Place-Value Notations in the Ur III Period: Marginal Numbers in Administrative Texts

Abstract

The use of sexagesimal place-value notation (hereafter SPVN) is one of the most striking features of cuneiform mathematics. The earliest attestations of a systematic use of SPVN in cuneiform sources are found in a small set of mathematical texts dated to the Ur III period (ca. 2112 to 2004 BCE). Besides this mathematical corpus, traces of numbers written in positional notations have been found in some Ur III administrative texts. Just a few dozen tablets, among tens of thousands of known Ur III administrative documents, exhibit such numbers noted in positional notation. Moreover, such numbers noted in positional notation appear almost only as a kind of graffiti in the margins. This chapter focuses on these scanty ‘marginal numbers’. Marginal numbers in Ur III administrative texts testify to diverse practices with positional notations and sexagesimal factors in an administrative context, and, in this way, exemplify different ‘cultures of computation and quantification’ in the Ur III period. Through a close analysis of the positional notations found in Ur III administrative texts, we detect a diversity of graphical systems for what was considered until now as a uniform notion of SPVN. We show that these graphical systems vary according to the operations (multiplication, reciprocal, addition, subtraction), the contexts (administrative or mathematical), and the archaeological sites considered in this study (Umma, Girsu, Puzriš-Dagan, Nippur). Our goal is to show that this diversity of notations reflects different computational methods.

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant Agreement No. 269804. On the part of Xiaoli Ouyang, this article was finished during the period when she received general support from the ‘Eastern Scholar’ talent grant (2013–02) awarded by the Shanghai municipal government in China. This work deals with notations which are often omitted in publications and copies, and would not have been possible without the help of curators and colleagues working in different museums and collections. Our warmest thanks go to Irina Antonova, Boris Perlov and Yuriy Saveliev from the Pushkin State Museum of Fine Arts, Benjamin Foster, Ulla Kasten and Elizabeth Payne from the Yale Babylonian Collection, Béatrice André Salvini from the Musée du Louvre, Jean-Luc Chappaz from the Musée d’Art et d’Histoire of Geneva and Kenneth Woodrow Henke from the Special Collections of Princeton Theological Seminary for their kind authorization to work on tablets or use photos or both. We are also very grateful to numerous colleagues who facilitated our work and provided photos or access to archives, including Alassi Mahmoud and Laure-Cassandre Devic who helped with working on tablets and consulting archives at the Department of Near Eastern Antiquities of the Louvre, and Emmert Clevenstine who helped us with the Geneva tablets.

Appendices

Appendix 1: Notations and Chronology

(A map of Southern Mesopotamia in Ur III period is provided at the end of the book, Annex B, map 1).

1.1 Transliterations and Translations

• For the transliterations and translations of numbers and measurement values, we follow the conventions provided in Annex A.1 at the end ofthis volume. However, given the peculiarity of the sources studied in this chapter, we add the following adjustment: when a semi-positional number uses horizontal wedges, we specify ‘aš’ in the transliteration, as in the example of 5(aš) 1:30 in Text 3.

• In commentaries, we use capital letters to refer to individual cuneiform signs isolated from their context, e.g. AŠ versus aš, such as in our discussion of how the number of gur is written in the marginal numbers of Text 3.

• The symbol ‘/’ is used to indicate layout features (e.g. /space/).

• The notation <  < x >  > means that the sign ‘x’ is not expected.

• In the tables summarizing the data from the texts (Sect. 5.2), we use parentheses to mark quantities and numbers in our calculation that are not attested in the texts.

1.2 Location and Orientation

The location of a certain line of a text on a tablet is specified in the following format: ‘side, column, line’. For example, ‘obv. col. ii 3’ means ‘obverse, column ii, line 3’; ‘rev. col. i 2’ means ‘reverse, column i, line 2’.

Upper and lower edges are defined in relation to the obverse. As tablets are read by rotation around the lower edge, notations on the upper edge are a continuation of the text of the reverse.

1.3 Chronology

General chronology, following the so-called middle chronology, after CDLI.⁶⁶

Period	Approximate dates
Early Dynastic I-II	ca. 2900–2700 BCE
Early Dynastic IIIa	ca. 2700–2500 BCE
Early Dynastic IIIb	ca. 2500–2340 BCE
Old Akkadian (or Sargonic)	ca. 2340–2200 BCE
Lagash II	ca. 2200–2100 BCE
Ur III (or Third Dynasty of Ur)	ca. 2100–2000 BCE
Old Babylonian	ca. 2000–1600 BCE
Old Assyrian	ca. 1950–1850 BCE

Ur III chronology

Ur III administrative texts are almost always dated, and historians refer to the dates provided by tablets using the year-month-day format in the following way: abbreviated name of the ruler, year of his reign, month in roman numerals (i, ii, …, xii and ‘diri’ which means ‘additional’ for intercalary months) and day.

The Ur III dynasty includes five rulers (the dates follow the middle chronology):

Ruler	Abbreviation
Ur-Namma (2112–2095)	UN
Šulgi (2094–2047)	Š
Amar-Suen (2046–2038)	AS
Šu-Suen (2037–2029)	ŠS
Ibbi-Suen (2028–2004)	IS

For example, the date labelled in modern publications as ‘AS 5 ii 17’ represents the seventeenth day of the second month of the fifth year of Amar-Suen’s reign. Of course, the Sumerian system for naming years and months in cuneiform texts has nothing to do with this modern representation.

Appendix 2: System S

2.1 A Broad Definition of System S

System S, a sexagesimal additive system, is attested since the beginning of writing in Mesopotamia, and was used primarily for counting items such as animals, workers, days, years and other items of discrete collections. Diagram a of Fig. 5.25 represents the shape of the graphemes of system S used in the Ur III period, as well as the factors which define the value attached to each grapheme.

The numerical system used for expressing most of the measurement values exhibits the same features as system S (see diagram c, c’ and d in Fig. 5.25). The only variant is that the number 1 is represented by a horizontal wedge (aš) for counting the highest measurement units of capacity and weight (see diagram b of Fig. 5.25).⁶⁷

Small measurement units, namely, all of the units except the largest of each metrological system, were generally counted with numerical values less than sixty, noted with graphemes one ( ) and ten ( ) repeated as many times as necessary (see diagram c in Fig. 5.25). However, in the Ur III period, the notations were quite flexible, and, for example, the units ninda and sar may have been counted with numbers larger than sixty (see see diagram c’ in Fig. 5.25 and examples in Text 5).

Figure 5.25 shows that the systems represented by diagrams a, b, c, c’ and d share the same graphical repertory, the same base (alternation of factors ten and six), and the same additive principle. The only variation is the sign for 1, which is a horizontal wedge in b, but vertical in a, c, c’ and d. For the sake of simplicity, we term all of them as ‘system S’.⁶⁸

Fig. 5.25

Diagrams representing various forms of System S and SPVN

2.2 Distinguishing System S from SPVN

In diagrams a, c and c’, the cuneiform graphemes representing 1 and 60 are the same, namely, a vertical wedge ( ). In early texts, the wedge for sixty is bigger than the wedge for one. However, the sizes of both signs tended to become the same and confusion between one and sixty became inevitable. Subsequently, in the Old Babylonian period, the scribes differentiated one from sixty in ambiguous cases by specifying ‘sixty’ (šu-ši) when necessary (see Proust 2009: Sect. 5.5 for details), or by introducing new units (for example the length unit UŠ for sixty ninda), or by using fractions of superior units (for example, 1/2 gan for fifty sar).

