1_A 3405. an Unusual Astronomical Text From Uruk (Steele, 2000)

8/10/2019 1_A 3405. an Unusual Astronomical Text From Uruk (Steele, 2000)

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Arch. Hist. Exact Sci. 55 (2000) 103135. c Springer-Verlag 2000

A 3405: An Unusual Astronomical Text from Uruk

John M. S teele

Communicated by A. J ones

Introduction

The Tablet Collection of the Oriental Institute of the University of Chicago con-tains several astronomical texts among the series bearing registration numbers A 3400ff.These tablets, all bought from dealers, apparently come from Uruk. 1 The majority of thetexts contain mathematical astronomy and have been published by Otto Neugebauer inhis Astronomical Cuneiform Texts (Lund Humphries, London, 1955). One (A 3456) isa collection of observations of Mercury and the dates of solstices, equinoxes and Siriusphenomena for the years SE 116 to 132. 2 A 3405, the text discussed here, contains acollection of the dates and longitudes of planetary phenomena and lunar eclipses for theperiod SE 60 to 70.

In answer to a query by Neugebauer, A 3405 was identied by J. Schaumberger ascontaining planetary observations from the same period as those cited by Ptolemy inhis Almagest . Working from a photograph, Neugebauer and Abraham Sachs studied A3405, and in his 1948 classication article Sachs described it as follows:

[A 3405] covers astronomical phenomena for the years 6070 SE, though it seems likelyfrom what can be read of the colophon that the text was written about 50 years later. Thesections are arranged by year, subsections month by month. Within this framework, onthe relevant days of the month, there appear the following entries: a. The Planetary Phe-nomena [i.e., the characteristic Greek Letter phenomena] . . . but in contrast to similarinformation in all four of the main categories of non-tabular texts [i.e., Diaries, Almancs,Normal Star Almanacs, and Goal Year Texts] . . . they are accompanied by the men-tion of the exact degree within the zodiacal sign. b. Lunar eclipses with indications of the moment of opposition, the longitude, the eclipse magnitude, and the type of node. Inmentioning the type of node and in giving the exact degree within the zodiacal sign for thelongitude, the eclipse items deviate from those found in the four main types of non-tabularastronomical documents. No other information whatsoever is given. The logograms for

1 This is certain for many of these texts (including A 3405) on account of the colophon. SeeO. Neugebauer, Astronomical Cuneiform Texts (Lund Humphries, London, 1955), 4.

2 H. Hunger, A 3456: eine Sammlung von Merkurbeobachtungen, in E. Leichty, M. DeJong Ellis and P. Gerardi (eds.), A Scientific Humanist: Studies in Memory of Abraham Sachs(University Museum, Philadelphia, 1988), 201223.


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104 J.M. S teele

Mercury and Jupiter are given in the abbreviated forms GU 4 and BABBAR, which areotherwise exceedingly rare. 3

Nothing further was written about the text bar a brief comment by Neugebauer in1951 that it proved exceedingly interesting in many respects. 4 It was catalogued bySachs in his Late Babylonian Astronomical and Related Texts (Brown University Press,Providence, 1955) as number *1479. In their book Astral Sciences in Mesopotamia(Brill, Leiden, 1999), p. 178, Hermann Hunger and David Pingree summarise Sachssdescription of A 3405, and remark, although without detailing their reasons, that it ishighly likely that the longitudes were computed by means of ACT-type systems. A fulledition of A 3405 has now been prepared by Hermann Hunger for publication in volume5 of A. J. Sachs and H. Hunger, Astronomical Diaries and Related Texts from Babylonia

(Osterreichische Akademie der Wissenschaften, Wien). What follows is based upon histransliteration of the text, generously made available to me in advance of publication.

Any errors of interpretation etc. are, of course, my own.As Neugebauer remarked, A 3405 is indeed exceedingly interesting. Its contents

are unique: no other text contains a mixed collection of data for the planets with degreesof longitude given for the phenomena. In the ACT ephemerides, planetary longitudesare never rounded to the nearest degree, whilst the NMAT texts such as the Diaries nevergive degrees within zodiacal signs. Furthermore, data from different planets are nevercombined in the ACT ephemerides.

A 3405 is made additionally interesting by its colophon. This reveals that the textwas written more than 50 years after its contents, unusual in itself, and that it was ownedby Anu-b elsunu, son of Nidinti-Ani, who is well known from the ACT material andfrom his horoscope.

I offer below an astronomical interpretation of the data recorded on A 3405. In do-ing so, however, I must acknowledge that several (perhaps unsurmountable) problemsremain, in particular with the dates of the Mercury phenomena and the lunar eclipsedata. In the nal section of this paper I discuss the importance of this text in the broadercontext of Mesopotamian astronomy and astrology of the Seleucid period, and offersome suggestions for why it was compiled.

The text

When complete A 3405 contained 4 columns on each of the obverse and reverse.Columns IV (obverse) and V (reverse) are now destroyed, and little remains of columnIII (obverse). Within each column, each line is devoted to a single astronomical phenom-enon, with the exception of the eclipse data which are spread over 2 lines. The beginningof each year is separated from the last by a horizontal ruling, and the new year number

begins the next entry. When a new month starts, the month name is given before the day

3 A. Sachs, A Classication of the Babylonian Astronomical Tablets of the Seleucid Period, Journal of Cuneiform Studies 2 (1948), 271290.

4 O. Neugebauer, The Babylonian Method for the Computation of the Last Visibilities of Mercury, Proceedings of the American Philosophical Society 95 (1951), 110116, esp. 111.


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A 3405: An Unusual Astronomical Text from Uruk 105

number; otherwise the day number was considered sufcient. Month names follow theusual Uruk conventions with Month XII 2 written DIRI rather than the Babylon normDIR- SE.

The astronomical data comprises lunar eclipse possibilities and the usual Greek Letter phenomena for the planets. 5 For the inner planets that is:

: rst visibility in the east (KUR . . . IGI): last visibility in the east (KUR . . . SU): rst visibility in the west ( SU . . . IGI): last visibility in the west ( SU . . . SU)

and for the outer planets:

: rst visibility in the east ( . . . IGI): stationary point in the east ( . . . US): acronychal rising ( . . . ana ME a ): stationary point in the west ( . . . US): last visibility in the west ( . . . SU)

where . . . is the longitude of the phenomena. In addition to being highly abbreviat-ed, 6 there is some difference between the terminology used for these phenomena andthe usual Babylon conventions. In particular, the logogram KUR is used for east/morn-ing, whereas texts from Babylon usually have NIM. Longitudes are given to the degree

within the zodiacal signs. The logograms used for the signs are the usual ones for Uruk (eg., LU for Aries, G IR-TAB for Scorpio, zib for Pisces). The names of the planetsMercury and Jupiter are abbreviated to GU 4 and BABBAR respectively (instead of thenormal GU 4-UD and M UL-BABBAR). 7

A schematic translation of A 3405 is presented in Table 1. Note that horizontal align-ment is not preserved in this translation. For further textual details, see the full editionin Sachs-Hunger. Several scribal errors are evident in the text. I have marked likelycorrections to the text in the margin. Most of these are the addition or subtraction of anextra sign for 10. The reasons for these proposed corrections are given in the discussion

below. In this discussion, I have highlighted those numbers I correct by underlining the(uncorrected) number in the text.

Astronomical commentary

The astronomical data recorded on A 3405, namely the dates and longitudes of theGreek Letter phenomena of the planets and several lunar eclipse possibilities, must have

5 I follow here the traditional definitions of the planetary phenomena. In the light of P. J.Huber, Astronomical Dating of Babylon I and Ur III (Undena Publications, Malibu, 1982) and

should probably be dened as rst disappearance rather than last visibility.6 Through the omission of the preposition ina . We would normally expect, eg., ina SU ina

. . . SU.7 This abbreviated name for Mercury is also found in A 3456.


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106 J.M. S teele

T a

b l e 1

. S c h e m a t i c t r a n s l a t i o n o f A 3 4 0 5 ( n o t e : h o r i z o n t a l a l i g n m e n t i s n o t p r e s e r v e d )

I

I I

I I I

I V ( d e s t r o y e d )

1 4 [ .

. . ]

1 3 , [ . . . ]

[ . . .

]

2 5 , J

u p i t e r [ C a ] n

2 6 ?

( e c l i p s e ) 2 2

, [ x ] 0 Hp A B L A L

I [ I I

. . . ]

I V , 4 , V

e n u s

C a n

2 8

2 8 , V

e n u s

S a g 2 5

1 0 + [ x

. . . ]

6 , M e r c u r y

L e o 3

2 8 , M

e r c u r y

S a g

5

I V , 4

[ . . .

]

2 8 1 8

1 2 , S

a t u r n

S c o 2 6

X , 4 , S

a t u r n

S a g 1 9

2 5 [ .

. . ]

2 4 , M

a r s

L e o 2 3

1 0 , J

u p i t e r

V i r 1 0 + x

V [ .

. . ]

2 4 , J

u p i t e r

C a n 3 0

1 2 , M

a r s

[ .

. . ] 2 5

[ . . .

]

2 6 , M

e r c u r y

C a n

2 8

2 4 , M

e r c u r y

[ A ] q u 8

[ . . .

]

V , 1

8 , M e r c u r y

L e o 1 8

X I , 1 8 , M e r c u r y

[ A ] q u 3 0

[ . . .

]

V I I

, 9 , M

e r c u r y

S c o 8 D I B

2 9 , V

e n u s

[ P i ] s 1

[ . . .

]

2 6 , M

e r c u r y

S c o

2 1

X I I

, 6 , M e r c u r y [ A q ] u 2 3

[ . . .

]

V I I I , 9 , S a t u r n

S a g

5

7 , J u p i t e r

V i r 1 1

[ . . .

]

1 1 , M

a r s

S c o 7

X I I

2 , 1

0 M e r c u r y

P i s 2 3

[ . . .

]

1 2 , M

e r c u r y

S c o

1 4

S E 6 2 , I , 3 , S a t u r n

S a g 2 6

2 0 + [ x

. . . ]

2 9 , J

u p i t e r

L e o 1 7

9 M e r c u r y

T a u 1 8

V I I I [ .

