Cécile Michel
email: cecile.michel@cnrs.fr.

Computation Practices of the Assyrian Merchants during the Nineteenth Century BCE

Among Old Assyrian school texts from Aššur and Kaneš, a group of lenticular tablets presents conversion exercises. Their statements, as well as the numerical data employed, are very similar to those given by merchants in their letters. For their everyday activities, the Assyrians used the Mesopotamian weight system to quantify the metalgold, silver, tin and copperobjects of their commercial exchanges. Weighed silver was often used as a means of payment. In order to compute the value of a given metal in silver, it was necessary to multiply or to divide the quantity of metal by the specified conversion ratio. As we do not have tablets showing the intermediary steps, we do not know, up to now, how the merchants carried out the conversions. A systematic analysis of the data given by the Assyrians when purchasing metals and the results they obtained gives clues about the computation methods they might have been using. These appear to be very different from those utilized by contemporaneous Babylonian administrators.

Introduction

The hundreds of thousands of cuneiform tablets found in Near Eastern archaeological sites allow scholars to reconstruct the history of this area during the last three millennia before our era. This huge collection of written sources highlights different cultures of quantification and computation according to the period, the geographical area or the milieu under consideration. 2 During the first centuries of the second millennium BCE, Assyrian merchants were involved in a long-distance trade with Central Anatolia, where they left thousands of tablets, mainly linked to commercial accounting. These private archives have been found at Kültepe, ancient Kaneš, 22 km north-east of Kayseri. For their everyday activities, the Assyrians used the Mesopotamian weight system to quantify the metalgold, silver, tin and copperobjects of their commercial exchanges. A close look at the notation of quantities shows that merchants always preferred to use fractions of the higher metrological unit. Weighed silver was often used as a means of payment. In order to compute the value of a given metal in silver, it was necessary to multiply the quantity of metal by the specified conversion ratio, or to divide it by the conversion ratio. A group of school texts on lenticular tablets presents exercises for such conversions. Their statements, as well as the numerical data employed, are very similar to those given by the merchants in their letters sent to their correspondents in Anatolia.

As we do not have tablets showing the intermediary steps, we do not know, up to now, how the merchants carried out the conversions. With this chapter, I propose a systematic analysis of the computations carried out by Assyrian merchants when purchasing or selling metals. The results given by merchants are often correct, but there are also errors, i.e. incorrect results, or approximations, including rounding upwards or downwards. 3 A detailed examination of the results obtained allows us to present some hypotheses on their culture of computation. Did the Assyrians convert their data into the sexagesimal place value notation to carry out their computations, like the contemporaneous Babylonian administrators? Or did they compute directly with fractions? Are the notations of quantity linked to the merchants' computational practices?

After a general presentation of the documentation studied and the notations used to express numbers and quantities, I will analyse the conversions carried out by the merchants, first in the school texts, then in the texts of practice, in order to present the various clues I have found on the computational methods employed by the Assyrian merchants.

Numbers and Quantities in the Old Assyrian Archives

The Old Assyrian textual corpus constitutes the first large group of private archives in the history of humanity. 4 These sources document the activities of merchants engaged in longdistance trade between the cities of Aššur, on the Tigris (modern Iraq), and of Kaneš, central Anatolia (site of Kültepe, near the modern city of Kayseri, modern Turkey). These merchants used a metrological system of weights to quantify the metals that they traded from the East to the West and back.

The Archives of the Assyrian Merchants at Kaneš and Their Context

At the beginning of the second millennium BCE, some Assyrian merchants left Aššur and settled in forty or so towns in Anatolia, in order to develop long-distance trade. Only three of these settlements have been excavated. Kültepe, the ancient town of Kaneš, was the administrative centre of this trade network. 5 The Assyrian merchants' archives, concentrating on the first half of the nineteenth century BCE, were preserved in their houses located in the lower town at Kaneš. Up to now, the archives, which belonged to two or three generations of merchants, include some 22 500 cuneiform tablets. 6 The local palace, seat of the Anatolian authority, did not yield any tablets, and the central Assyrian administration in both Kaneš and in Aššur have not been recovered. Thus, all that can be reconstructed for the Old Assyrian period relies on private archives with a strong focus on trade. In Aššur, only two dozen texts dating to this period were found in later levels.