In some instances, when numbers are less than 600 and use vertical wedges as units (see diagrams a and c), there is no graphical difference between SPVN and system S. However, some criteria can be used to recognize system S:

• The function: system S is used for counting discrete items or measuring units.

• The textual context: in main texts, a number in system S is always followed by the name of the items counted or a measurement unit; moreover, fractions never appear just after a number in SPVN.⁶⁹

• The paleography: in the exemple we analyse in this article, the non-normalized paleographyPaleography is adopted in sytem S, while the normalized paleography is adopted for positional systems (SPVN and different forms of partial-SPVN).

Of course, for numbers more than 600, there is no ambiguity. For example, in Text 1, the marginal number (transliteration 23:30) cannot be interpreted as a number noted in system S, the paleography of which should be (transliteration 2(geš’u) 3(ges₂) 3(u)). Another example: the positional system adopted for the number 48:30 found in Text 6 cannot be confused with system S .

Appendix 3: Catalogue of Ur III Administrative Texts with Positional Notations

Text numbers given in the first column of the catalogue below are the numbers used in the present chapter. Documents without a text number are not studied in detail here.

Typology of tablets

M(n,n’) means a multi-column tablet, on which the text is divided into n columns on the obverse, and n’ columns on the reverse.

S means single-column tablet.

Date: See chronology in Appendix 1.

Numerical systems:

SPVN means sexagesimal place-value notation.

Partial-SPVN means that the notation is partially sexagesimal or partially positional or both.

MN means marginal number.

Ø means not inscribed.

Text No.	Museum No	Date	Type of tablet	Type of text	Quantity in relation to MN	Location of MN	Numerical system of MN
	MM 396	AS 1?	Frag	Deliveryof precious metals and objects	Weight of silverand gold	Left edge	SPVN?
1	Nik. 2.402	AS 4	S	Balanced accountfor silver in-value	Weight of silver	Obv. bottom	Partial-SPVN
2	YBC 16487	AS 5	S	Balanced accountfor silver in-value	Weight of silver	Rev. bottom	Partial-SPVN
3	YBC 4179	AS 6	M(2,2)	Balanced accountfor grain	Capacity of grain	Rev. col. ii middle section	Partial-SPVN
						Rev. upper Balanced accounton aromatics edge	Partial-SPVN
	FMB 39.2	AS 7	S		Weight and capacity of aromatics	Left edge	SPVN?
	Nik. 2.403	AS 9	S	Balanced accountfor silver in-value	Capacity of cash crops or weight of silver	Rev. middle section	Partial-SPVN?or SPVN?
	Erlenmeyer 152	ŠS 2	M(5,5)	Balanced accountfor workdays	Number of workdays	Obv. col. iii upper section	SPVN
						Lo. edgeof obv. col. iii–v, rev. col. i–iv	System S
4	YBC 16607	ŠS 5	S	Balanced accountfor silver	Weight of silver	Lower edge	Partial-SPVN
	YBC 3883	ŠS 5	M(2,2) sealed	Agricultural work measured in workdays	Number of workdays	Obv ii upper section	SPVN? (normalized)
5	E 15550	IS 2	S	Earthwork for different sections of a dike	Volume of earth	Left edge	SPVN
	Puzriš-Dagan
6	PTS 473	Š 48 vii	S	Two batches of livestock as booty	Number of animals	Rev. lower section	SPVN
	WCMA 20.1.07	ŠS 6 diri	S(1, Ø)	Distribution of barleyas rations	Capacity of grain	Obv. lower section	Partial-SPVN
7	NBC 6641	ŠS 8 ix	S	Distribution of silver for purchase of gold	Weight of silver	Lower edge	SPVN
						Left edge	SPVN
8	YBC 13418	No date	S	Deliveriesof gold	Weight of silver	Upper edge	Partial-SPVN?
						Rev. bottom	Unknown
	YBC 1778	Date damaged	S	Balanced accountfor sheep and goats	Numbers of animals	Obv. middle section	SPVN? (normalized)
	Girsu
	BM 19027	Š 48	M(4,4)	Grain balanced account	Capacity of grain	Left edge	Partial-SPVN?or SPVN?
	SM 1909.05.224	No date?	S	Survey of two fields	Surfaceof fields	Obv. lower section	SPVN
9	AO 27307	Date lost	M(2,2)	Seed for given surfaces	Capacity of seeds	Rev. col. ii lower section	SPVN
	Nippur
	CBS 11661	IS 2 xi 30	M(2,2)		Capacity of grain		SPVN? (damaged)
	Uncertain
10	YBC 1793	AS 5 ix	M(2,Ø)	Value in-silverof different deliveries, or deliveries of silver	Weight of silver	Obv. col. i upper section (main text)	SPVN
						Obv. col. ii lower section	SPVN

Appendix 4: Texts

4.1 Mathematical Text

AO 2728 (=AOT 304 = RTC 413).

Location of marginal number: reverse.

Provenience: Girsu

Date: Ur III (no date written on the tablet).

Location of tablet: Musée du Louvre, Paris, France.

Reference No.: BDTNS 000853; CDLI P128566.

Ed. Thureau-Dangin (1903): No. 413.

Photo: http://www.cdli.ucla.edu/dl/photo/P128566.jpg

	Transliteration	Translation
Obverse
1	6(diš) ninda 4(diš) 1/3 kuš3⌈gid2⌉	6 ninda4 1/3 kuš the length,
2	1/2 ninda sukud	1/2 nindathe height,
3	2(diš) kuš35(diš) šu-si dagal	2 kuš5 šusi the width
4	sahar-bi 3(diš) 1/2 sar 2(diš) 1/2 gin2	Its volume 3 1/2 sar2 1/2 gin,
5	sig4-bi 2(u) 5(diš) 1/2 sar	its brick-volume 25 1/2 sar
Lower edge	30? 6
Reverse
1	6:31:50	6:31:50
2	3 10:50	3 10:50

Commentary:

Our transliteration follows the works of Thureau-Dangin (1903: No. 413) and Robson (1999: 66), and the collation in the Musée du Louvre on February 6, 2014, by C. Proust.

Lower edge: The numerical signs are visible, but they do not appear in Thureau-Dangin’s copy.

4.2 Administrative Texts

The following editions of texts rely on previous publications, on transliterations provided by CDLI and BDTNS, on digital photos, and, in most cases, on our own examination of the tablets. Both databases were last accessed in February 2014 unless otherwise stated. Only photos of the tablets (obverse and reverse) without images in CDLI are provided here. Photos of the edges with marginal numbers in Texts 1–10 appear in Sect. 5.2.