. . ]

I X , 1

1 , S a t u r n

S a g 7

1 0 J u p i t e r

V i r 7

I X , 1

0 + [ x

. . . ]

1 4 , 2

0 b e f o r e s u n s e t G e m 2 6

I I , 1

5 , 1

a f t e r s u n s e t , S

a g 1 1

2 0 + [ x

. . . ]

( e c l i p s e ) 1 1

, 4 0 Hp A B L A L

( e c l i p s e ) 3 0

, 2 0 Hp A B S I G

2 9 [ .

. . ]

2 8 , M

e r c u r y

S a g

2 8

2 4 , M

e r c u r y

G e m 3 0

X , 5 , M

e r [ c u r y

. . . ]

X , 2

7 , J u p i t e r

L e o 1 3

2 8 S a t u r n

S a g 2 3

1 5 , M

e r c u r y [

. . . ]

2 9 , M

e r c u r y

A q u 2 5

I I I , 1 9 [ M e r c u r y ] G e m 2 8

2 1 , S

[ a t u r n

. . . ]

[ X I ]

, 2 4 , M e r c u r y

P i s 1 6

I V , 8 , M

e r c u r y

C a n 1 7

X I , 5 , M a [ r s

. . . ]

[ X I I

, 1 ] 7

, M e r c u r y

P i s 1 3

2 9 , S

a t u r n

S a g 1 9

[ . . .

]

[ 2 ] 7

, J u p i t e r

L e o

8

V , 1

7 J u p i t e r

V i r 2 2

X I I [ .

. . ]

[ S E 6 1

. . . ]

[ . . .

]

[ . . .

V e n u s ] A r i 1 2

2 5 M a r s

L i b 1

[ . . .

] S a t u r n

S a g 1 5

[ V ] I [ .

. . ]

[ . . .

] M e r c u r y [

. . .

]


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T a

b l e 1

. ( c o n t . )

I I I V I I I

V I I

V I

V ( d e s t r o y e d )

[ . . .

]

[ . . .

x ] + 3 a f t e r s u n r i s e C a p 2 1

[ . . .

]

[ . . .

]

( e c l i p s e ) 6 , 1 0 Hp A B L A L

2 6 S a [ t u r n

. . . ]

[ . . .

]

1 5 , M

a r s C a n 7

X I , 6 , M e r [ c u r y

. . . ]

[ . . .

]

1 9 , M

e r c u r y

C a n 1 1

9 , J u p i t e r [

. . . ]

[ . . .

]

2 3 , S

a t u r n

P i s 2 4

2 2 , M

a r s [

. . . ]

[ . . .

]

V , 2

9 , M e r c u r y

V i r 1 6 D I B

2 4 , M

e r [ c u r y

. . . ]

[ . . .

]

V I , 5 , J u p i t e r

, T

a u 6

2 8 , S

a [ t u r n

. . . ]

6 1 6

[ . . .

] M e r c u r y [ .

. . ]

1 7 , S

a t u r n

P i s 2 0

X I I

, 8 , J

u [ p i t e r

. . . ]

[ . . .

] 5 [ .

. . ]

2 3 , M

e r c u r y

L i b 8 D I B

2 3 , M

e r [ c u r y

. . . ]

[ ( e c l i p s e )

. . . ]

2 0 Hp [ A B ] S I G

V I I

, 1 1 , M

e r c u r y

L i b 4

S E 6 8

, I , 1 , M

a [ r s

. . . ]

[ . . .

J u p i t e r ]

G e m

1 5

V I I I , 2 , J u p i t e r

T a u 1 2

2 5 , M

e r [ c u r y

. . . ]

[ . . .

M e r ] c u r y

S a g 2 9

1 6 , M

e r c u r y

S c o 8

2 8 , [ . . . ]

[ . . .

M e r ] c u r y

C a p 1 6

1 7 , S

a t u r n

P i s 1 5

I I I , 9 , M e r [ c u r y

. . . ]

[ . . .

M e r ] c u r y

C a p 4

I X , 2

4 , V e n u s

S a g 1 2

2 8 , S

a [ t u r n

. . . ]

1 2 2 2

[ . . .

x ] + 1 0 J u p i t e r

G e m 1 0

2 9 , M

e r c u r y

C a p 1 6

3 0 , V

e n u s [

. . . ]

[ . . .

M e r ] c u r y

A q u 1 6

X , 3 , J

u p i t e r

T a u 6

I V , 3

M e r c u r y [

. . . ]

[ . . .

M e r ] c u r y

A r i 1 2

1 3 , 2

4 a f t e r s u n r i s e

1 4 , 5

0 [ .

. . ]

[ . . .

] S a t u r n

A r i 9

( e c l i p s e ) 3 5

, 1 0 Hp A B S I G

( e c l i p s e ) 1 0

, 2 0 [ Hp A B L A L ]

C o l o p h o n

2 2 , M

e r c u r y

A q u 6

1 7 , J

u p i t e r 1 0 + [ x

. . . ]

X I , 2 , M e r c u r y

C a p 2 2

2 6 , M

e r c u r y [

. . . ]

1 5 , V

e n u s

A q u 2 8

V , 2

2 , S a [ t u r n

. . . ]

1 5 2 5

X I , 8 , M a r s

S c o 3

V I , 1 2

, M e r c u r y [

. . . ]

1 6 , M

e r c u r y

P i s 4

1 4 , J

u p i t e r [

. . . ]

6

1 6 , S

a t u r n

P i s 2 8

2 9 , M

e r c u r y

[ .

. . ] 1 0 + [ x ]

2 8 2 5

X I I

2 , 1

4 , M e r c u r y

A r i 2 7

V I I

, 1 8 M e r c u r y

[ .

. . ]

1 7 , S

a t u r n

P i s 2 9

2 7 , M

a r s L i b 2 7

[ S E 7 0

. . .

]


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servations in the Babylonian Diaries, which is what we would expect from observerslocated in these two cities. Thus, it seems highly likely that the data on A 3405 were notobserved.

Option (ii) also seems an unlikely source for the astronomical data on A 3405. BothNormal Star Almanacs and Almanacs contain the dates and zodiacal signs of the Greek Letter phenomena of the planets. However, as with the planetary data in the Diaries,precise longitudes within the zodiacal signs are never given. Theoretically, it would bepossible to obtain planetary longitudes either from the distances to the Normal Starsgiven in the Normal Star Almanacs, or from the dates of the entrances of the planetsinto zodiacal signs given in the Almanacs. However, this seems to me to be unlikely,especially given the relatively small number of non-mathematical astronomical textsrecovered from Uruk.

This leaves us with option (iii), namely that the planetary data in A 3405 came fromthe texts of mathematical astronomy. As we shall see below, this is almost certainly thecorrect option. Babylonian planetary theory has as its principal goal the prediction of allfuture dates and longitudes of a particular Greek Letter phenomenon of a planet given aninitial date-longitude pair. Two general systems were developed to obtain these results,which for convenience we call Systems A and B. In System A, the synodic arc be-tween two consecutive phenomena of the same kind is functionally dependent upon thelongitude , whereas in System B it is functionally dependent upon the previous value.The synodic time t is usually given by adding a constant to . Two lunar theories

are known, also called System A and B because they treat the longitude of successivesyzygies in a way analogous to the respective planetary theories. For a full treatment of Babylonian mathematical astronomy, I refer to reader to the works of Neugebauer andothers. 11

To test whether the data in A 3405 comes from the ACT texts it will be necessary todiscuss each planet in turn. Unfortunately, the longitudes in A 3405 are only expressedto integer degrees and for some phases of particular planets there is only a small amountof data preserved. It may not always be possible, therefore, to assign a unique model toall the data. Furthermore, it may be that some of the data was calculated by models that

are currently unknown. Due to the comparatively small amount of data preserved it is,however, not possible to uncover the details of any new models from this text. It will beuseful to note that the years SE 61, 64, 66, and 69 all contained an intercalary MonthXII 2 .

(i) Mercury

Due to the relatively short mean synodic period of Mercury (c. 116 days) moreGreek Letter phenomena are preserved in A 3405 for this planet than for the other four

11 See, for example, O. Neugebauer, ACT , idem , A History of Ancient Mathematical Astrono-my (Springer-Verlag, Berlin, 1975), A. Aaboe, On Period Relations in Babylonian Astronomy,Centaurus 10 (1964), 213231, and N. M. Swerdlow, The Babylonian Theory of the Planets(Princeton University Press, Princeton, 1998).


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110 J.M. S teele

combined. This gives us a good chance of identifying the model by which the data wascalculated. Two systems for Mercury, A 1 and A 2 , are known. In System A 1 , only and are calculated independently; and are determined by adding pushes whoselength is dependent upon the longitude of the preceding phase. Let us recompute thedates and longitudes of and over the period covered by A 3405. For the initiallongitude is taken as Cancer 28 and the date as SE 60, IV, 26. For , the initial longitudeas Scorpio 8;30 and the date as SE 60, VII, 9.

