BURMESE MONTH .

‘ S u n .

Kason

hdon .

Wagau ng Mon .

Wed. Tawth a li n M on .

T ha di ngyut Wed.

T asa u ngm on Wed.

N a tda w

Py atho

' Ta bodww

Ta ba u ng

9 2

TABLE X . — WAGY ITAT Y . PART I II . EAR

-DAY O F A A IN H II WEEK N Y GIVEN D Y AG BURMESE MONTH .

Wed.

Kason Wed.

Wed. Th .

Fi rst Wazo

n a ed. Seco dW zo Mon . W

Wagau ng

Tawt halin

T ha di ngyu t

T a sa u n gm on

N atdaw

Py atho

T abodwe 6 We d.

Ta baung e T h W d. .

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