Text 1-Nik. 2 402

Location of marginal number: Obverse, bottom.

Provenience: Umma

Date: AS 4.

Location of tablet: Pushkin State Museum of Fine Arts, Moscow, Russia.

Museum No.: Unavailable.

Reference No.: BDTNS 004641; CDLI P122085.

Copy: Nikol'skij (1915): No. 402 (Fig. 5.26).

Fig. 5.26

Nik. 2 402 (Photos courtesy of Pushkin state Museum of Fine Arts)

	Transliteration	Translation
Obverse
1	1(u) 3(diš) 1/3 gin2ku3	13 1/3 gin of silver,
2	ša3-bi-ta	From its within:
3	1(barig) 3(ban2) 6(diš) 1/2 sila32(diš) gin2 i3-šah2	1 barig3 ban 6 1/2 sila 2 gin of lard
4	ku3-bi 5(diš) 1/2 gin22(u) 3(diš) 1/2 še	Its value in-silver 5 1/2 gin 23 1/2 še;
5	1(u) 1(diš) ma-na [uruda?]	11 mana of …
6	ku3-bi 7(diš) 1/3 gin2	Its value in-silver7 1/3 gin;
7	12:50 /space/ 23:30	12:50 /space/ 23:30
Reverse
1	šu-nigin21(u) 2(diš) 5/6 gin2 2(u) 3(diš) 1/2 še	In total: 12 5/6 gin 23 1/2 še
2	zi-ga-am3	Expended;
3	la2-NI 1/3 gin2 6(diš) 1/2 še	Deficit 1/3 gin 6 1/2 še
4	Blank line
5	nig2-kas7-ak lugal-he2-gal2	A balanced accountof Lugal-hegal
6	mu en-mah-gal-an-na en dnanna ba-hun	Year when Enmahgal-ana, the en-priestess of Nanna, was installed

Commentary:

Obv. 5: The name of the product appears lost in BDTNS but is restored as [uruda] in CDLI. We find the rate in-kind of this product to be 1 1/2 mana per gin of silver, which is close to the rates in-kind of copper calculated by Snell (1982: 150) based on the Ur III evidence.

Obv. 7: The copy of the tablet indicates an erasure of three vertical wedges right above the second sign, 2(diš), of the marginal number. The images of the tablet show only an erasure, probably from the tip of a finger, in the same place, but we cannot tell how many wedges may have been erased.

Text 2-YBC 16487

Location of marginal number: Reverse, bottom.

Provenience: Umma

Date: AS 5.

Dimensions (cm): 4.9 × 4.5 × 2.

Location of tablet: Yale Babylonian Collection, New Haven, Connecticut, USA.

Reference No.: BDTNS 024111; CDLI P112497.

Copy: Snell (1982): No. 5 (Fig. 5.27).

Fig. 5.27

YBC 16487 (Photos courtesy of Yale Babylonian Collection)

	Transliteration	Translation
Obverse
1	1(diš) 1/2 ma-na 6(diš) 1/3 gin22(u) 7(diš) še ku3-babbar	1 1/2 mana 6 1/3 gin 27 še of silver,
2	si-i3-tum	Carried-over balance,
3	ša3-bi-ta	From its within:
4	1/2(diš) ma-na 8(diš) gin2ku3-babbar	1/2 mana 8 gin of silver
5	mu-kux(DU)	As delivery;
6	4(barig) 1(ban2) 9(diš) sila3esir2 e2-a	4 barig 1 ban 9 sila of bitumen
7	ku3-bi 2(diš) 5/6 gin2	Its value in-silver 2 5/6 gin;
8	[…] ┌1┐(barig) ┌5┐(ban2) 6(diš) sila3naga si-e3 gur	[…] + 1 barig 5 ban 6 sila sprouted alkaline plants,
9	[ku3-bi x] ┌gin2┐[x] ┌še┐	Its value in-silverx gin x še;
	Rest broken
Reverse
	Beginning broken
	Blank line
1’	┌šu-nigin22/3┐ ma-na 8(diš) 5/6 gin2 1(u) še ku3	In total: 2/3 mana 8 5/6 gin 10 še of silver
2’	zi-ga-am3	Expended;
3’	la2-NI 2/3 ma-na 7(diš) 1/2 gin21(u) 7(diš) še ku3	Deficit 2/3 mana 7 1/2 gin 17 še of silver
4’	nig2-kas7-ak pad3-da dam-gar3	A balanced accountconcerning Pada the merchant
5’	mu en-unu6-gal dinanna ba-hun	Year when En-unugal of Inanna was installed
6’	48:40sic?/space/ 10	48:40 /space/ 10

Text 3-YBC 4179

Location of marginal numbers: Upper edge and middle section of rev. col. ii.

Provenience: Umma

Date: AS 6.

Dimensions (cm): 15.2 × 8.8 × 2.5

Location of tablet: Yale Babylonian Collection, New Haven, Connecticut, USA.

Reference No.: BDTNS 015950; CDLI P111807.

Copy: Ellis (1970): 268–269 (Fig. 5.28).

Fig. 5.28

YBC 4179 (Photos courtesy of Yale Babylonian Collection)