Mercury

System A 1 Longitude System A 1 Date Text Longitude Text Date

Can 28 60, IV, 26 Can 28 60, IV, 26Sco 13;37,30 60, VIII, 15;8,9 Sco 14 60, VIII, 12Pis 14;10 60, XII, 19;11,18 Pis 13 60, XII, 17Can 13;40 61, IV, 22;11,57Lib 27;30 61, VIII, 9;32,36Aqu 22;40 61, XII, 8;13,15 Aqu 23 61, XII, 6Gem 29;20 62, III, 18;23,51 Gem 28 62, III, 19Lib 11;22,30 62, VII, 3;57Aqu 1;10 62, X, 27;15,9

Gem 15 63, III, 14;35,48Vir 25;15 63, VI, 28;21,27Cap 11;15 63, X, 17;52,6 63, X, 15Gem 0;40 64, III, 10;47,45Vir 9;7,30 64, VI, 22;45,54Sag 25;7,30 64, X, 12;16,33Tau 9;30 65, II, 0;9,42Leo 23 65, V, 17;10,21Sag 9 65, IX, 6;41Ari 18 66, I, 19;12,39Can 26;52,30 66, V, 1;35,48Sco 23;52,30 66, IX, 1;6,27Pis 26;30 66, XII 2 , 8;14,36Can 21;53,20 67, IV, 7;8,35Lib 26;45 67, VII, 15;30,54Pis 5 67, XI, 27;16,33 67, XI, 24Can 7;33,20 68, IV, 3;20,33 68, IV, 3Lib 20;37,30 68, VII, 19;55,22 68, VII, 18Aqu 13;30 68, XI, 16;18,31

Gem 23;13,20 69, III, 29;32,30Lib 4;30 69, VII, 14;19,49 Lib 4 69, VII, 11Cap 22 69, XI, 5;20,28 Cap 22 69, XI, 2Gem 8;53,20 70, II, 25;44,27Vir 18;22,30 70, VI, 8;44,16Cap 4;22,30 70, IX, 28;14,55 Cap 4


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Mercury

System A 1 Longitude System A 1 Date Text Longitude Text Date

Sco 8;30 60, VII, 9 Sco 8 DIB 60, VII, 9Aqu 25;10 60, X, 29;10,39 Aqu 25 60, X, 29Gem 2;39 61, II, 10;10,18Lib 20;25 61, VII, 1;26,57Aqu 8;56,40 61, X, 23;29,16 Aqu 8 61, X, 24Tau 18;3 62, I, 6;6,15 Tau 18 62, I, 9Vir 26;5 62, V, 17;38,51Cap 22;43,20 62, IX, 17;47,47Tau 3;27 63, I, 2;2,6

Vir 1;45 63, V, 3;50,45Cap 6;30 63, IX, 12;6,24Ari 18;51 63, XII, 27;58,3Leo 7;25 64, IV, 20;2,42Sag 20;16,40 64, IX, 6;25,1Ari 4;15 64, XII, 23;54Can 13;5 65, III, 6;14,39Sag 4;3,20 65, VIII, 0;43,38Pis 19;39 65, XI, 19;49,57Gem 25;39 66, II, 29;20,36

Sco 17;50 66, VII, 25;2,15Pis 4;30 66, XI, 15;12,54Gem 11;3 67, I, 25;16,33Sco 1;36,40 67, VI, 19;20,52Aqu 18;16,40 67, X, 9;31,31Tau 26;27 68, I, 21;12,30 68, I, 25Lib 10;5 68, VI, 8;21,9 68, VI, 12Aqu 2;3,20 68, X, 3;50,8Tau 11;51 69, I, 17;8,27Vir 16;45 69, V, 24;33,6 Vir 16 DIB 69, V, 29

Cap 15;50 69, IX, 28;8,45 Cap 16 69, IX, 29Ari 27;15 69, XII 2 , 13;4,24 Ari 27 69, XII 2 , 14Leo 21;25 70, IV, 10;45,3Sag 29;36,40 70, VIII, 22;27,22 Sag 29Ari 12;39 70, XII, 9;0,21 Ari 12

The longitudes of and computed by system A 1 are in good, but not perfect,agreement with those found in A 3405: all are within 1 of the System A 1 values. How-

ever, the dates are in very poor agreement with those given by System A 1 . For , onlyone date, SE 68, IV, 3 is exactly as expected; the others generally being two or three daysearlier. Similarly, for , only the date SE 60, X, 29 is in agreement with the computeddate; the others being up to ve days late.

In System A 1 and are calculated using pushes from the longitudes and datesof and respectively. These pushes are dependent upon the position of the planet inthe ecliptic at and . Several tables for computing the pushes are preserved. They are


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112 J.M. S teele

published as ACT 800a to 800e. 12 Below I give the longitudes and dates of and calculated using pushes. In the rst pair of columns the pushes have been applied to thelongitudes and dates calculated using System A 1 above. In the second pair the pusheshave been applied to the and data preserved on A 3405 (dates in parenthesis werecalculated by applying pushes to the recorded dates, but using longitudes taken fromSystem A 1 since they are not preserved in the text). The nal pair contains the preserved

and data on A 3405.

Mercury

A1 + Pushes A 1 + Pushes Date + Pushes + Pushes Text Text DateLongitude Longitude Date Longitude

Leo 21;44 60, V, 21;18 Leo 21;44 60, V, 21;18 Leo 18 60, V, 18Sag 27;10 60, X, 1;8,9 Sag 27;40 60, IX, 27;40 Sag 28 60, IX, 28Ari 8;26,40 61, I, 13;27,58 Ari 7;40 61, I, 11;40Leo 5;26,40 61, V, 15;58,37Sag 5;40 61, IX, 19;42,36 Sag . . . 61, IX, 28Pis 24;6,40 61, XII 2 , 9;39,55 Pis 24;20 61, XII 2 , 7;20 Pis 23 61, XII 2 , 10Can 19;14,40 62, IV, 9;47,11 Can 17;44 62, IV, 10;10 Can 17 62, IV, 8Sco 14;53,30 62, VII, 8;13,30Pis 8;51,20 62, XII, 5;51,49Can 3 63, IV, 3;35,48

Lib 26;37 63, VIII, 0;24,27Aqu 16;15 63, XII, 2;7,6 (63, XI, 29;15)Gem 16;45,20 64, III, 28;21,45Lib 7;0,30 64, VII, 22;10,39Aqu 8;7 64, XI, 27;36,3Tau 22;28 65, II, 15;47,42Vir 20;4 65, VI, 14;58,21Cap 23 65, X, 22;41Tau 0;12 66, II, 3;24,39Leo 20;27,30 66, V, 26;47,3Cap 7;52,30 66, X, 17;6,27

Ari 15;54 66, XII 2 , 28;24,36Leo 14;48,26,40 67, V, 1;49,55Sag 4;40 67, VIII, 25;25,54Ari 2;20 67, XII 1 , 24;36,33 (67, XII, 21;20) 67, XII, 23Can 28;33,46,40 68, IV, 26;6,6,20 (68, IV, 25;45,33,20) 68, IV, 26Sco 26;30 68, VIII, 27;47,52 (68, VII, 25;52,30)Pis 17;54 68, XII, 20;48,31Can 12;19,4,40 69, IV, 19;54,43,20 Can 11 69, IV, 19Sco 7;6 69, VIII, 18;13,46 Sco 6;32 69, VIII, 14;13,49 Sco 8 69, VIII, 16Pis 2;8 69, XII, 17;0,28 Pis 2;8 69, XI, 13;40 Pis 4 69, XII, 16Gem 26;4,26,40 70, III, 18;43,20,20

Lib 18;49,30 70, VII, 9;24,46Aqu 17;5 70, XI, 12;57,25 Aqu 16;44 Aqu 16

12 See O. Neugebauer, ACT , 293295 for a summary of these tables.


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Mercury

A1 + Pushes A 1 + Pushes Date + Pushes + Pushes Text Text DateLongitude Longitude Date Longitude

Leo 2;57 60, IV, 1;56,21 Leo 3 60, IV, 6Sco 22;30 60, VIII, 24 Sco 22 60,VIII,24 Sco 21 60, VII, 26Pis 17;10 60, XI, 23;10,39 Pis 17 60, XI, 23 Pis 16 60, XI, 24Can 17;0,12 61, III, 25;42,6Vir 4;25 61, VII, 16;26,57Pis 0;32,36,40 61, XI, 17;52,40 Aqu 29;32 61, XI, 17;32 Aqu 30 61, XI, 18Can 0;27,24 62, II, 18;42,15 Can 0;24 62, II, 21;36 Gem 30 62, II, 24Lib 15;7,40 62, VI, 5;48,1Aqu 13;14,13,20 62, X, 10;18,40,20Gem 14;27,36 63, II, 11;43,30Lib 13;49 63, V, 1;47,45Cap 25;22 63, X, 2;24,24 63, X, 5Tau 25;37,12 64, II, 4;44,15Leo 21;25 64, V, 29;33,42Sco 6;58,53,20 64, IX, 23;28,21Ari 5;14 64, XII 2 , 25;36Leo 19;28 65, IV, 20;29,59Sag 22;35,46,40 65, VIII, 19;46,58Ari 13;49,12 65, XII, 15;41,33Leo 10;13,48 66, IV, 15;55,24Sag 2;1,20 66, VIII, 10;7,55Pis 26;30 66, XII, 9;12,54Can 26;31,24 67, III, 12;29,9Sco 16;43,6,40 67, VII, 4;20,52Pis 10;16,40 67, XI, 3;31,31 67, XI, 6Can 9;58,36 68, III, 5;29,54 (68, III, 9;17,24) 68, III, 9Lib 25;23,40 68, VI, 24;20,9 (68, VI, 27;49,10) 10 + x 68, VI, 29Aqu 21;8,13,20 68, X, 26;58,21,20Gem 23;13,12 69, II, 28;30,39Lib 8;17 69, VI, 14;15,36 Lib 7;44 69, VI, 18;50 Lib 8 DIB 69, VI, 23Aqu 5;53,20 69, X, 20;12,5 Aqu 6;4 69, X, 21;4 Aqu 6 69, X, 22Gem 5;42 70, I, 21;31,24 Gem 5;24 70, I, 22;24Vir 24;25,20 70, V, 14;54,3Cap 17;33,33,20 70, IX, 11;22,42 Cap 16;52 Cap 16

The longitudes are on the whole in fairly good agreement with those given by ap-plying pushes to the longitude of and . For , discrepancies of up to 3 degrees exist,but for , discrepancies never exceed 1 degree. The cause of these discrepancies is notknown; sometimes they are reduced when we apply the pushes to the longitudes of

and which were recomputed using System A 1 rather than the longitudes recorded onA 3405. However, in about as many cases the opposite is true. The dates obtained fromthe pushes, however, often deviate considerably from those recorded on the text. Oncemore, sometimes it is possible to reduce the discrepancy by using the recomputed Sys-tem A 1 dates, rather than those preserved in the text, but sometimes this has the oppositeeffect. Another possible explanation for the discrepancies may be that the pushes werenot applied accurately, which is quite common among the preserved ACT material. For


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example, in ACT 301, the length of the pushes are assumed to be constant within eachsign. 13 The date SE 61, IX, 18 for is most likely a scribal error for SE 61, IX, 28.