These Old Assyrian written sources represent the first evidence of a complex, long-distance commercial system. In Aššur, merchants bought tin, originating from the Far East, presumably Uzbekistan, and textiles. Some of the textiles were imported from Babylonia, and the rest were produced locally by the merchants' wives and daughters. They also acquired robust black donkeys able to transport the merchandise all the way to Anatolia, a journey of six weeks across some 1 300 kilometres. 7 Once in Anatolia, the Assyrians sold their goods for cash or on credit, via the local trade in copper and wool. 8 On the return journey, they brought gold and silver to Aššur. These precious metals were used to purchase merchandise in order to set up new caravans, were hoarded or invested into real estate and slaves. Despite the numerous and often high taxes that had to be paid to the Assyrian and Anatolian authorities and en route, the Old Assyrian trade was extremely profitable. The tin was sold for twice its purchase price in Anatolia, and the textiles three times their cost.

The merchant archives deal with the purchase and the sale of merchandise, as well as the computation of the various taxes. One of the main operations carried out by the merchants is the conversion of the value of one metal into another, often silver. Texts also testify to a great variety of joint ventures, for which it was necessary to calculate the dividends and the share of each associate, taking into account profits and losses. All these data may be reconstructed from the variety of cuneiform texts which were recovered. The Old Assyrian texts include letters and legal texts, among which are many commercial and financial contracts, and various types of personal memoranda. All these are usually referred to as text of practice, which means that these archives served a practical purpose. The other types of texts found in the merchants' archives are rare literary and historical texts, incantations, and school texts. Old Assyrian school texts are quite scarce, about twenty tablets were found in Aššur and in Kaneš; some of these are still unpublished. School texts reflect the school curriculum followed by some educated merchants. Thirteen small round tablets bear conversion exercises (see below), 9 and four others consist mostly of lexical and metrological lists written over several columns on large tablets. 10 The following study is based on both school texts and texts of practice. Before studying their content, I will first explain the notations used by nineteenth century BCE Assyrian merchants to express numbers and quantities. 7 Michel (2008a); Veenhof (2008b). 8 Dercksen (1996). 9 Donbaz (1985). There are more similar school texts, still unpublished, which are preserved both in Berlin and Ankara. 10 Hecker (1993); Michel (2006b); Michel (2008b). The tablet (Kt 00/k 12) is a list of personal names arranged according to the theophoric element by which they start (Donbaz 2004, 185). A long list contains expressions and phrases quite common in merchants' letters (Kt v/k 7 + u/k 31, Hecker 1993; Michel 2010a).

The Notation of Numbers and Quantities as Illustrated by a List of Weights

Among the school texts excavated at Kaneš, a large metrological list, dated to the eighteenth century BCE, presents a progressive list of weights from 1 gin to 60 or 100 gu. 11 This list, which has been the subject of another article,12 is very different from those found in Southern Mesopotamia; it has no systematic order. Its author's intention was both to help in memorizing the weight system and to practice the different notations of integers and fractions. This list of weights reproduces the notation of numbers and quantities that were in use during the Old Assyrian period. The Assyrian merchants favoured the use of fractions in their notation and invented new signs to express 1/6 and 1/4. 1/6

1/4 1/3 1/2 2/3 5/6

The weight system, the first metrological system used by the merchants, is the standard Mesopotamian weight system. In the list, the scribe used subtractive notation repeatedly. For example (col. ii:13), the quantity 1 mana 19 gin is expressed with the subtractive notation 1 1/3 ma-na la2 1 gin2, thus '1 1/3 mana minus 1 gin'. Later, the scribe writes (col. iii:18) 20 la2 1 ma-na, '20 mana minus 1 mana', thus '19 mana ', and (col. iv:19) 20 la2 1 gu2, '20 minus 1 gu', thus '19 gu'.