	Transliteration	Translation
Obverse
Col. i
1	8(aš) 1(ban2) 8(diš) sila3 še gur	8 gur 1 ban 8 sila of barley
2	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
3	Erased line
4	mu en dnanna	Year of Š 43;
5	8(aš) 1(ban2) 8(diš) sila3gur	8 gur 1 ban 8 sila
6	iti 1(u) 2(diš)-kam	For twelve months,
7	3(barig) 2(ban2) 1(diš) 1/2 sila3iti diri	3 barig 2 ban 1 1/2 sila for the additional month,
8	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
9	(erasureat beginning) še kaš mu-kux(DU)	Delivery of barley for beer
10	mu si-mu-ru-um lu-lu-bum2ki	For the year of Š 44;
11	8(aš) 1(ban2) 8(diš) sila3gur	8 gur 1 ban 8 sila
12	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
13	(erasureat beginning) še kaš mu-kux(DU)	Delivery of barley for beer
14	mu ur-bi2-lumki	For the year of Š 45;
15	8(aš) 1(ban2) 8(diš) sila3gur	8 gur 1 ban 8 sila
16	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
17	(erasureat beginning) še kaš mu-kux(DU)	Delivery of barley for beer
18	mu ki-maškiba-hul	For the year of Š 46;
19	[8(aš)] 1(ban2) 8(diš) sila3iti 1(u) 2(diš)-kam	8 gur 1 ban 8 sila for twelve months
20	[3(barig) 1(ban2)] ⌈6⌉(diš) 1/2 sila3iti diri	3 barig 1 ban 6 1/2 sila for the additional month
21	[še kaš] ⌈u4⌉-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
22	(erasureat beginning) ⌈sila3⌉ še kaš mu-kux(DU)	Delivery of barley for beer
23	[mu us2]-⌈sa⌉ ki-maški	For the year of Š 47;
24	[8(aš) 1(ban2) 8(diš) sila3] gur	8 gur 1 ban 8 sila for twelve months
25	[še kaš u4-sakar gišgigir]-⌈ra⌉	Barley for beer for the chariot’s crescent
26	(erasureat beginning) še kaš [mu]- ⌈kux(DU)⌉	Delivery of barley for beer
Col. ii
1	mu ha-ar-šiki	For the year of Š 48;
2	8(aš) ⌈1(ban2)⌉ [8(diš) sila3] ⌈gur⌉	8 gur 1 ban 8 sila
3	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
4	(erasureat beginning) še kaš mu-kux(DU)	Delivery of barley for beer
5	mu damar-dsuen lugal	For the year of AS 1;
6	8(aš) 1(ban2) 8(diš) sila3gur	8 gur 1 ban 8 sila
7	iti 1(u) 2(diš)-kam	For twelve months,
8	3(barig) 1(ban2) 6(diš) 1/2(diš) sila3iti diri	3 barig 1 ban 6 1/2 sila for the additional month,
9	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
10	(erasureat beginning) še kaš mu-kux(DU)	Delivery of barley for beer
11	mu damar-dsuen lugal-e	For the year of AS 2
12	ur-bi2-lumkimu-kux(DU)	Delivery;
13	8(aš) 1(ban2) 8(diš) sila3gur	8 gur 1 ban 8 sila
14	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
15	(erasureat beginning) sila3 še kaš mu- < kux(DU) >	Delivery of barley for beer
16	mu gu-za den-lil2-la2	For the year of AS 3;
17	8(aš) 1(ban2) 8(diš) sila3iti 1(u) 2(diš)-kam	8 gur 1 ban 8 sila for twelve months
18	3(barig) 1(ban2) 6(diš) 1/2(diš) sila3iti diri	3 barig 1 ban 6 1/2 sila for the additional month,
19	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
20	(erasureat beginning) še kaš mu-kux(DU)	Delivery of barley for beer
21	mu en-mah-⌈gal⌉ […]	For the year of AS 4;
22	8(aš) 1(ban2) 8(diš) sila3gur	8 gur 1 ban 8 sila
23	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
24	3(barig) 3(ban2) še kaš mu-kux(DU)	3 barig 1 ban, delivery of barley for beer
25	mu en-unu6-gal	For the year of AS 5;
26	8(aš) 1(ban2) 8(diš) sila3⌈gur⌉	8 gur 1 ban 8 sila
27	iti 1(u) 2(diš)- ⌈kam⌉	For twelve months
Reverse
Col. i
1	3(barig) 1(ban2) 6(diš) 1/2(diš) sila3iti ⌈diri⌉	3 barig 1 ban 6 1/2 sila for the additional month
2	še kaš u4-sakar gišgigir-ra	Barley for beer for the chariot’s crescent
3	4(barig) 3(ban2) še kaš mu-kux(DU)	4 barig 1 ban, delivery of barley for beer
4	mu ša-aš-rukiba-⌈hul⌉	for the year of AS 6;
5	7(aš) 1(barig) 4(ban2) 6(diš) 1/2 sila3še kaš mu-kux(DU)	7 gur 1 barig 4 ban 6 1/2 sila, delivery of barley for beer
6	mu en dnanna-ta mu en-mah-gal-še3	From the year of Š 43 to AS 4;
7	šu-nigin21(geš2) 4(u) 8(aš) 4(barig) 5(ban2) še gur	In total: (60 + 48) gur 4 barig 5 ban
8	ša3-bi-ta	From its within:
9	8(aš) gur mu en dnanna maš2-e i3-pa3	8 gur in the year of Š 43,
10	8(aš) gur mu si-mu-ru-um lu-lu-bu-umki	8 gur in the year of Š 44,
11	9(aš) 1(ban2) 5(diš) sìla gur	9 gur 1 ban 5 sila
12	mu ur-bí-lumki	In the year of Š 45,
13	9(aš) 1(ban2) 5(diš) sila3gur	9 gur 1 ban 5 sila
14	mu ki-maški	In the year of Š 46,
15	9(aš) 1(ban2) 5(diš) sila3gur	9 gur 1 ban 5 sila
16	mu us2-sa ki-maški	In the year of Š 47,
17	3(u) 9(aš) 1(barig) 6(diš) 1/2 sila3gur	39 gur 1 barig 6 1/2 sila
18	mu ha-ar-šiki-ta	From the year of Š 48
19	mu en-mah-gal-še3	To the year of AS 4,
20	9(aš) 3(barig) gur	9 gur 3 barig
21	mu gu-za ba-dim2	In the year of AS 3,
22	2(u) 2(aš) še gur	22 gur of barley
23	mu en-unu6-gal u3mu ša-aš-ruki	In the years of AS 5 and AS 6,
24	⌈kišib?⌉ lu2-dnin-šubur	Sealed tablet of Lu-Ninšubur,
Col. ii
1	šu-nigin21(geš2) 5(u) 3(aš) 4(barig) 5(ban2)1(diš) 1/2 sila3 še gur	In total: (60 + 53) gur 4 barig 5 ban 1 1/2 sila of barley
2	zi-ga-am3	Expended
3	diri 5(aš) 1(diš) 1/2 <  < 5(diš) >  > sila3še gur	Surplus: 5 gur 1 1/2 sila of barley
	5(aš) /erasure/ 1:30	5(aš) 1:30
4	nig2-ka9-ak še kaš u4-sakar gišgigir-ra	The balanced accountconcerning the barley for beer for the chariot’s crescent
5	lú-dnin-šubur	In the charge of Lu-Ninšubur
6	mu1(u) 2(diš)-kam mu en dnanna maš2-e i3-pa3-ta	Twelve years from the year of Š 43
7	mu ša-aš-rukiba-hul-šè	To AS 6
Upper edge
	7(aš) 1:46:30	7(aš) 1:46:30

Commentary:

Obv. col. i 7: The amount for the additional month happens to equal the annual total in obv. col. i 5 divided by twelve. However, the amount for the additional month in other years (Š 47, AS 2, AS 4, AS 6) turns out to be 5 sila less than the annual total divided by twelve (see summary of data in Sect. 5.2).

Obv. col. i 19: Restoration of [8(aš)] based on parallel amounts attested for other years.

Obv. col. i 20: Restoration of [3(barig) 1(ban₂)] ⌈6⌉(diš) 1/2 sila₃ based on the numerical relationship between quantities of different years (see summary of data in Sect. 5.2).

Obv. col. i 24: Restoration of [8(aš) 1(ban₂) 8(diš) sila₃] based on parallel amounts attested for other years.

Obv. ii 2: Restoration of [8(diš) sila₃] based on parallel amounts attested for other years.

Rev. col. i 5: Although there appears to be no ruling between this line and the following line 6, the latter does not have an indenture at the beginning. So we separate these two lines in our numbering.

Text 4-YBC 16607

Location of marginal number : Lower edge

Provenience: Umma

Date: ŠS 5.

Dimensions (cm): 8.8 × 4.7 × 2.2

Location of tablet: Yale Babylonian Collection, New Haven, Connecticut, USA.

Reference No.: BDTNS 024119; CDLI P112505.

