ANCIENT STANDARDS OF VOLUME:

THE STUDY OF NEGEBITE IRON AGE CYLINDRICAL VESSELS AND

JUDAHITE ROYAL LMLK STORAGE JARS

Itzhak Benenson$, Israel Finkelstein&, Elena Zapassky&

$Department of Geography and Human Environment, & Institute of Archaeology,

Tel Aviv University

bennya@post.tau.ac.il, fink2@post.tau.ac.il, lehna@post.tau.ac.il

Could people in antiquity estimate volumes in a quick and

robust way, without applying complex formulae or having

to pour liquids and solids into pre-measured containers?

Could they make containers with pre-planned volumes?

A logical way to check this is to investigate ancient

pottery vessels aiming at revealing possible regularities

in their size and volume.

Our research seeks for the rules of volume measurement for two groups of Iron Age vessels:

NEGEBITE CYLINDRICAL VESSELS

and

JUDAHITE ROYAL LMLK STORAGE JARS

Negev Highlands: isolated area of the arid zone of southern Israel.

Sharp oscillations of the occupational history: short waves of relatively strong activity versus long periods with no remains at all.

The origin of the Iron IIA Negev Highlands people remains unclear, exchange with the outer world is evident in the ceramic record.

The system of volume units used for the production of pottery vessels reflects knowledge of methods used in neighboring, more developed regions.

1. NEGEV HIGHLANDS IN IRON IIA ANDNEGEBITE IRON AGE CYLINDRICAL VESSELS

The stages of the 3D-model construction of a vessel from Har Boqer

The 3D model with the outer

side shaded.

An image of the vessel

The vessel’s manually-drawn profileThe vessel’s 3D model, with

the inner side shaded

To estimate the vessels‟ volume their 3D models were constructed

0 20cm

The models of all 38 Negebite vessels, in order of increasing volume (inner side, volume diapason: 1.5 – 10.6 liters)

Is there any order in the Negebite vessels’ shape and volume or,

Are these just close-to-cylindrical shapes with randomly established diameter and height?

What units can be “natural” for the Negebite potters?

Length:Numerous pieces of evidence attest to the widespread use of

Egyptian units of length in ancient Israel, and we apply them to the Negebite vessels:

Royal cubit

1 cubit (c) ~ 52.3−52.5 cm. 1 cubit = 28 fingers (f), 1f = 1.865–1.875 cm

1 cubit = 7 palms, 1 palm = 4 fingers.

Volume:The basic units in ancient Israel were bath (used for liquids) and ephah (used for dry products):

Bath1 bath ~ 20 - 24 liters, usually between 21 – 23 liters

1 bath = 10 assirons

Volume, l iters

10.6

10.2

9.8

9.4

9.0

8.6

8.2

7.8

7.4

7.0

6.6

6.2

5.8

5.4

5.0

4.6

4.2

3.8

3.4

3.0

2.6

2.2

1.8

1.4

6

5

4

3

2

1

0

Is there any order in the volumes of Negebite vessels?

Volume distribution of the 38 Negebite cylindrical vessels

Mean volume of the first group equals to 2.26 liters. We relate

this volume to 1 assiron!

Distribution of the Negebite vessels‟ volume as expressed in assirons

(1 assiron = 2.26 liters)

Volume, issarons

4.6

4.4

4.2

4.0

3.8

3.6

3.4

3.2

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

.8

.6

7

6

5

4

3

2

1

0

The vessels’ volumes group around 1 and 2 assirons(and, maybe, higher values, but the larger vessels are few)

Diameter, fingers

1211109876

Hei

ght,

finge

rs

8

7

6

5

4

3 Rsq = 0.3712

1.371.32

1.281.16

1.15

1.14

1.05

1.02

1.02

1.00

1.00

.96

.94

.91

.90

.90

.88

.80

.77

.76

.68

For the vessel of a given weight group

the height depends on the diameter of its base

Relationship between inner height and base diameter (in fingers)

in the 21 Negebite vessels of the first modal class (around 1 assiron)

The Palm Rule

Given the base, the ancient potter knew what should be the vessel‟s height in order to obtain the necessary volume

1 assironD + H = 16f

2 assironsD + H = 20f

3 assironsD + H = 24f

2. THE KINGDOM OF JUDAH IN THE IRON IIB AND JUDAHITE ROYAL LMLK STORAGE JARS

In the Iron IIB the Kingdom of Judah reached

full-blown statehood and developed an

advanced bureaucratic system which

operated under the hegemony of the Assyrian

empire.

One of the manifestations of Judah’s

bureaucratic apparatus is the late 8th century

BCE lmlk storage jars (in biblical Hebrew

“belonging to the king”).