The Assyrian merchants did not use the Mesopotamian sexagesimal system in which a vertical wedge corresponds to 1 or 60. Instead, they used an additive and decimal system in which 60 was written with six times the sign for 10. The numbers 100 and 1000 were expressed by their Akkadian names, meat and lim respectively. When using the metrological system of weights, 11 Kt t/k 76+79; Michel (1998). The reverse of this tablet bears a lexical list enumerating various metals, stones and plants. The fragment (k/-129) also belongs to the lexical list genre; it gives names of stones, animals, aromatics, and multiplication formulas using a-ra2 'multiply' in a broken context. they preferred using fractions of the higher unit instead of integers of the lower unit, for example, they wrote 1/3 mana instead of 20 gin. 13

Conversions

The most frequent computations carried out by the merchants were conversions. The scribe had to calculate the weight of silver necessary for the purchase of a fixed weight of another metal. 14 Two different operations were carried out depending on the value of the metal to be converted into silver. When the value of the other metal was higher than that of silver, as for gold, the merchant had to do a multiplication, while when the value of the other metal was lower than that of silver, as for tin, he had to do a division. Such computations are found both in school texts and in texts of practice, i.e. letters and personal memoranda.

Conversions in School Texts

The vast majority of the Old Assyrian school tablets found in Aššur and Kaneš present a round shape which was quite frequent for such exercises as they were easy to produce; they contain conversion exercises. Only some have been published up to now. In the following examples, the first two lines include the statement of the exercise and the last line gives the solution, i.e. the result of the conversion of the initial quantity of gold into silver.

To reach this result one simply needs to multiply the quantity of gold by the price of one gin of gold to find its price in silver. The intermediary steps of the operation are never given on the tablets.

13 Such use of fractions is a constant in merchants' milieus, as witness for example the Middle Ages written sources (Benoit 1992). According to Patrice Baubeau (personal communication), it is only in the middle of the 1970s that the New York Stock Exchange abandoned fractions for decimal numbers, because of its computerization. The result is correct.

The operation is the following: (5 +1/3) mana × (3+1/3) = 17 2/3 mana + 1/9 mana = 17 2/3 mana 6 2/3 gin

10.3.1.B [1]4 ma-[na ku3-g]i [li]q-tum [5 1/2 gin2-t]a ku3-bi 1 gu2 17 ma-[na]
' [1] This text, which was found in a private house at Kaneš, shows the same exercise as the previous one unearthed at Aššur. The first line with only a MAŠ or 1/2 sign does not make sense. The result is correct.

The operation is the following: 5 mana × 15 = 75 mana = 1 gu 15 mana

The next exercise is a little more complicated since the scribe had to calculate the weight of silver necessary for the purchase of copper which is quantified by a top-pack (elītum), whose weight was 30 mana according to other texts. 15 The computation was presumably done by a rule of three, which might have been part of the arithmetical training of apprentice merchants.

In order to solve this exercise, the scribe had to multiply the given quantity of copper by the exchange rate, and divide the result by the weight of an elītum-package. This tablet was found in Aššur; copper was rated at between 90 and 100 gin of copper for 1 gin of silver. Here the rate is slightly above, i.e. 50 gin of copper for 1 gin of silver, which is very expensive compared to the highest rates attested in Anatolia for refined copper (60 gin of copper for 1 gin of silver The correct result is 2 1/2 mana 6 1/3 gin. The operation is the following:

(2 gu + 14 mana) × (1/2 mana + 5 gin)30 mana = (4 mana + 14/30 mana) × (1/2 mana+5 gin) = 2 mana + 7/30 mana + 20 gin + 70/30 gin = 2 mana + 36 gin + 1/3 gin = 2 1/2 mana 6 1/3 gin. The scribe could have computed keeping the fractions as I did, or he could have used other methods to find the correct result. There is no indication about the way he reached his solution.

Conversions Operated by Merchants in Their Everyday Activities

Such school texts can be seen as on-the-job training. Indeed, conversions were the most common operations carried out by the merchants. A comparison of these exercises with computations made in the merchants' accounts confirms this fact. The authors of this letter explained to their correspondent how they sold his gold. They specify the quantity of gold at their disposal, the rate on the market and the price of silver they obtained. The result is correct. The operation, which is not given on the tablet, is the following:

(1+1/2) mana × (8+1/4) = 8 mana + 4 mana + 1/4 mana + 1/8 mana = 12 mana + 22 1/2 gin = 12 1/3 mana 2 1/2 gin
As in the school exercises, we observe that the conversion ratio between the gold and the silver is given with fractions, here 8 1/4 gin of silver for 1 gin of gold.