Copy: Snell (1982): No. 13.

Photo: http://www.cdli.ucla.edu/dl/photo/P112502.jpg

	Transliteration	Translation
Obverse
1	1(geš2) 1(u) še gur 1(aš) 5(ban2) gur-ta!	60 + 10 gur of barley (at the rate of one gin of silver) per 1 gur 5 ban,
2	1(geš2) 5(u) gur 1(aš) 4(ban2) gur-ta	60 + 50 gur (at the rate of one gin of silver) per 1 gur 4 ban,
3	ku3-bi 2(diš) 1/2 ma-na 7(diš) gin2 9(diš) 1/2 še	Their value in-silver 2 1/2 mana 7 gin 9 1/2 še,
4	mu dšu-dsuen lugal	Year when Šu-Sin (became) king (ŠS 1);
5	1(geš2) 1(u) gur	60 + 10 gur,
6	ku3-bi 1(diš) ma-na 1(u) gin2	Its value in-silver 1 mana 10 gin,
7	mu ma2 dara3 ab-zu den-ki ba-ab-du8	Year when the boat ‘ibex of the abzu’ was caulked for Enki (ŠS 2);
8	2(geš2) 1(u) ┌4┐(aš) gur	60 × 2 + 14 gur,
9	ku3-bi 2(diš) 1/2┌ma┐- < na > 7(diš) 1/2 < gin2 >	Its value in-silver 2 1/2 mana 7 1/2 gin,
10	mu si-ma-num2ki ba-hul	Year when Simanum was destroyed (ŠS 3);
11	Blank line
12	še ku3-še3 sa10-a	Barley sold for silver;
Lower edge
	6:57:20 /space/ 15	6:57:20 /space/ 15
Reverse
1	1/2 ma-na 2(diš) 5/6 gin2 5(diš) še ku3-babbar	1/2 mana 2 5/6 gin 5 še of silver,
2	la2-NI su-ga ugula kikken2 sa2-du11 ensi2-ka	Repaid arrears of the overseer of a milling house, as the sadu-offering of the governor;
3	Blank line
4	[6(diš)] ┌5/6┐ ma-na 7(diš) 1/3! gin2 1(u) 5(diš) še	6 5/6 mana 7 1/3 gin 15 še
5	┌ki?┐ […]-ta	From …
6	1(u) 4(diš) 2/3(diš) gin2 sám x x x zabar uruda šu-nir-ra x	14 2/3 gin as price … for bronze and copper for the emblem …;
7	4(diš) 1/2 ma-na ku3-babbar	4 1/2 mana of silver,
8	┌kišib┐┌ensi2┐-ka	Sealed receipt of the governor;
9	la2-NI 2(diš) ma-na 1(u) 3(diš) gin2 ku3-babbar	Deficit: 2 mana 13 gin of silver
10	nig2-ka9-ak ku3ensi2-ka	A balanced account on the silver of the governor,
11	gir3 lu2-kal-la	Conveyed by Lu-kala
12	mu dšu-dsuen lugal-ta	From the year when Šu-Sin became king (ŠS 1)
13	mu us2-sa bad3 mar-tu ba-du3-še3	To the year after the western wall was built (ŠS 5)

Commentary:

Rev. 4: Restoration of [6(diš)] based on the relationship that the quantities in obv. 3, 6, 9 and rev. 1 add up to the total in rev. 4 (see summary of data in Sect. 5.2).

Regarding the fraction before gin₂, both BDTNS and CDLI read it as 1/2, but we expect it to be 1/3 instead. Our collation of the tablet reveals two short vertical strokes below and above the horizontal stroke but to the right of the vertical stroke in the MAŠ sign representing 1/2. These two may indicate a long but half-erased vertical stroke. If so, then we may restore the fraction as 1/3.

Text 5-E 15550

Location of marginal number : left edge

Provenience: Umma

Date: IS 2.

Dimensions (cm): 10.6 × 5.5 × 2.5

Location of tablet: Peabody Essex Museum, Salem, Massachusetts, USA.

Reference No.: BDTNS 191620; CDLI P416398.

For photos, transliteration and translation, see Ouyang and Brookman (2012): 3.4.

Text 6-PTS 473

Location of marginal number: Reverse, middle section.

Provenience: Puzriš-Dagan

Date: Š 48 vii.

Location of tablet: Princeton Theological Seminary, Princeton, New Jersey, USA.

Dimensions (cm): 7.5 × 4.5 × 1.5

Reference No.: BDTNS 032993; CDLI P126749.

Copy: Sigrist (1990): No. 60.

Photo: http://www.cdli.ucla.edu/dl/photo/P126749.jpg

	Transliteration	Translation
Obverse
1	[2(geš2)] 4(u) ┌5(diš)┐ ab2	2 × 60 + 45 cows
2	[…] [6 + ]2(geš2) [3(u)] 4(diš) udu	[…] + 8 × 60 + 34 sheep
3	[…] [5 + ]2(geš2) 2(u) 1(diš) maš2	[…] + 7 × 60 + 21 sheep
4	2(geš2’u) 2(geš2) ┌3(u)┐ 4(diš) ud5 gun3	2 × 600 + 2 × 60 + 34 speckled female goats
5	[2 + ]1(geš2’u) ┌2(u)┐ 7(diš) ud5	3 × 600 + 27 female goats,
6	(Blank space) 2(geš2) 4(u) 5(diš) ab2 2(šar2) 8(geš2) 5(u) 6(diš) udu	(In total) 2 × 60 + 45 cows 2 × 3600 + 8 × 60 + 56 sheep
7	┌gir3┐ bu-bu	Conveyed by Bubu;
8	1(geš2) 6(diš) ab2	60 + 6 cows
9	5(geš2’u) udu maš2 hi-a	5 × 600 sheep and goats of various kinds
10	gir3 šu-den-lil2	Conveyed by Šu-Enlil;
11	nam-┌ra┐-ak	Booty
12	ki-maški┌ha┐-ar-šiki	Of Kimaš and Harši
Reverse
1	[…]-x┌ki┐	[…]
2	šušin x […]-x-ra	Susa …
3	kišib sà-┌sí┐ […] x	Sealed receipt of …
4	šu-┌d┐[…] ┌TI?┐.A […] di-ku5-┌x┐	…
5	┌tum3┐-dam	To bring
	2/space/ 8:56 1	2:8:56 1
6	iti [ezem]-┌d┐šul-gi	The month of the ‘Festival of Šulgi’
7	mu ┌ha-ar┐-šiki u3 ki-maš┌ki┐ ba-hul	The year when Harši and Kimaš were destroyed

Commentary:

Obv. 1: Restored according to the first part of obv. 6.

Obv. 2: Partially restored based on the numerical relationship of this line with Obv. 3–6 (see summary of data in Sect. 5.2).

Obv. 3: Partially restored based on the numerical relationship of this line with Obv. 2, 4–6 (see summary of data in Sect. 5.2).

Obv. 4: In contrast to the hand-copy by Sigrist and the reading of BDTNS and CDLI, our collation of the tablet shows no A sign at the end.

