Sources: the diagrams below represent data provided by metrological lists and tables from Nippur scribal schools. These sources are available on CDLI (here).

Scope: Similar metrology is attested in other Old Babylonian scribal schools. The metrology taught in scribal schools was adopted in a large part of Mesopotamia. However, some minor variants may be observed in some administrative or economic archives from Southern Mesopotamia.

Bibliography:

• Proust, Christine. 2007. Tablettes mathématiques de Nippur. Istanbul: Institut Français d'Etudes Anatoliennes, De Boccard.
  
• Proust, Christine. 2009. "Numerical and metrological graphemes: from cuneiform to transliteration." Cuneiform Digital Library Journal, 2009:1.
  
• Robson, Eleanor. 2002. "More than metrology: mathematics education in an Old Babylonian scribal school." Pp. 325-365 in Under One Sky. Astronomy and Mathematics in the Ancient Near East, vol. 297, Alter Orient und Altes Testament (AOAT), edited by J. M. Steele and A. Imhausen. Münster: Ugarit-Verlag.
  

sar		ca. 36 m2
↓ × 100
GAN23)		ca. 3600 m2

System G, used before the sign GAN2

× 10 ←

× 6 ←

× 10 ←

× 3 ←

× 6 ←

× 2 ←

šar’u

šar2

bur’u

bur3

eše3

iku

ubu

10 800 iku

1 080 iku

180 iku

18 iku

6 iku

1 iku

½ iku

Examples:
1(iku) GAN₂ represents ca. 3600 m²
2(eše₃) GAN₂ represents ca. 2×6×3600 m², that is, 43 200 m²

šu-si		ca. 16 mm
↓ × 30
kuš3		ca. 50 cm
↓ × 12
ninda		ca. 6 m
↓ × 60
UŠ		ca. 360 m
↓ × 30
danna		ca. 10,5 km

Note: in mathematical texts, the unit gin₂ is also used for sub-dividing the surface unit sar into 60 parts, and the unit še is also used in capacity and surface systems for sub-dividing the unit gin₂ into 180 parts. In other words, if we consider all of the OB mathematical texts, the sequence ←×60− gin2←×180−še can be grafted in capacity and surface systems.

Bridge between length and surface units: 1 ninda × 1 ninda = 1 sar
Bridge between surface and volume units: 1 volume-unit = 1 surface-unit × 1 kuš₃ (example: 1 sar-volume = 1 sar-surface × 1 kuš₃).
Bridge between volume and capacity units: 1 sar-volume is equivalent to 60 gur (ca. 18 m³ or 18 000 liters).

	× 10 ←		× 6 ←		× 10 ←		× 6 ←		× 10 ←
šar’u		šar2		geš’u		geš2		u		diš
36 000		3 600		600		60		10		1

Some metrological lists or tables provide very large (and unrealistic) numbers:

• 1 šar₂ gal (60 times 1 šar₂) appears in CBS 10990, CBS 8214, CBS 10181, HS 249, Ist Ni 4840, YBC 2392, CBS 472, Ash 1931.137
• 1 šar₂ gal šu-nu tag (60 times 1 šar₂ gal) appears in CBS 10990, CBS 8214, CBS 10181, Ist Ni 4840 (for another reading and interpretation, see Chambon & Robson 2011, "Untouchable or unrepeatable? The upper end of the Old Babylonian metrological systems for capacity and area 127", Iraq 73)

A school tablet from Nippur CBS 11319 +) contains on the obverse the unique known text which displays the entire System S in a systematic way (see copy and transliteration in Proust 2008, in Proceedings of the 51st Rencontre Assyriologique Internationale, Biggs et al. ed., SAOC 62, p. 151-152).

The highest units of capacity (gur) and weight (gun₂) are counted with a variant of System S, where the number 1 is represented by the sign aš (and not the sign diš as in the System S used for discrete item).

The other measuring units (sila₃, gin₂, še, sar, danna, UŠ, ninda, kuš and šu-si) are counted with (1) and (10) repeated as many times as necessary.

1/6	(igi-6-gal2)
1/3
1/2
2/3
5/6

Page prepared by CP
(digital version prepared by BG)