In general, computation which consisted in converting a quantity of gold into silver, corresponding to a simple multiplication, is correct. This is less true when the metal to be converted into silver has a value inferior to that of silver, like tin, or copper, presumably because the operation to be carried out is a division of the weight of the metal by the conversion ratio. This is the case in the following example: The result is an approximation of the correct amount. The operation is the following:

(2 gu + 10 mana)  (16 + 1/2) = (2 gu + 10 mana)  33/2 = (2 gu + 10 mana) × 2/33 = 7 mana + 16 gin + 12/33 gin + 36 gin + 12/33 gin = 7 5/6 mana 2 24/33 gin 2/3 gin is the best approximation among the fractions known by the merchants for 24/33 gin, a fraction unknown to the Assyrians.

Computations Carried out in such Letters: A Combination of Conversions and Additions

Many letters, described by M. Larsen as caravan accounts, were sent from Aššur to Kaneš giving detailed accounts linked to the purchase activities in Aššur. 17 The following letter was found in 1993 in the archives of Ali-ahum and his son Aššur-taklāku. 18 Its authors explain to an anonymous merchant and to a man called Šū-Bēlum how they spent the gold that they received from them: they converted the gold into silver, and with the silver they bought textiles, tin and donkeys, and paid taxes and the personnel of the caravan which departed for Kaneš with someone called Bazia. Larsen (1967: 97-140). For the Old Assyrian letters see Michel (2001).

18 About 1000 tablets were found during the 1993 excavations in one or two much destroyed houses. I thank the former Tahsin Özgüç and the current director of Kültepe excavations, Fikri Kulakoğlu, for their permission to publish this archive.

10.3.3.A Letter. Photo Cécile Michel ©Archaeological mission of Kültepe

Ob. a-na dam-gar3 u3 Šu-be-lim 2 qi2-bi-ma um-ma Ah-ša-lim I-ku-pi2-a u3 Ba-zi-a-ma 4 2 2/3 ma-na ku3-gi ku-nu-ki-ma ! Ba-zi-a ub-lam ku3-gi 6 8 2/3 gin2-ta ta-dí-in ku3-bi 23 ma-na 6 2/3 gin2 8 ša3-ba 28 tug2 hi-a sig5 diri 42 tug2 hi-a qá-áb-li-<ú>-tum 10 ù 46 tug2 hi-a ša qá-tim šu-nigin2 1 me-at 16 tug2 hi-a 12 qá-dum : ša li-wi-tim ku3-bi-šu-nu 9 1/3 ma-na 9 1/2 gin2 14 2 gu2 an-na ku-nu-ku 14 gin2-ta ku3-bi 16 8 1/2 ma-na 4 1/4 gin2 lo.e.21 ma-na an-na ak /qá-tim 18 13 1/2 gin2-ta rev. ku3-bi 1 1/2 ma-na 3 1/2 gin2 20 6 anše hi-a ṣa-lá-mu ku3-bi 2 ma-na 12 gin2 22 1/3 ma-na 1 gin2 ku3-babbar ú-nu-sú-nu ù ú-/kul-ta-áš-nu 24 2/3 ma-na 5 gin2 ku3-babbar ša 3 sà-ri-dí : a-dí 26 Ha-hi-im : a-na ta-ba-lim ni-dí-in 11 1/2 gin2 28 ku3-babbar wa-ṣí-tám ni-dí-in lu-qú-ut-ku-nu 30 gam-ra-[ku ? ]-nu-tí 3 5/6 gin2 ku3-babbar 32 té-ṣú-bi4 : Ba-zi-a ú-lá il5-qé u.e. mì-ma a-nim ku-nu-ki-ni le.e. Ba-zi-a i-ra-dí-a-ku-nu-ti

The three senders of this letter, including the man in charge of the caravan, first exchanged the gold they received into silver, then purchased tin, textiles and donkeys. The transactions may be summarized as follows:

Conversion of gold into silver 2 2/3 mana of sealed gold at 8 2/3 gin of silver per gin of gold. Value in silver: 23 mana 6 2/3 gin. The result is correct. The operation is the following: The total of the expenses indicated on the tablet amount to 23 mana 6 3/4 gin of silver. The quantity of silver obtained by selling the gold, was 23 mana 6 2/3 gin, which means that the expenses exceeded the silver available by 1/12 gin or 15 še (+ 15 še of silver). If we take into account the error made by the scribe in converting the unsealed tin into silver and thus correct 1/2 gin into 1/3 gin, then the total expenses are 23 mana 6 7/12 gin. With this corrected value, the silver obtained by the sale of the gold has been spent, except for 15 še, which represents about 0,7 g (-15 še of silver). Note that 2/3 gin is the best approximation among the fractions known by the merchants for 7/12 gin. The difference between the two results is thus 30 še of silver.