Map of JUDAH in IRON IIB

The lmlk storage jarsThe handles of lmlk jars carry a seal impression that consists of three components:

• The legend lmlk

• Four-winged or two-winged emblem, widely regarded as royal insignias

• The name of one of four Judahite towns: Hebron, Ziph, Sochoh or mmst

Construction of the 3D models of lmlk jars (the set SJ7 of directly measured jars)

For each jar, 24 images were taken at each 15o angle

5 more models were constructed on the basis of one or two published vertical profiles

SJ12 set of lmlk jars – 7 directly measured + 5 jars with published profiles

Construction of the 3D models of the SJ7 lmlk jars

The width of the jars‟ wall

as measured through ten holes between the pasted sherds of restored Lachish Storage Jar 8162/6(2)

Precision of volume estimates

Table 1. Precision of the 3D digital models‟ volume estimates

# Calculated V Measured V Relative error

75-244(1) 44.23 44.25 0.000

78-1418(2) 46.25 46.75 -0.011

8162/6(2) 39.53 39.75 -0.005

Lachish Storage Jar 8162/6(2):

Two photos of the real jar (a, b) and of the models constructed with the 3D scanner shown at different angles (c, d)

Special thanks to Avshalom Karasik and Talia Goldman, Weizmann Institute of Science

The profiles of SJ7 lmlk jars look similar, while their volumes essentially differ

SJ7:

Mean = 20.10a,

STD = 2.10a

CV = 10.4%

SJ12:

Mean = 20.06a,

STD = 1.55a,

CV = 7.5%

Are jar profiles really similar? To check, let us scale them to have the same height

Let HS is the height of a Lachish Storage Jar 10074/1 of 19.8a volume

Reduce/enlarge all linear dimensions of each jar J HJ/HS times

Scaling output: SJ7 SSJ7; SJ12 SSJ12

Variation of the SSJ7 maximal width (profiles of the same jar and between the jars): Mean (for 12 profiles of the same jar): 41.0 - 44.9 cm,

STD (for 12 profiles of the same jar): 0.27 - 0.74 cm CV (for 12 profiles of the same jar): 0.6% - 1.7%CV (for all 7x12 jars‟ profiles): 2.9%

SJ7:

Mean = 20.10a,

STD = 2.10a

CV = 10.4%

SJ12:

Mean = 20.06a,

STD = 1.55a,

CV = 7.5%

SSJ7:

Mean = 19.85a,

STD = 0.68a

CV = 3.42%

SSJ12:

Mean = 19.50a,

STD = 0.86a,

CV = 4.30%

Variation of the volume of the SSJ7/SSJ12 (scaled) lmlk jarsversus

variation of the volume of the SJ7/SJ12 (original) lmlk jars

The precision of 1-2% (the form of a single jar) is characteristic of human-made objects produced by professionals without employing

measurement tools.

Had the potters produced jars of the same height, the variation in their

shape could have resulted in 3-4% accuracy in the volume.

However, the variation in lmlk jars volume is about 10%.

1. Why did not the potter aim at constructing identical jars despite an ability to do so?

2. Why preserve non-standard jars?

3. How did the potters (plus officials and customers) know the real volume of each jar?

We believe that there must have been an easy and quick way to measure the volume of the lmlk jars and therefore there was no need to reproduce jars of equal shape/volume…

We assume that:

1. The measuring of jars filled with liquid must have been performed on the basis of their external dimensions.

2. The seal with the royal insignia guaranteed no more than the standard shape of the jar and the standard width of its wall.

3. An „algorithm‟ must have been a simple one, providing volume estimate at least at 5% precision and applicable to lmlk jars of close to two baths volume.

4. The algorithm should be simple enough to be calculated on the spot by every potter/administrator/consumer.

We hypothesis that the „algorithm‟ might have been the following:

Take a convenient linear measurement and subtract the constant, i.e. estimate volume as

V = D – const

As we know, given the shape of a solid, its volume V depends on any of its linear dimension D, as V ~ const*D3 . That is, the „algorithm‟ can be valid for limited interval of D.

We aim at approximating close to 2 bath volumes

D is half of the maximal horizontal circumference P

V(a) = P(f) – 16(f)

D is half of the half of the vertical circumference L

V(a) = L(f) – 19(f)

What could be linear measurement D and the const for close to two bath volumes? The choice of linear dimension D is limited

D is half of the maximal horizontal circumference P plus

half of the half of the vertical circumference L

V(a) = P(f) + L(f) – 56(f) [2 cubits!]

All jars

V(a) = P(f) + L(f) – 2(c) [56(f) = 2(c)]

The “easiest” approximations of a V = D – const kind

Thank you!