Although the agreement between the preserved longitudes of Mercury on A 3405and those calculated by System A 1 is not perfect, they are clearly too close to resultfrom mere coincidences. The only other well known ACT scheme for Mercury, SystemA2 , only roughly ts the preserved data, with many serious discrepancies. This is onlyto be expected, of course, since the synodic arcs which result from applying SystemsA1 and A 2 differ by up to 10 in some parts of the zodiac. 14 Therefore, I conclude thatthe longitudes of Mercury were indeed computed by System A 1 . The discrepancies inlongitude may simply be due to scribal errors resulting from copying from a longerephemeris, which may itself have contained errors. However, the discrepancies betweenthe System A 1 dates and those preserved in our text are more serious, and are less like-ly to be the result of simple scribal errors. It is worth noting here, therefore, that forthe preserved System A 2 ephemerides the standard relation between synodic time andsynodic arc was not used. 15 Instead the difference between these two quantities varied,possibly depending upon the longitude. Perhaps some similar correction was applied tothe System A 1 dates in this text.

Finally, let me remark on the use of the term DIB omitted after the longitude onthree occasions. Because Mercurys orbit results in a variation of both longitude and lati-tude, certain phases of its visibility are occasionally missed. Ptolemy ( Almagest , XIII, 3)writes that around the beginning of Scorpio, Mercury does not appear as an evening-star,

and at the beginning of Taurus, it does not appear as a morning-star. He then correctlyexplains that this is caused by the highly negative latitude of the planet in these sectionsof the zodiac, and the fact that the ecliptic is only slightly inclined to the horizon. Evenat greatest elongation from the sun, then, the planet does not rise high enough above thehorizon to become visible. Although not explained in these terms, the fact that phases of Mercurys visibility do not occur when the planet is in certain sections of the zodiac wasknown to the Babylonians. Several examples are found in the Diaries where a date of rstappearance (and the subsequent last appearance) is followed by DIB, indicating that thephenomena did not occur. 16 The date and rough position of the phenomena must then

have been calculated, as was also the case when bad weather prevented observation.In the Almanacs also, some of the predicted phenomena are marked DIB, indicatingthat they were not expected to prove visible. 17 Obviously some criterion was applied tothe predicted dates or positions of Mercurys phases to determine whether they wouldbe omitted, but we do not yet know what that criterion was. In the ephemerides, somephases of Mercury are marked DIB. Again, we do not know the exact basis upon which

13 O. Neugebauer, ACT , 294295 and 318321.14 See gure 7 on p. 78 of O. Neugebauer, Babylonian Planetary Theory, Proceedings of the

American Philosophical Society , 98 (1954), 6089.15 O. Neugebauer, ACT , 298.16 Eg. Diary 283a, obv. 8: . . . GU 4-UD i na SU SU- s u DIB Mercurys last appearance in

the west, omitted.17 Eg. LBAT 1174, obv. 3: . . . GU 4-UD NIM UD.DA IGI DIB . . . Mercurys rst appearance

in the east, omitted.


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this was done, but Neugebauer estimates that within reasonably small errors, is omit-ted between Aries 10 and Taurus 20 (hence also omitted between Aries 24 andGemini 5 ), and is omitted between Libra 0 and Scorpio 5 (hence also omittedbetween Libra 18 and Scorpio 30 ).18 In A 3405, is said to be omitted on SE 60,VII, 9 at Scorpio 8 and on SE 69, V, 29 at Virgo 16 , and is omitted on SE 69, VI,23 at Libra 8 and, although it is not marked, also on SE 60, VII, 26 at Scorpio 22

since the preceding was omitted. This seems to suggest that the region of the zodiacin which Mercury does not appear as an evening-star was considered to be somewhatlonger than in the usual ephemerides. None of the preserved appearances of Mercury asa morning-star are marked with DIB, as is to be expected since they do not take place inAries or Taurus.

(ii) Venus

Our knowledge of ACT type schemes for Venus is hampered by the small num-ber of texts preserved: 9 ephemerides, 1 (at that time unidentied) template text, and 3procedure texts were published in ACT, 19 and a further 3 texts have been published sub-sequently. 20 At the heart of all of these Venus texts is the period relation that 5 synodicperiods are very close to 8 years. More precisely, after 5 synodic periods, the longitudeof a phenomenon decreases by 2;30 , and the date by 4;10 tithis . The equivalence of 8

years with 5 synodic periods is used in the Goal-Year texts, and was probably knownmuch earlier. It is implied in a unusual omen text from the time of the Assyrian kingAssurbanipal (7th century BC), 21 and is stated explicitly on BM 45728 which probablydates to before the 4th century BC, 22 BM 41004, probably from the 4th or 5th centuryBC, 23 and LBAT 1515, obv. 8. Furthermore, these last three texts also state that after 8years the Venus phenomena will recur 4 days earlier, and (in BM 41004 only) 4 back to the west.

The 8 year period of Venus is used directly in all of the ephemerides. Thus, if oneknows the date and longitude of one phenomenon, the date and location of the phenom-

enon 8 years hence can be determined simply by reducing the date by 4;10 tithis and thelongitude by 2;30 . This is just what is done in System A 0 , although in the preservedephemerides, 4;10 tithis is approximated by 4;5 days; in Systems A 1 and A 2 , however,the change in date is approximated by 4 days, and for System A 2 , the longitudes aredecreased by 2;40 rather than the expected 2;30 . In order to use this 8 year rule to

18 O. Neugebauer, HAMA, 404.19 ACT 400ff, 812, 815, 821b, and 1050.20 BM 36301, BM 37151, and BM 33552.21 H. Hunger, Kryptographische Astrologische Omina, in M. Dietrich and W. R ollig (eds.),

li san mithp urti: Festschrift Wolfram Freiherr von Soden (Butzon & Bercker, Kevelaer, 1969), 133145.

22 F. X. Kugler, Sternkundeund Sterndienst in Babel I (Aschendorffsche Verlagsbuchhandlung,Munster in Westfalen, 1907), 4548.

23 Text E in O. Neugebauer and A. Sachs, Some Atypical Astronomical Cuneiform Texts I, Journal of Cuneiform Studies 21 (1967), 183218.


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116 J.M. S teele

calculate all future events, however, one needs to know the dates and positions of theve phenomena within the rst 8 year period. Several systems are known to obtain thisinformation. The simplest, known as A 0 , just uses the mean synodic arc for the planet. InSystems A 1 and A 2 the synodic arcs and times are determined by the sign of the zodiacin which the preceding phenomena took place. Due to the small amount of preservedmaterial, the synodic arc used in Systems A 1 and A 2 are not known for all signs of the zodiac. Because these synodic arcs are not modied when they result in a crossingbetween zones, these systems are not true System A schemes. A true System A schemedoes exist, however. It was used in calculating the template text ACT 1050.

A 3405 contains only 7 Greek letter phenomena for Venus: 4 rst visibilities in thewest, 2 last visibilities in the east, and 1 rst visibility in the east. They are:

SE 60, IV, 4 Cancer 28[SE 60, ...] Aries 12SE 61, IX, 28 Sagittarius 25SE 61, XI, 29 Pisces 1SE 68, III, 30 [. . . ]SE 69, IX, 24 Sagittarius 12SE 69, XI, 15 Aquarius 28

First let me remark that apart from two obvious scribal errors (on SE 69, IX, 24, mustbe at Sagittarius 22, and must taken place on SE 69, XI, 25 not SE 69, XI, 15), all of the data are consistent with the 8 year rule where we can make the following pairs ( tand are given as an excess of integer months and signs):

SE 60, IV, 4: Can 28 SE 68, III, 30: [. . . ] t = 4 days, = ?SE 61, IX, 28: Sag 25 SE 69, IX, 24: Sag 22 t = 4 days, = 3

SE 61, XI, 29: Pis 1 SE 69, XI, 25: Aqu 28 t = 4 days, = 3

Because the longitudes are not given more precisely it is not possible to say whether = 3 reects a rounding of 2; 30 or some other close value.

The method by which the intermediate phases were calculated is not fully determinedby the preserved data. However, the following information may be drawn from the text( t and are given as an excess over integer years and complete revolutions of thezodiac):

SE 60, IV, 4: Can 28 SE 61, XI, 29: Pis 1 t = 235 tithis , = 213

SE 68, III, 30: [. . . ] SE 69, XI, 25: Aqu 28 t = 235 tithis , = ?

SE 60, IV, 4: Can 28 [SE 10, . . . ]: Ari 12 t = ?, = 254

[SE 61, . . . ]: Ari 12 SE 61, IX, 28: Sag 25 t = ?, = 253

[SE 61, . . . ]: Ari 12 SE 61, XI, 29: Pis 1 t = ?, = 319

SE 60, IV, 4: Can 28 SE 61, IX, 28: Sag 25 t = 174 tithis , = 147

SE 68, III, 30: [. . . ] SE 69, IX, 24: Sag 22 t = 174 tithis , = ?SE 61, IX, 28: Sag 25 SE 61, XI, 29: Pis 1 t = 61 tithis , = 66

SE 69, IX, 24: Sag 22 SE 69, XI, 25: Aqu 28 t = 61 tithis , = 66


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This allows us to narrow down the possible means by which the text was computed. Therst pair of data shows that for the synodic arc is about 213 and the synodic timeabout 235 tithis when Venus is near the end of Cancer. Thus, the data cannot have beencalculated using System A 0 , since then the synodic arc would be 215;30 and the synodictime 233;10, irrespective of the initial longitude. This is also the case for the second pairof data, as it should be since this pair is 8 years after the rst pair. The synodic arcsand times for in Cancer are not known for Systems A 1 or A2 . The System A schemeuncovered by Hamilton, 24 would also not quite give the required synodic arcs, and inany case it is not known how this scheme would be used to obtain synodic times.

It is known from procedure texts and elsewhere that several schemes existed forsubdividing the synodic period of Venus, sometimes into as many as 11 sections. Usingone of these schemes, it is possible to obtain longitudes and dates for all of the Greek Letter phenomena from an initial date-longitude pair. However, none of the currentlyattested schemes t the data on A 3405 very well. Sections 11 to 16 of the procedure textACT 812 states that and are separated by 331;30 when is in Aries, where our texthas 319 . Sections 17 to 24 of that same tablet state that the and are separated by 60tithis , where our text has 61 tithis .25 BM 33552 has and separated by 60 days (ratherthan tithis ), with a mean velocity of 1;15 /day. 26 BM 37151 also implies that the velocityis 1;15 /day, but this time lasting either 62 (?) days (or tithis ?) or 56 days (or tithis ?).27

In A 3405 and are separated by 61 tithis and 66 . Finally, BM 36301 implies thatto lasts 70 tithis with a velocity of 1;12 /tithi .28 None of these schemes dividing the

synodic arc agree perfectly with the material preserved on A 3405; however, it is quitepossible that other schemes were also known. Unfortunately, we are unable to deducemany details from the small amount of Venus data preserved on A 3405.