Rev. middle section: A DIŠ sign appears in a second line and right below the 8(diš) sign of the marginal number. We do not understand the meaning of this sign.

Text 7-NBC 6641

Location of marginal numbers: Lower edge and left edge.

Provenience: Puzriš-Dagan

Date: ŠS 8 ix.

Dimensions (cm): 11.1 × 6.2 × 2.7

Location of tablet: Yale Babylonian Collection, New Haven, Connecticut, USA.

Reference No.: BDTNS 077468; CDLI P298493.

Copy: Garfinkle (2008)

Edition: Garfinkle (2008), Paoletti (2008) and Paoletti (2012): 448–9 (Fig. 5.29).

Fig. 5.29

NBC 6641 (Photos courtesy of Yale Babylonian Collection)

	Transliteration	Translation
Obverse
1	1(aš) gu21(u) ma-na ku3-babbar	1 gu 10 mana of silver
2	nig2-sa10-ma ku3-sig171(u)-ta-še3	As purchase price of gold at the rate of 10:1
3	sag-nig2-gur11-ra-kam ša3-bi-ta	This is the total of the receipts. From its within:
4	9(diš) 1/2 ma-na 2(diš) 2/3 gin21(u) 1(diš) še	9 1/2 mana 2 2/3 gin 11 še
5	kur-bi-la-ak	For Kurbilak;
6	9(diš) 1/2 ma-na 2(diš) 2/3 gin21(u) 1(diš) še	9 1/2 mana 2 2/3 gin 11 še
7	lu2-dašašgigi4	For Lu-Ašgi;
8	9(diš) 1/2 ma-na 2(diš) 2/3 gin21(u) 1(diš) še	9 1/2 mana 2 2/3 gin 11 še
9	lu2-zabala4ki	For Lu-Zabala;
10	7(diš) 5/6 ma-na 7(diš) gin2igi-4(diš)-gal2 3(diš)70 še	7 5/6 mana 7 1/4 gin 3 še
11	i3-li2-an-dul3	For Ili-andul;
12	7(diš) ma-na 9(diš) 1/2 gin28(diš) 1/2 še 1/2 še	7 mana 9 1/2 gin 9 še
13	dsuen-kal	For Sin-kal;
14	6(diš) 1/3 ma-na 1(diš) 5/6 gin2	6 1/3 mana 1 5/6 gin
15	nu-ur2-dutu	For Nur-Utu;
Reverse
1	4(diš) 2/3 ma-na 6(diš) 1/3 gin25(diš) 1/2 še	4 2/3 mana 6 1/3 gin 5 1/2 še
2	lu2zimbirki-ke4-ne	For people of Zimbir;
3	3(diš) ma-na 1(u) 5/6 gin21(u) 5(diš) še	3 mana 10 5/6 gin 15 še
4	dingir-ba-ni	For Dingir-bani;
5	3(diš) ma-na 1(u) 5/6(diš) gin21(u) 5(diš) še	3 mana 10 5/6 gin 15 še
6	bu3-su2-num2	for Busunum;
7	2(diš) 2/3 ma-na 2(diš) gin2igi-6(diš)-gal2 1(u) 8(diš) 1/2 ┌še┐	2 2/3 mana 2 1/6 gin 18 1/2 še
8	ku3lu2 uri5ki-ke4-ne	For people of Ur;
9	2(diš) [1/3 ma]-na 3(diš) gin2igi-6(diš)-gal2 3(diš) še	2 1/3 mana 3 1/6 gin 3 še
10	┌ku3┐[…]-ruki-ke4-ne	For […];
11	[…]-la	[…]
12	2(diš) [1/3 ma-na 3(diš) gin2igi-6(diš)]-gal2 3(diš) še	2 [1/3 mana 3 1/6 gin] 3 še
13	[ku3lu2 …ki]-ke4-ne	For people of […];
14	[…] 2(u) 2(diš) 1/2(diš) še	[…] + 22 1/2 še of silver
15	[…]-um	[…]
	Blank line
17	[šu-nigin2] 1(aš) ┌gu2┐1(u) ma-na ku3-babbar	In total: 1 gu 10 mana of silver
18	gaba-ri kišib dam-gar3-e-ne	Copy of the sealed receipt of the merchants
19	iti ezem-dšu-dsuen	The month of the ‘Festival of Šu-Sin’
20	mu dšu-dsuen lugal uri5ki-ma-ke4ma2-gur8-mah den-lil2 dnin-lil2-ra mu-ne-dim2	Year when Šu-Sin, king of Ur, constructed a grand boat for the gods Enlil and Ninlil
Bottom edge	5(u) / space / 6(diš) 5(u)	50 / space / 6:50
Left edge	2(u) / space / 1(u) 2(diš) 1(u) 7(diš) 3(u)	20 / space / 12:17:30

Commentary:

Obv. 12: Last two signs read as << 1/2 (diš) še >> ^sic in CDLI, but as 1/2 (diš) še in the two editions above and BDTNS.

Rev. 9: The fraction before ma-na read as ⌈2/3⌉ in BDTNS, Paoletti (2008) and Paoletti (2012): 448–9, but as [1/3] in Garfinkle (2008) and CDLI.

Text 8-YBC 13418

Location of marginal numbers: Upper edge and bottom of reverse.

Provenience: Puzriš-Dagan

No date.

Dimensions (cm): 9.6 × 5.5 × 2.5

Location of tablet: Yale Babylonian Section, New Haven, Connecticut, USA.

Reference No.: BDTNS 061651; CDLI P210091.

No copy of this tablet is available (Fig. 5.30).

Fig. 5.30

YBC 13418 (Photos courtesy of Yale Babylonian Collection)

	Transliteration	Translation
Obverse
1	1(diš) 1/3 ma-na ku3-sig17huš-a	1 1/3 mana of ‘red’ gold
2	lu2-zabalam4ki	(From) Lu-Zabalam,
3	1(diš) ma-na 6(diš) 2/3 gin2	1 mana 6 2/3 gin
4	puzur4-er3-ra	(From) Puzur-Erra,
5	5/6 ma-na 3(diš) 1/3 gin2	5/6 mana 3 1/3 gin
6	nu-ur2-dutu	(From) Nūr-Utu,
7	1/3šaba-sa6-ga	1/3 mana(from) Basaga,
8	1/3ša6(diš) 2/3 gin2	1/3 mana 6 2/3 gin
9	dingir-ba-ni	(From) Ilum-bani,
10	1(u) 3(diš) 1/3 gin2i-re-eb	13 1/3 gin (from) Ireb,
11	1/2 ma-na 3(diš) gin2igi-6-gal2 8(diš) še	1/2 mana 3 1/6 gin 8 še
Reverse
1	lu2-dašaš7-gi4	(From) Lu-Ašgi,
2	2(diš) 5/6 ma-na 6(diš) še	2 5/6 mana 6 še
3	nu-ur2-eš4-tar2	(From) Nūr-Eštar,
4	5/6 ma-na 6(diš) gin2	5/6 mana 6 gin
5	er3-ra-dan	(From) Erra-dan,
6	šu-nigin25(diš) ma-na 1(u) 1(diš) ┌gin2?┐1(u) 4(diš) še	In total: 5 mana 11 gin 10 še
7	ku3-bi 1(aš) gu22(u) 8(diš) ma-na ┌la2┐ 1(u) gin2	Its value in-silver1 gu 28 mana minus 10 gin
8	2(u) /space/ 4(u) 5(diš)	20 /space/ 45
Upper edge
	1(aš) 2(u) 7(diš) 5(u)	1(aš) 27:50

Commentary:

Obv. 7–8: The ša serves as the phonetic complement for the fraction of 1/3 (read as šušana). In the absence of the weight unit ma-na, this ša combined with the fraction implies that 1/3 mana is meant (Powell 1971: 133).