(iii) Mars

Two ACT systems are known for Mars: System A and System B. In System A, thephases , and are treated independently and calculated by the usual system A

rules. The two retrograde phases, and , however, are treated as satellites of . Fourschemes for calculating these retrograde arcs are currently known (called by Neugebauer

24 N. T. Hamilton and A. Aaboe, A Babylonian Venus Text Computed According to SystemA: ACT No. 1050, Archive for History of Exact Sciences 53 (1998), 215221. Note the errorin Table 1 of this article: last line of the table: w i for between Capricorn 18 and Cancer 12

should read 215;30 .25 O. Neugebauer, ACT , 336339.26 J. P. Britton and C. B. F. Walker, A 4th Century Babylonian Model for Venus: BM 33552,

Centaurus 34 (1991), 97118.27 A. Aaboe and P. J. Huber, A Text Concerning Subdivision of the Synodic Motion of Venus

from Babylon: BM 37151, in M. De Jong Ellis, Essays on the Ancient Near East in Memory of Jacob Joel Finkelstein (Archon Books, Hamden, Connecticut, 1977), 14.

28 Text C in O. Neugebauer and A. Sachs, Atypical Astronomical Cuneiform Texts I. Seealso the further discussion by J. P. Britton and C. B. F. Walker, A 4th Century Babylonian Modelfor Venus.


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R, S, T, and U), 29 but others may well have existed. System B is only attested on onesmall fragment, ACT 510. 30

The following data is preserved for Mars on A 3405:

SE 60, IV, 4 Leo 23SE 60, VIII, 11 Sco 7SE 61, X, 12 [. . . ] 25?

SE 62, V, 25 Lib 1SE 63, XI, 5 [. . . ]SE 67, XI, 22 [. . . ]SE 68, I, 1 [. . . ]SE 69, IV, 15 Can 7

SE 69, XII, 8 Sco 3SE 69, XII 2 , 27 Lib 27

Although this is not a great amount of information, it is possible to say at least that and are consistent with System A, as is shown below:

Mars

System A Longitude System A Date Text Longitude Text Date

Sco 7;30 SE 60, VIII, 11 Sco 7 SE 60, VIII, 11Cap 11;15 SE 62, X, 8;22,52Ari 0;56,15 SE 64, XII 2 , 21;41,59Tau 25;37,30 SE 67, II, 10;1,6Can 7;5 SE 69, IV, 15;6,28 Can 7 SE 69, IV, 15

Mars


Leo 23;40 SE 60, IV, 24 Leo 23 SE 60, IV, 24Lib 1;20 SE 62, V, 25;27,52 Lib 1 SE 62, V, 25Sco 17 SE 64, VIII, 4;45,44Cap 25;30 SE 66, X, 6;53,36Ari 11;37,20 SE 69, I, 16;38,58

The retrograde phases are determined from the date and location of . To check whether they are consistent with System A, therefore, it is necessary to rst recomputea run of s over the period of the text, as I have done below:

29 See O. Neugebauer, ACT , 305306 and A. Aaboe, A Late-Babylonian Procedure Text forMars, and Some Remarks on Retrograde Arcs, in D. A. King and G. Saliba (eds.), From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E. S. Kennedy (The New York Academy of Sciences, New York, 1987), 114.

30 This was recognised by Peter Huber. See A. Aaboe, On Babylonian Planetary Theories,Centaurus 5 (1958), 209277, esp. 246.


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Mars


Gem 9;45 SE 61, VII, 10;45,32Can 16;30 SE 63, VIII, 11;8,24Leo 16;30 SE 65, IX, 4;46,16Vir 22 SE 67, X, 3;52,8Sco 3 SE 69, XII, 8;30 Sco 3 SE 69, XII, 8

It is now possible to extract the lengths of the retrograde arcs from of the preserved and :

SE 61, VII, 10: Gem 9 SE 61, X, 12: [Tau] 25 ? t = 92 tithis , = 14 ?

SE 63, VIII, 11: Can 16 SE 63, XI, 5: [. . . ] t = 84 tithis , = ?SE 67, X, 3: Vir 22 SE 67, XI, 22: [. . . ] t = 49 tithis , = ?SE 67, X, 3: Vir 22 SE 68, I, 1: [. . . ] t = 88 tithis , = ?SE 69, XII, 8: Sco 3 SE 69, XII 2 , 27: Lib 27 t = 49 tithis , = 6

In all of the known retrogradation schemes, the length of the retrograde arc is dependentupon the longitude of . For to , it may vary between 6 and 7;30 . It is only possi-ble to extract one retrograde arc for to from A 3405: when is 8 in Scorpius,then

is 6 behind . The 4 currently attested retrogradation schemes give this arc as 6;24 (R and S), 6;30 (T) and 6;43,30 (U). Since the 6 implied in A 3405 is the result of rounded longitudes, we can only say that it is consistent with all of the currently knownretrogradation schemes. According to ACT 500 the length of time between and is47;55,4 tithis . The two preserved timed intervals in A 3405 are 49 tithis , which may sim-ply be a consequence of the rounding of the day numbers. The retrograde arc betweenand is also preserved once on A 3405: when is 9 in Gemini, then is 14 behind

. From known retrogradation schemes, we would expect about 17 ; however, the lon-gitude of is damaged and so we should not read too much into this. The length of theinterval between and is not known for the retrogradation schemes. Since the retro-grade arc = 5/ 2( ) , Neugebauer postulated that the corresponding timeintervals may follow the same rule. 31 This would mean that the two stationary pointsare separated by 119;47,40 tithis . However, as he later noted, this amount considerablyexceeds the true time interval. 32 In A 3405 this time interval appears to be dependentupon the longitude of , but is about 90 tithis , which is not too far wrong.

For the parts of direct motion, it is known that there existed for Mars at least twomethods for subdividing the synodic arc (and presumably also the synodic time).These are based upon the concept of steps, dened as i = wi /Z .33 From theprocedure text ACT 811a we know that when we are dealing only with mean mo-

31 O. Neugebauer, ACT , 306.32 O. Neugebauer, HAMA, 459460.33 O. Neugebauer, HAMA, 420421, which is based upon A. Aaboe, Period Relations, who

designated these steps I rather than .


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tion, = 33, = 60, and = 58. This text does notdiscuss the case of true motion as System A attempts to model but from some date-less lists of longitudes of the phenomena of Mars, Aaboe-Sachs extracted the rule that

= 33i , = 63i , and = 55i .34 Unfortunately, no standardephemerides for Mars that give (in different columns) longitudes for the consecutivephases are known at this time and so it is impossible to tell whether this method of dividing the synodic arc was used rigorously in practice. On A 3405, the difference inlongitude between on SE 60, IV, 4 and on SE 60, VIII, 11 is 74 , and 33 i = 73 ,which is nearly the same. However, the difference in longitude between on SE 69,IV, 15 and on SE 69, XII, 8 is 116 , whereas 66 i = 127 . Unless other texts come tolight, however, it is impossible to say whether this is evidence for a variant scheme forsubdividing the synodic arc, or just a discrepancy in this text.

(iv) Jupiter

Jupiter is better represented among the preserved ACT material than any otherplanet. We know of two main System A type schemes (plus variants), and twoSystem B schemes. A further scheme of the System A type has been identied in a Greek source, 35 and may also be of Babylonian origin.

The following Jupiter data is preserved on A 3405:

SE 60, III, 25 Can 26SE 60, IV, 24 Can 30SE 60, VIII, 29 Leo 17SE 60, X, 27 Leo 13SE 60, XII, 27 Leo 8SE 61, X, 10 Vir 10 + xSE 61, XII, 7 Vir 11SE 62, I, 10 Vir 7SE 62, V, 17 Vir 22SE 67, XI, 9 [. . . ]SE 67, XII, 8 [. . . ]SE 68, IV, 17 [. . . ] 10 + xSE 68, VI, 14 [. . . ] 6SE 69, VI, 5 Tau 6SE 69, VIII, 2 Tau 12SE 69, X, 3 Tau 6SE 70 [ . . . ] Gem 15SE 70 [ . . . x] + 10 Gem 10

34 A. Aaboe and A. Sachs, Some Dateless Computed Lists of Longitudes of CharacteristicPlanetary Phenomena from the Late-Babylonian Period, Journal of Cuneiform Studies 20 (1966),133. See also O. Neugebauer, HAMA, 424425.

35 J. P. Britton and A. Jones, A New Babylonian Planetary Model in a Greek Source, Archive for History of Exact Sciences 54 (2000), 349373.


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Unfortunately not enough and data are preserved to make an attempt at recal-culating by System B worthwhile. Nevertheless, it is clear that the , and dataare in very good agreement with the reconstructed System B data. There are occasionaldiscrepancies, but these are very small, except for an obvious scribal error (SE 69, VI,5 at Taurus 16 not Taurus 6). Indeed it may be possible to eliminate some of theseby further rening the chosen initial values of the longitude, date and zigzag function.Since all the data are rounded to integer degrees and days, however, there is probablylittle to be gained by attempting this. Furthermore, the rounded data also prevent us fromchoosing between System B and System B (whose parameters vary only slightly) as themethod of computation.

(v) Saturn

We know of two main schemes for Saturn. System A, which is attested on two pro-cedure texts and three template texts (although with variations), 36 and System B whichis known from several ephemerides and procedure texts.

The following Saturn data is found on A 3405:

SE 60, IV, 12 Sco 26

SE 60, VIII, 9 Sag 5SE 60, IX, 11 Sag 7SE 61, [ . . . ] Sag 15SE 61, X, 4 Sag 19 ?

SE 62, I, 3 Sag 26SE 62, II, 28 Sag 23SE 62, IV, 29 Sag 19SE 63, X, 21 [. . . ]SE 67, X, 26 [. . . ]SE 67, XI, 28 [. . . ]

SE 68, III, 28 [. . . ]SE 68, V, 22 [. . . ]SE 69, IV, 23 Pis 24SE 69, VI, 17 Pis 20SE 69, VIII, 17 Pis 15SE 69, XII, 16 Pis 28SE 69, XII 2 , 17 Pis 29SE 70, [ . . . ] Ari 9

Recalculating by System B we nd excellent agreement with this data. For , webegin with 11;42 increasing and 23;9 tithis increasing for the longitude and date zigzagfunctions respectively. For , 11;42 and 23;45 tithis , both increasing; for , 11;30

36 A. Aaboe and A. Sachs, Dateless Computed Lists.


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and 23;9 tithis , both increasing; for , 11;18 and 23;7 tithis , both increasing; for ,11;30 and 23;21 tithis , both increasing.

Saturn

System B Longitude System B Date Text Longitude Text Date

Sag 7;20 SE 60, IX, 11;50 Sag 7 SE 60, IX, 11Sag 19;12 SE 61, X, 4;59 Sag 19 SE 61, X, 4Cap 0;56 SE 62, IX, 28;20Cap 13;2 SE 63, X, 22;51 [ . . . ] SE 63, X, 21Cap 25;20 SE 64, XI, 15;38

Aqu 7;50 SE 65, XI, 9;35Aqu 20;32 SE 66, XII, 3;54Pis 3;26 SE 67, XI, 28;15 [ . . . ] SE 67, XI, 28Pis 16;32 SE 68, XII, 22;38Pis 29;50 SE 69, XII 2 , 17;23 Pis 29 SE 69, XII 2 , 17

Saturn


Sag 15 SE 61, I, 9;27 Sag 15 [ . . . ]Sag 26;36 SE 62, I, 3 Sag 26 SE 62, I, 3Cap 8;36 SE 63, I, 26;45Cap 20;42 SE 64, II, 20;42Aqu 3 SE 65, II, 24;9Aqu 15;30 SE 66, III, 9;12Aqu 28;12 SE 67, IV, 3;45Pis 11;6 SE 68, III, 28;30 [ . . . ] SE 68, III, 28Pis 24;12 SE 69, IV, 23;27 Pis 24 SE 69, IV, 23Ari 7;30 SE 70, IV, 18;36

Saturn


Sco 29;48 SE 60, II, 11;30Sag 11;18 SE 61, III, 4;39Sag 23 SE 62, II, 28 Sag 23 SE 62, II, 28Cap 4;54 SE 63, III, 21;33

Cap 17 SE 64, IV, 15;18Cap 28;18 SE 65, IV, 9;15Aqu 11;48 SE 66, V, 3;24Aqu 24;30 SE 67, V, 27;45Pis 7;24 SE 68, V, 22;18 [ . . . ] SE 68, V, 22Pis 20;30 SE 69, VI, 17;3 Pis 20 SE 69, VI, 17Ari 3;48 SE 70, VI, 12


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124 J.M. S teele

Saturn


Sco 26;30 SE 60, IV, 12;40 Sco 26 SE 60, IV, 12Sag 7;48 SE 61, V, 5;47Sag 19;18 SE 62, IV, 29;6 Sag 19 SE 62, IV, 29Cap 1 SE 63, V, 22;37Cap 12;54 SE 64, VI, 16;20Cap 25 SE 65, VI, 10;15Aqu 7;18 SE 66, VII, 4;22Aqu 19;48 SE 67, VI, 28;41Pis 2;30 SE 68, VII, 23;12

Pis 15;24 SE 69, VIII, 17;33 Pis 15 SE 69, VIII, 17Pis 28;30 SE 70, VIII, 12;30

Saturn


Sag 5 SE 60, VIII, 9 Sag 5 SE 60, VIII, 9

Sag 16;30 SE 61, IX, 2;21Sag 28;12 SE 62, VIII, 27;48Cap 10;6 SE 63, IX, 19;39Cap 22;12 SE 64, X, 13;36Aqu 4;30 SE 65, X, 7;45Aqu 17 SE 66, XI, 2;6Aqu 29;42 SE 67, X, 26;39 [ . . . ] SE 67, X, 26Pis 22;36 SE 68, XI, 21;24Pis 25;42 SE 69, XII, 16;21 Pis 28 SE 69, XII, 16Ari 9 SE 70, XII, 11;30 Ari 9 [ . . . ]

There are two instances where the text does not agree with this recomputation. Thedate of rst appearance ( ) in SE 63 is given as day 21 of Month X, whereas our re-computed date is day 22. It may be possible to change the recomputed dates slightly inorder to correct this, but I see little to be gained by such an attempt. The day number inthe text may simply be a scribal error. Saturns last appearance ( ) in SE 69 is said tobe at 28 in Pisces, but this is most likely a scribal error for 25 .

(vi) Lunar eclipses

Information is preserved in A 3405 about 7 lunar eclipse possibilities. In addition tothe date of the eclipse, the moons longitude is given to the nearest degree, the time of the eclipse relative to sunrise or sunset, and a number followed by H p AB and either LALor SIG, which I will call . The preserved data is summarised below:


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Date Time Longitude

SE 60, IX, 14 20 before sunset Gem 26 11,40 H p AB LALSE 61, IX, 13 [ . . . ] [. . . ] 22,[x]0 Hp AB LALSE 62, II, 15 1 after sunset Sag 11 30,20 H p AB SIGSE 68, IV, 14 50 [. . . ] [. . . ] 10,20 ? [. . . ]SE 69, IV, [ . . . ] 3 ? after sunrise Cap 21 6,10 H p AB LALSE 69, X, 13 24 after sunrise Can 16 35,10 H p AB SIGSE 70, [VIII, . . . ] 5 ? [. . . ] [. . . ] [x],20 Hp AB SIG

Two systems for calculating longitudes of syzygies (and much more besides) areknown from the ACT material. 37 In one, the longitude is calculated by means of a twozone step function; in the other a zigzag function is used. Thus these two systems aresimilar to Systems A and B of the planetary theory, and indeed it is customary callthem by these names. Although System A is found predominantly on texts from Bab-ylon, at least two (probably three) ephemerides calculated using this system are fromUruk. 38 Conversely, System B is found fairly evenly at both sites, although most of theolder texts are from Uruk.

The longitude function of a System A full moon ephemeris, known as column B, iscalculated by a step function with two zones: a fast arc stretching from 13 in Pisces to27 in Virgo with a characteristic velocity w1 = 30 per month, and a slow arc from27 in Virgo to 13 in Pisces with a characteristic velocity w2 = 28;7,30 per month.System A has such a tight theoretical structure that, with only very occasional minorvariations, all of the ephererides are connectable. It is possible, therefore, to recomputea complete System A lunar ephemeris over any period. Below I compare the results of these recomputed System A longitudes with the longitudes on A 3405:

Date System A Longitude Text Longitude

SE 60, IX, 14 Gem 24;52 Gem 26SE 62, II, 15 Sag 9 Sag 11SE 69, IV, [ . . . ] Cap 18;52,30 Cap 21SE 69, X, 13 Can 15;16 Can 16

The poor agreement between System A and A 3405 indicates immediately that the

eclipses were not calculated by means of this System.

37 For a detailed discussion of the ACT lunar schemes, see O. Neugebauer, ACT , 4185, andidem, HAMA , 474540.

38 ACT 1 (probably), ACT 2, and W 22340a. This last text is published as number 99 inH. Hunger, Spa tbabylonische Texte aus Uruk Teil I (Gebr. Mann Verlag, Berlin, 1976).


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126 J.M. S teele

In the other ACT lunar theory, System B, the longitudes of syzygies are calculatedusing a zigzag function with a maximum value for the solar velocity of 30;1,59 permonth, a minimum of 28;10,39,40 per month, and a monthly difference of 0;18. Theperiod of this zigzag function, 12;22,8,53,20, gives the number of lunar months afterwhich there is a precise return of solar velocity (in other words, the number of meansynodic months in an anomalistic year). Unlike System A, System B ephemerides arenot necessarily connectable, and so we cannot reconstruct a System B lunar ephemerisfor an arbitrary date. As only 4 longitudes are preserved on A 3405, it is not possible toperform a rigorous test of whether they were computed by System B. However, we canat least say that they could have been. For example, computing according to the SystemB rules beginning with a velocity of 30 per month on the descending branch we get:

Date System B Longitude Text Longitude

SE 60, IX, 14 Gem 26;1 Gem 26SE 62, II, 15 Sag 11;0,9,20 Sag 11SE 69, IV, [ . . . ] Cap 21;26,36,40 Cap 21SE 69, X, 13 Can 16;45,33,40 Can 16

Outside of the ACT corpus, we know of a handful of texts dealing with eclipse pos-

sibilities which use a more primitive longitude scheme. 39 These assume that after 12months, the longitude of the syzygy increases by 1 rotation less 10;30 , and after 11months the longitude increases by 1 rotation less 10;30 and 1 sign. Since there are 33six month intervals and 5 ve month intervals between eclipse possibilities in one Sarosof 223 months, this implies a solar progress in one Saros of 18 rotations + 10;30 , inturn implying a year length which is very nearly correct. 40 Adding on another 12 monthswe obtain 235 months = 19 complete rotations, which is simply the Metonic cycle, andmay well have been the basis for these schemes. 41 Dividing the progress in longitudeover 12 months by two to yield the progress in six months gives 174;45 . In the texts,

however, the six month progress in longitude alternates between two values with thisas the mean. In all probability this was done simply to avoid fractions of 0;45. Attestedpairs are 175 and 174;30 , 176 and 173;30 , and 175;30 and 174 . In each case thehigher value is for the progress in longitude from ascending to descending node, thelower from descending to ascending node.

39 BM 36599+36941 with duplicates BM 36737 and BM 47912 published a Texts B, C andD in A. Aaboe and A. Sachs, Two Lunar Texts of the Achaemenid Period from Babylon, Cen-taurus 14 (1969), 122. BM 36737 was joined to BM 36580 and republished as Text S in J. P.Britton, An Early Function for Eclipse Magnitudes in Babylonian Astronomy, Centaurus 32(1989), 152, and in A. Aaboe, J. P. Britton, J. A. Henderson, O. Neugebauer, and A. J. Sachs,Saros Cycle Dates and Related Babylonian Astronomical Texts (American Philosophical Society,Philadelphia, 1991). BM 36651+36719+37032+37053 (reverse known as Text L) and BM 36400were published as Texts E and F in this latter work.