Rev. 6: This total turns out to be 3 mana 28 1/6 gin less than the expected total 8 1/2 mana 9 1/6 gin 14 še, which is calculated by adding all the numbers from the preceding individual entries. Our collation of the tablet reveals that a fraction before the MA sign might have been erased.

Rev. 7: Restoration of ^┌lá^┐ based on our collation of the tablet and the correspondence between the metrological notation here and the marginal number on the upper edge.

Rev. 8: The first part of the marginal number, 2(u), appears slightly above the second part, 4(u) 5(diš). For the digit 4(u), the two U signs on the top row appear much fainter and smaller than the two on the bottom.

Text 9-AO 27307 (=AOT c-61 = RTC 408)

Location of marginal number: Reverse, end of col. ii.

Provenience: Girsu

Date: Ur III (date probably written on the tablet, but lost).

Location of tablet: Musée du Louvre, Paris, France.

Reference No.: BDTNS 000848; CDLI P128561.

Edition: Thureau-Dangin (1897): 26–27; pl. 30 No. 79; Thureau-Dangin (1903): No. 408.

Photo: http://www.cdli.ucla.edu/dl/photo/P128561.jpg, accessed October 2015.

	Transliteration	Translation
Obverse Col. i
1	[…] 3(bur’u) 6(bur3) [1(eše3)] 3(iku) GAN21(aš) 2(barig) ⌈3(ban2)-ta⌉	[…] 3 buru 6 bur [1 eše] 3 iku gan; (the rate is) 1 gur 2 barig 3 ban [per (bur)]
2	1(bur’u) 4(bur3) 1(iku) GAN21(aš) 4(barig)-ta	1 buru 4 bur 1 iku gan; (the rate is) 1 gur 4 barig per (bur)
3	2(bur’u) 8(bur3) 1(eše3) 2(iku) GAN21(aš) 1(barig)-ta	2 buru 8 bur 1 eše 2 iku gan; (the rate is) 1gur 1 barig per (bur)
4	⌈še⌉-bi 4(geš’u) 7(geš2) 4(u) 1(aš) 2(barig) 2(ban2) 5 sila3gur	Its grain 4 × 600 + 7 × 60 + 41 gur 2 barig 2 ban 5 sila
5	GAN2uru4-a	The field for seeding
6	2(šar2) 7(bur3) 2(eše3) GAN21(aš) 2(barig) 3(ban)-ta	2 šar 7 bur 2 eše gan; (the rate is) 1 gur 2 barig 3 ban per (bur)
7	1(šar2) 2(bur’u) 4(bur3) 2(eše3) 1(iku) 1/4 GAN21(aš) 4(barig)-ta	1 šar 2 buru 4 bur 2 eše 1 iku 1/4 gan 1 gur 4 barig per (bur)
8	4(bur’u) 1(bur3) GAN21(aš) 1(barig)-ta	4 buru 1 bur gan; (the rate is) 1 gur 1 barig per (bur)
9	4(bur3) 2(eše3) 5(iku) GAN21(aš)-ta	4 bur 2 eše 5 iku gan; (the rate is) 1 gur per (bur)
10	še-bi 6(geš2) 3(u) 8(aš) 5(ban2) 5/6/ sila3gur	Its grain is 6 × 60 + 38 gur 5 ban 5/6 sila
11	GAN2bala-a	The field of bala
12	[šu-nigin2] 3(u) 8(aš) ⌈3(barig) 1(ban)?3 sila3 gur⌉ […]	[Total] 38 gur 3 barig? 1 ban 3 sila […]
Col. ii
	[…]	[…]
3	[1(šar’u) 8(šar2) 5(bur’u) 9(bur3) 2(ese3)] 4(iku) 1(ubu)sicGAN2 [24 sar 2/3 gin2 1(aš) 2(barig) 3(ban2)-ta]	[1 šaru 8 šar 5 buru 9 bur 2 ešê] 4 iku 1/4! gan [24 sar 2/3 gin (the rate is) 1 gur 2 barig 3 ban]
4	3(šar2) 8(bur3) 2(eše3) 1(aš) 1/4 GAN2 1(aš) 4(barig)-ta	3 šar 8 bur 2 eše 1 iku 1/4 gan; (the rate is) 1 gur 4 barig per (bur)
5	3(šar2) 4(bur’u) 2(bur3) 2(eše3) 3(iku) 1(ubu) 1/4 GAN2/ 1(aš) 1(barig)-ta	3 šar 4 buru 2 bur 2 eše 3 iku 1/2 1/4 gan; (the rate is) 1 gur 1 barig per (bur)
6	1(bur)32(eše3) GAN2 1(aš)-ta	1 bur 2 eše gan; (the rate is) 1 gur per (bur)
7	še-bi 3(geš’u) 8(geš2) 3(u)/ 8(aš) 3(barig) 3(ban) 4 5/6 sila35 gin2	Its grain 3 × 600 + 8 × 60 + 38 gur3 barig 3 ban 4 5/6 sila 5 gin
8	GAN2⌈uru4-a⌉	The field for seeding
9	2( šar2) 4(bur’u) 4(bur3) 1(eše3) 2(iku) [GAN2] 1(aš) 2(barig) ⌈3(ban2)⌉-[ta]	2 šar 4 buru 4 bur 1 eše 2 iku gan; (the rate is)1 gur 2 barig 3 ban [per (bur)]
10	⌈2(bur’u) 2 bur3⌉ […]	2 buru 2 bur [gan …]
Reverse Col. i
	[…]	[…]
	[…]	[…]
1'	šu-nigin2[…]	Total […]
2'	šu-nigin2[…]	Total
3'	še-bi […]	Its grain
4'	GAN2bala-a	The field for bala
5'	šu-nigin2	Total
6'	šu-nigin2	Total
7'	šu-nigin2	Total
8'	šu-nigin2	Total
9'	še-bi	Its grain
10'	GAN2bala-[a]	The bala of the field
Col. ii
1'	[…]	[…]
2'	x x ŠU x […] /space/	In Girsu? […] /space/
3’	20?2? 4? […] 5:41:56?:55 ⌈3⌉ /space/ 10? 3? 1:20 1:20 45	20?2? 4? […] 5:41:56?:55 ⌈3⌉ /space/ 10? 3? 1:20 1:20 45

Commentary:

Note on fractions of iku:

Cuneiform	Transliteration	Translation
	1(iku) GAN2	1 gan
	1(ubu) GAN2	1/2 gan
	1/4 GAN2	¼ gan

Obv. col. i 2: Contra Thureau-Dangin’s copy, the first sign of the line is visible; it is 1(bur’u).