40 A. Aaboe and A. Sachs, Two Lunar Texts of the Achaemenid Period, 18.41 J. P. Britton, An Early Function for Eclipse Magnitudes, 33.


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We can see straight away that a longitude scheme of this kind could not have beenused to give the longitudes of the eclipse possibilities in A 3405. Between SE 62, II, 15and SE 69, X, 13 there are 6 twelve month intervals and 2 eleven month intervals. Inthese schemes, this corresponds to a decrease in longitude over full rotations of 144 .However, in the text we have a decrease of 145 .

The situation regarding the times of the eclipses is particularly unclear. In both Sys-tem A and System B ephemerides, the time of syzygy is given in a column known as M.In System A these are recorded with respect to sunset, which would seem to precludeSystem A as the source of the timings given in A 3405. However, in System B theyare quoted relative to the nearer of sunrise or sunset, as we have in this text. In thenon-mathematical astronomical texts such as the Diaries, predicted eclipse times relatenot to the moment of syzygy but instead to the moment that the eclipse was expectedto begin. These were calculated either by applying the Saros period to earlier eclipserecords, or by estimating the time from observations of the lunar six. 42 It is worth notingthat the times of the eclipses given in A 3405 agree better with modern computations of the time these eclipses began than the time of syzygy. However, we should not draw toomuch from this since only 4 timings are fully preserved.

The numbers I have called must relate to either the magnitude of the eclipse orthe latitude of the moon at that time. Below I compare with modern computationsof the magnitudes and latitudes. ( and indicate ascending and descending latituderespectively.)

Date Computed Magnitude Computed Latitude

SE 60, IX, 14 11,40 Hp AB LAL 1.03 0.8 SE 61, IX, 13 22,[x]0 Hp AB LAL 1.46 0.1 SE 62, II, 15 30,20 Hp AB SIG 0.51 1.3 SE 68, IV, 14 10,20 [ . . . ] 1.32 0.9 SE 69, IV, [ . . . ] 6,10 Hp AB LAL 1.12 0.3 SE 69, X, 13 35,10 Hp AB SIG Penumbral 1.6 SE 70, [VIII, . . . ] [x],20 Hp AB SIG Penumbral 1.0

It is my belief that represents the magnitude of the eclipse. In the ACT material,magnitudes of eclipses are given in and related columns ( and ). Taking themaximum magnitude of an eclipse as c, as one would expect magnitudes increase from0 to c. However, because of the way column is dened, magnitudes then decrease

again from c to 2c .43 This is because it is useful to make a continuous function that

42 SeeJ. M. Steele, Eclipse Prediction in Mesopotamia, Archive for History of Exact Sciences54 (2000), 421454.

43 For details, see O. Neugebauer, Studies in Ancient Astronomy VII: Magnitudes of LunarEclipses in Babylonian Mathematical Astronomy, Isis 36 (1945), 1015 and A. Aaboe and J. A.


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128 J.M. S teele

can be calculated not only when an eclipse is possible, but for all syzygies. When isgreater than 2 c it simply acts as a mathematical function without any direct astronomicalsignificance. 44 In System A, is determined from column E which characterises thelatitude of the moon. It has the units SI ngers, and the maximum magnitude c =17;24 ngers. In System B, is calculated directly and is measured either in ngers orin terms of the greatest possible eclipse magnitude. Thus c = 18 ngers or 1 maximumeclipse.

Assuming that is measured in ngers (and so 11,40 should be read 11;40, etc.),then we see that those values close to 18 indeed correspond to the largest eclipses. Thegreatest value of is 35;10, which is just larger than 2 c (34;48) in System A, and justsmaller than 2 c (36) in System B, and again as we would expect this is a very smalleclipse (in fact penumbral). In the observational texts, a total lunar eclipse is denedto have a magnitude of 12 ngers. In System B, therefore, the maximum magnitude of an eclipse is taken to be 3/2 that of a total eclipse. Thus values between 12 and 24ngers should correspond to total eclipses. All of the values in this range do indeedcorrespond to total eclipses. In addition, the eclipse on SE 60, IX, 14 has a value of 11;40, i.e., just less than totality. Modern computations give this eclipse a magnitudeof 1.03 (i.e., just total), so the Babylonian calculations are not far wrong. However, theeclipse in SE 69, IV has a of 6;10 and modern computation gives this eclipse as totalalso with a magnitude of 1.12. Perhaps 6;10 is a scribal error for 16;10 (mistakes of 10are common in this text).

In support of my interpretation of as the eclipse magnitude is the fact that it isfollowed by the term H p AB. This term, sometimes written in other texts in the fuller formHp AB- rat , seems to mean disc in the broad sense of the moons disc, or sometimes themore technical eclipse magnitude. 45 Hp AB is even used to refer to column in someof the ACT ephemerides.

Comparison of the computed latitudes with immediately suggests that we interpretthe logograms LAL and SIG as increasing and descending latitude respectively. A betterway of expressing this would be to say that LAL indicates that the eclipse takes placenear the ascending node, and SIG near the descending node. Similar usage is attested,

eg, in ACT 135 which is also from Uruk.46

To summarise, I suspect that the lunar longitudes were taken from a System Bephemeris or eclipse text such as ACT 135, and that the function is closely related tothe System B function or one of its family. However, with the small amount of datapreserved, this can be no more than a working hypothesis.

Henderson, The Babylonian Theory of Lunar Latitude and Eclipses According to System A, Archives Internationales dHistoire des Sciences 25 (1975), 181222.

44 Neugebauer reserved for the function when it was calculated only for eclipse possibilities,and used and for those functions calculated for all syzygies. For simplicity, I call all thesefunctions since the difference between and or is irrelevant for the present discussion.

45 O. Neugebauer, ACT , 197198. See also A. Livingstone, Mystical and Mythological Ex- planatory Works of Assyrian and Babylonian Scholars (Clarendon Press, Oxford, 1986), 90.

46 O. Neugebauer, ACT , 162.


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(vii) Summary

I have shown above that the astronomical data on A 3405 is on the whole consistentwith having been calculated by means of ACT schemes. But does this imply that it doesindeed come from these ACT schemes? In my opinion, the answer to this question isyes. Comparison of the dates of the planetary phenomena on A 3405 with the dates of the observations in the Diaries showed considerable discrepancies which prove that theA 3405 data cannot have been observed.

The dates of planetary phenomena calculated by the ACT schemes may vary con-siderably from the true dates of the phenomena. 47 Nevertheless, the dates in A 3405 are,with the exception of those for Mercury, in very close agreement with dates given by theACT schemes. Similarly, ACT longitudes can vary by a considerable amount from the

true longitudes of the phenomena. Taking the rst visibility in the east ( ) of Mercuryas an example, the synodic arc around Capricorn in System A 1 is about 10 greater thanthat given by modern computations, and about 10 less around Taurus. 48 Nevertheless,the longitudes of in A 3405 are in exact agreement with the System A 1 values in thispart of the zodiac. Thus the longitudes for the Mercury data almost exactly t an ACTscheme that does not itself always agree well with the actual astronomical situation.Although not so extreme, similar arguments could be made for the other planets.

Probably the most convincing argument, however, is not that any individual planetalmost exactly ts an ACT scheme, but rather that they all t so well. For example,

with the moon we only have four longitudes. If this information was all that had beenpreserved on the text, it could rightly be argued that, although these longitudes can betted into a lunar System B scheme, this is nothing more than coincidence. However,the fact that they are preserved on a tablet where all of the other data is consistent withACT methods allows us to say that this lunar data is highly likely to also come from anACT scheme. The internal self-consistency of the tablet if it is assumed to have beencalculated by ACT methods is striking.

Context

At the end of column VIII, 10 lines of a colophon are partially preserved:

12[x] x13[ t . u] p-pi

Id1-EN- s u-nu A s a14 INi -din -tu 4-d 1luGALA d115 ma -r u Idsin -TI- IR UNUG ki -u16 qat Id 1-AD-GUR DUMU.A- s u17 luUMBISAG DI S-UD- d 1-d EN-L IL-L A

18 UNUG ki itu GAN -14-KAM19 [MU-1]- me -21 IAn -t i -i -i -ku -su LUGAL

47 See, e.g., gures 2.2ff in N. M. Swerdlow, Babylonian Theory of the Planets , which compareobserved and theoretical synodic times with those from the ACT schemes.

48 A. Aaboe, On Babylonian Planetary Theories.


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130 J.M. S teele

20 [ . . . ] UDU-IDIM me s

21 [ . . . ] 30

12 [ . . . ]13 [Tab]let of Anu-b elsunu, son of 14 Nidinti-Ani, lamentation priest of Anu,15 descendant of Sin-leq e-unninn , the Urukean.16 Hand of Anu-aba-ut er, his son,17 t .up sar En uma Anu Enlil .18 Uruk, Month IX, the 14th,19 [year 1]21, king Antiochus.20 [ . . . ] planets

21 [ . . . ] moon ? .

The owner and scribe, Anu-b elsunu and his son Anu-aba-ut er, are both well knownfrom astronomical texts found at Uruk (see Table 2), as well as other texts including anillustrated astrological text which links zodiacal signs with the names of cities, temples,planets, trees and stones, 49 a ritual text, 50 the mathematical text TU 33, and variousadministrative documents. 51

The date that A 3405 was written ts in well with the dates of the texts mentionedabove. Most of the ACT texts from Uruk may be dated to between about SE 90 andSE 150. Although the site from which these tablets were recovered is unknown, theGerman excavations of 1912/13 were made in the vicinity of the R es sanctuary, 52 andmany of the tablets were probably found at this time. The colophons of a number of theastronomical texts indicate that the astronomers had some connection with the temple, 53

and this led Neugebauer to suggest that the chronology of the Uruk ACT texts may havebeen related to the history of the R es sanctuary. He argues that this astronomical activitymay have ceased around SE 173 with the destruction of the R es sanctuary, shortly afterthe occupation of Babylonia by theParthians. However, a text published in 1984 indicates

49 E. Weidner, Gestirn-Darstellungen auf babylonischen Tontafeln (Hermann B ohlaus Nachf.,Graz, 1967), text 2.

50 W. R. Mayer, Seleukidische Rituale aus Warka mit Emesal-Gebeten, Orientalia 47 (1978),431458.

51 See H. Hunger, Babylonische und assyrische Kolophone (Verlag Butzon & Bercker Kevel-aer, Neukirchen-Vluyn, 1968), D. B. Weisberg, The Late Babylonian Texts of the Oriental InstituteCollection (Undena Publications, Malibu, 1991), 3637, and the tablets cited in G. J. P. McEwan,Priest and Temple in Hellenistic Babylonia (Franz Steiner Verlag, Wiesbaden, 1981), 12, and P.-A.Beaulieu and F. Rochberg, The Horoscope of Anu-B elsunu, Journal of Cuneiform Studies 48(1996), 8994, esp. 9394 and n. 1821.

52 O. Neugebauer, ACT , 10.53 See F. Rochberg, The Cultural Locus of Astronomy in Late Babylonia, in H. D. Galter

(ed.), Die Rolle der Astronomie in den Kulturen Mesopotamiens (Graz, 1993), 3145 and idem ,Scribes and Scholars: the t .up sar En uma Anu Enlil , in J. Marzahn and H. Neumann (eds.), As-syriologica et Semitica: Festschrift f u r Joachim Oelsner anl a lich seines 65. Geburtstages am 18.Februar 1997 (Kevelaer, Butzon & Berker, 1999).


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Table 2. Astronomical texts owned or written by Anu-b elsunu and Anu-aba-ut er

Text Owner Scribe Date Written Contents

ACT 102 Anu-b elsunu SE 121, XII, 12 System B lunarephemeris forSE 121

ACT 135 Anu-b elsunu [Anu-aba-ut er] SE 12[1], I System B eclipse textfor SE 113130

ACT 163 Sama s-et.ir Anu-aba-ut er System B auxiliarylunar text for SE117

ACT 165 Anu-aba-ut er System B auxiliary

lunar text for SE137156ACT 171 Anu-aba-ut er System B auxiliary

lunar text for SE115124

ACT 194 Anu-aba-ut er Ana-bal atsu-iqb SE 13[0], VI, 28 Daily lunar positionsfor SE 130

ACT 400 Anu-b elsunu Anu-aba-ut er Venus System A 0 forSE 111135

ACT 501 Anu-aba-ut er Anu-uballit . SE 124, IX, 4 Mars System A for SE

123202ACT 600 Sama s-et.ir Anu-aba-ut er SE 118, VII, 12 Jupiter System A for113173

ACT 640 Anu-b elsunu Anu-aba-ut er SE 119 Jupiter System Bfor 131161. Alsoprocedure text ACT820 for Jupiter

ACT 802 Anu-aba-ut er Procedure text for (atleast) Saturn

NCBT 1232 Horoscope of Anu-

bel- sunu placing hisdate of birth as SE63, X, 2

that the R es sanctuary was still functioning in at least SE 203. 54 Furthermore, a textcontaining a summary of astronomical observations for the years SE 212 to 214 almostcertainly also comes from Uruk, 55 and indicates that astronomical activity did not cease

54 W 18568, published by K. Kessler, Eine arsakidenzeitiche Urkunde aus Warka, Bagh-dader Mitteilungen 15 (1984), 273281. See also S. Sherwin-White, Seleucid Babylonia: A CaseStudy for the Installation and Development of Greek Rule, in A. Kuhrt and S. Sherwin-White, Hellenism in the East (University of California Press, Berkeley, 1987) 131.

55 BM 140677, published by A. J. Sachs and H. Hunger, Astronomical Diaries and Related Texts from Babylonia Volume III (Osterreichische Akademie der Wissenschaften, Wien, 1996),406ff.


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in the city after the Parthian conquest. It seems more likely that the concentration of astronomical material in the rst half of the second century of the Seleucid Era is relatedpurely to the excavations; perhaps they come from a small number of private or templearchives. 56

Although the date when A 3405 was written is similar to that of the other ACT texts,its contents are significantly earlier, covering the years SE 60 to 70. Among the generalACT corpus, the texts are usually contemporary with their contents, or else contain cal-culations for the near future. Why, therefore, does this tablet contain calculations forthis earlier period? Furthermore, why does it contain material for all of the planets andfor lunar eclipses arranged chronologically? Collections such as this are not attested inany other ACT texts.

I think we can discount the possibility that this computed material was gatheredtogether so that it might be compared with the observational record to test the reliabilityof the astronomical models. The owner and scribe of A 3405 knew of many more ACTplanetary schemes than were used in compiling this text, so why should these particularones have been chosen for comparison? In any case, it would seem much more sensibleto collect together data for a particular planet calculated by all the known schemes, andthen compare these with observations. Furthermore, I would question the idea that thereexisted such a simple relationship between observation and theory in Babylonianastronomy that theory would be tested in this way. 57

A more tempting answer to this question is to see A 3405 as a collection of astronom-

ical material used in making horoscopes. Only 28 horoscopes are known to us today. 58Most are from Babylon, but ve are from Uruk (one of these is a duplicate, another con-tains two horoscopes). Although all of these horoscopes have certain features in common(in particular they all contain positions of the sun, moon and planets in the zodiac), 59

it seems to me valid to divide them into two subsets based upon their provenance sincethere are noticeable differences between the texts from these two sites. In particular,none of the Uruk horoscopes includes references to eclipses, solstices or equinoxes orthe lunar three, data which is frequently recorded in the examples from Babylon, but dosometimes contain a statement about the moons latitude which is never found in the

horoscopes from Babylon. Furthermore, the Uruk horoscopes have a tendency to givelongitudes with degrees (5 out of 5 texts) whereas this is rare in the texts from Babylon(3 out of 22, all of which are comparatively late in date). Not all of the Uruk horoscopesgive degrees of longitude for all of the heavenly bodies, however. Texts 5 and 9 record

56 Private archives containing among other things astronomical texts did exist at Uruk. See,for example, the tablets from the library of Iq sa collected in E. von Weiher, Spa tbabylonischeTexte aus Uruk Teil II (Gebr. Mann Verlag, Berlin, 1983). On archives from Late Babylonian Uruk generally, see O. Peders en, Archives and Libraries in the Ancient Near East 1500300 B.C. (CDLPress, Bethesda, Maryland, 1998), 202213.

57 The only detailed discussion of the relationship between observation and theory in Babylo-nian astronomy is F. Rochberg-Halton, Between Observation and Theory in Babylonian Astro-nomical Texts, Journal of Near Eastern Studies 50 (1991), 107120.

58 Horoscopes are cited by their text number in F. Rochberg, Babylonian Horoscopes (Ameri-can Philosophical Society, Philadelphia, 1998).

59 Or, occasionally, non-zodiacal constellations.


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them only for the sun and moon; text 10 and 11 (duplicate) for the Sun and the visibleplanets (Mercury was said to be too close to the sun to be visible on that date); andthe two horoscopes on text 16 give degrees of longitude for the ve planets and, forhoroscope b only, the moon.

What was the source of the degrees of longitudes in the horoscopes? Sachs, basinghis comments on only the 6 horoscopes that were identied at the time, suggested thatthey come from the mathematical ephemerides. 60 Working from the complete corpus of currently known horoscopes, however, Rochberg has given a more cautious statement:we lack the evidence to conclude in any positive way that ACT tables or methods wereused by the scribes who prepared horoscopes. 61 The argument against identifying theACT texts as the source of the degrees of longitudes is that ACT planetary and lunartheory has as its primary goal the calculation of the dates and longitudes, etc., of partic-ular phenomena (the Greek Letter phenomena for the planets, syzygies for the moon)rather than longitudes at arbitrary times. This latter goal was apparently only treated asa secondary problem by the Babylonian astronomers, although their methods for its so-lution were mathematically highly astute. The very fact that such interpolation methodswere developed, however, means that they could have been used in making horoscopes,if the astronomers so desired.

Since the longitudes are only given to the degree, or occasionally half degree, in thehoroscopes, they could also have been calculated simply by a straightforward, probablylinear, interpolation between the longitudes of Greek Letter phenomena in an ephemeris.

In this respect, a text such as A 3405 which brings together all the planetary data wouldhave been extremely useful, and this could explain why the longitudes in A 3405 arerounded to the nearest degree. Lunar eclipses are not recorded in the preserved Uruk horoscopes, but a statement concerning the latitude of the moon often is, and this isgiven for each lunar eclipse possibility in A 3405. However, A 3405 does not providesolar and lunar longitudes, except on the date of a lunar eclipse possibility.

We must also consider whether any plausible sources exist apart from the ACTschemes for calculating degrees of planetary longitudes. Rochberg has argued that mostof the contents of the Babylonian horoscopes could have been taken from the Alma-

nacs.62

For the planets, these texts contain, for each month, the date of the Greek Letterphenomena together with the zodiacal sign in which it occurs, and the dates when theplanets enter into each sign. Interpolation between the dates of the sign entries wouldgive the planetary longitudes for any required date, providing the planet did not changethe direction of its motion. However, the Almanacs do not provide information on thelongitude of the sun or moon.

At Uruk, and probably also as Babylon, horoscopes were apparently written by thesame group of scribes who wrote the ACT texts of mathematical astronomy. Anyone who

60 A. Sachs, Babylonian Horoscopes, Journal of Cuneiform Studies 6 (1952), 4975.61 F. Rochberg, Babylonian Horoscopy: The Texts and their Relations, in N. M. Swerd-

low (ed.), Ancient Astronomy and Celestial Divination (The MIT Press, Cambridge, MA, 1999),3959, esp. 48.

62 F. Rochberg-Halton, Babylonian Horoscopes and their Sources, Orientalia 58 (1989),102123.


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made horoscopes would almost certainly have been a member of the intellectual elite,most likely a t . up sar En uma Anu Enlil . Only these individuals would h

Documents

1_A 3405. an Unusual Astronomical Text From Uruk (Steele, 2000)