Obv. col. ii 3: For explanations on the reconstruction of the damaged part, see Text 9 in Sect. 5.2. ‘4(iku) 1/2 GAN₂’ is noted on the tablet, but, according to the reconstitution, ‘4(iku) 1/4 GAN₂’ is expected.

Rev. col. ii 2’: CDLI and BDTNS restore ⌈ša₃^?⌉ ⌈gir₂^?-šu^?ki⌉ ⌈x⌉ (in Girsu).

Text 10-YBC 1793

Location of marginal numbers: Obverse, beginning of col. i and lower section of col. ii.

Provenience: Unknown.

Date: AS 5 ix.

Dimensions (cm): 9.3 × 7 × 2.2

Location of tablet: Yale Babylonian Collection, New Haven, Connecticut, USA.

Reference No.: BDTNS 005335; CDLI P142357.

Copy: Keiser (1919): No. 293 (Fig. 5.31).

Fig. 5.31

YBC 1793 (Photos C. Proust, courtesy of Yale Babylonian Collection)

	Transliteration	Translation
Obverse
Col. i
1	14:54	14:54
2	29:56:50	29:56:50
3	17:43:40	17:43:40
4	30:53:20	30:53:20
5	Blank line
6	šu-nigin2 1(diš) 1/2 ma-na 3(diš) 1/2 gin2 la2 7(diš) še ku3-a	In total: 1 1/2 mana 3 1/2 gin minus 7 še of silver,
7	mu-kux(DU) didli	various deliveries;
8	7(diš) ma-<na> 1(u) 9(diš) gin2 ku3-a mu-kux(DU) a-tu5-a lugal	7 mana 19 gin of silver, delivery for the lustration of the king;
9	Blank line
10	šu-nigin2 8(diš) 5/6 ma-na 2(diš) 1/2 gin2 la2 7(diš) še ku3-a	In (grand-)total: 8 5/6 mana 2 1/2 gin minus 7 še of silver,
11	ša3 im UD	Within the daily tablets
12	Blank line
13	[mu]-kux(DU) iti ezem-mah	Delivery in the month of ‘Grand Festival’
14	┌mu┐ en dinanna	During the year when the en-priest of Inanna (was installed)
Col. ii
1	8(diš) 5/6 ma-na 4(diš) 1/2 gin2 la2┌x┐ 2(diš) še	8 5/6 mana 4 1/2 gin minus x + 2 še
2	ša3 […]-a	[…]
	2:┌54┐ ┌45┐ ┌28┐ 17 2:28 27	2:┌54┐ ┌45┐ ┌28┐ 17 2:28 27
Reverse
	Not inscribed

Commentary:

We follow CDLI for the unknown provenience of this tablet. BDTNS identifies it as a tablet from Puzriš-Dagan.

Obv. col. i 6, 8, 10: Our search in both BDTNS and CDLI (accessed 2013 August) did not find the expression ‘kù-a’ in any other Ur III document. The exact meaning of this phrase remains unclear to us.

Obv. col. i 11: Read as ‘šà im-babbar’ in CDLI. Our search in both BDTNS and CDLI (accessed 2013 August) found the phrase ‘šà im UD' only in this text. We follow Friberg (2005: 9) for the translation here.

Obv. col. ii 1: Friberg (ibid.) restored the amount in this line as the same in obv. col. i 10, but our collation does not support his restoration. Instead of the 2 1/2 gin₂ as read by him, both the copy and our collation of the tablet show that the amount involved should be 4 1/2 gin₂. As for the amount subtracted, since the two DIŠ signs do not appear under the horizontal stroke of the LA₂ sign (cf. ‘la₂ 7 še' in obv. col. i 6, 10) but immediately after this sign, the amount subtracted may well exceed two še.

Obv. col. ii 2: Friberg (ibid.) restored the lost sign as bala without producing any evidence.

Primary sources

Museum number	Primary publication	CDLI number
AO 2728 = AOT 304 = RTC 413	Thureau-Dangin(1903: 149, No. 413)	P128566
AO 27307 = AOT c-61 = RTC 408 (Text 9)	Thureau-Dangin (1897: 26–27; pl. 30 No. 79); Thureau-Dangin (1903: No. 408)	P128561
AO 5674	Genouillac (1922)	P131745
AO 5676	Genouillac (1922)	P131747
AO 6038	Genouillac (1922)	P131752
Ashm 1924–0667	Grégoire (1996)	P142827
BM 19027	King (1898): pl. 27	P108470
CBS 11661	Myhrman (1910): 56	P105608
E 15550 (Text 5)	Ouyang and Brookman (2012): Sect. 3.4	P416398
Erlenmeyer 152	Englund (2003): No. 1	P109319
Erm 14994	Koslova (2000): No. 340	P212246
FLP 972	Owen (1975): No. 290	P113850
FMB 39.2	Clevenstine, forthcoming	P427641
HMA 9–02824	Lutz (1928): No. 100	P136004
HS 201	Neugebauer (1935); Oelsner (2001)	P254568
Ist L 7375	Delaporte (1911)	P254700
Ist L 9236	Genouillac (1921)	P227599
Ist Ni 374	Proust (2007)	P257557
MAH 16323	Sauren (1974): No. 168	P113467
MAH 16573	Sauren (1974): No. 105	P113404
MAH 16605	Sauren (1974): No. 104	P113403
MAH 19353	Sauren (1974): No. 24	P113323
MAH 19472	Sauren (1974): No. 175	P113474
MM 0396	Schneider (1932)	P101631
MSR 1	Goetze and Foster (2010): No. 158	P142394
MVN 3.290	Garfinkle (2008): 68	P215676
NBC 6501	Paoletti (2012): 447	P298413
NBC 6641 (Text 7)	Garfinkle (2008)	P298493
Nik. 2.402 (Text 1)	Nikol’skij (1915): No. 402	P122085
Nik. 2.403	Nikol’skij (1915): No. 403	P122086
PTS 473 (Text 6)	Sigrist (1990): No. 60	P126749
PUL Ex 662	Chiera (1922)	P130373
SM 1909.05.224	Owen (1982): 91	P116105
VAT 07042	Schneider (1930): No. 382	P125272
WCMA 20.1.07	unpublished according to CDLI	P424374
YBC 01778	Keiser (1919): No. 304	P142368
YBC 01793 (Text 10)	Keiser (1919): No. 293	P142357
YBC 03883	Keiser (1919): No. 225	P142289
YBC 04179 (Text 3)	Ellis (1970): 268	P111807
YBC 13418 (Text 8)	Sigrist and Ozaki (2009): No. 20	P210091
YBC 16487 (Text 2)	Snell (1982): No. 5	P112497
YBC 16607 (Text 4)	Snell (1982): No. 13	P112505