(2+2/3) mana × (8+2/3) =

Analysis of Conversions

A systematic analysis of the conversions of metals into silver, and the results obtained by the merchants can help us to better understand how they carried out their computations. The following tables bring together several examples, classified according to the metal to be converted. Only the examples which give incorrect results are edited, the others are summarized in the tables. The first section presents transactions on gold, a metal more expensive than silver. Such conversions can be solved with a simple multiplication. The second section groups transactions on tin, a metal cheaper than silver. Such conversions imply a division.

Conversions of Gold into Silver

The nine text extracts analysed in this section are referenced in the table below. I choose to study some texts presenting different conversion ratios often expressed with fractions. In the three following examples, either the scribe made an error, or he gave an approximate result.

10.4.1.A Extract of a letter 1/3 ma-na 6 1/3 gin2 ku3-gi ša A-šur3-ma-lik-ma ub-la2-ni 9 la2 1/6 gin2-ta-ma : ta-dí-in 3 5/6 ma-na 2 2/3 gin2 ku3-babbar ap 2-šu '1/3 mana 6 1/3 gin gold that Aššur-malik brought, you sold at 9 minus 1/6 gin (silver) each (gin gold); 3 5/6 mana 2 2/3 gin its (value in) silver'

The operation is the following respecting the subtractive notation:

(1/3 mana + 6 1/3 gin) × (9-1/6) = (3 mana + 54 gin + 3 gin) -(1/18 mana + 1 gin + 1/18 gin) = (3 5/6 mana + 7 gin) -( 41/3 gin + 1/18 gin) = 3 5/6 mana 2 2/3 gin -10 še Using this method of computation, the scribe has rounded the correct result up, giving up the -10 še.

The operation is the following when converting the subtractive notation into a positive one:

(1/3 mana + 6 1/3 gin) × (9-1/6) = (1/3 mana + 6 1/3 gin) × (53/6) = (1/18 mana + 1 gin + 1/18 gin) × 53 = (4 gin + 1/3 gin + 10 še) × 53 = 3 mana + 51 gin + 2/3 gin + 5/6 gin + 20 še = 3 5/6 mana 2 1/2 gin 20 še

If the scribe had used this method, then we would have presumably had the following result on the tablet: 3 5/6 mana 2 1/2 gin, the scribe would have probably rounded the correct result down, dropping the quantity of silver given in the smaller unit, 20 še.

There is a strong presumption that the scribe used the first method to compute this conversion, thus respecting the subtractive notation for the conversion ratio and computing with fractions. Instead of giving the conversion ratio with an additive notation, i.e. 8 5/6 gin, the scribe gave it with a subtractive notation: 9 minus 1/6 gin. Such a process may have a simple explanation: such a notation is intended to simplify the computation, which was to multiply the weight of gold by the conversion ratio. Since the original weight of gold is noted with twice the fraction 1/3, it was presumably simpler to multiply it by 9 instead of by 8, 9 being divisible by 3. The operation is the following:

(2/3 mana + 2 1/4 gin) × (7 + 1/3) = (2/3 mana + 2 1/4 gin) × 22/3 = (2/9 mana + 2/3 gin + 1/12 gin) × 22 = 4 mana + 8/9 mana + 14 gin + 2/3 gin + 1 gin + 5/6 gin = 5 mana 9 5/6 gin The given result, 5 mana 10 minus 1/4 gin, is incorrect; the scribe omitted 15 še, i.e. the difference between 1/6 and 1/4 gin. He provided the result using a subtractive notation because there is no sign to express 3/4.

In the seven following examples, either the scribe made an error, or he gave an approximate result, sometimes rounding the result. The operation is the following:

( The result given by the scribe is a rounding up; he added 10/17 gin to reach 5/6 mana.

It is possible to reverse the problem: the scribe knows the quantity of silver available and wants to compute how much tin he has to give to obtain this amount of silver, the correct result is 5 gu 3 mana 10 gin tin. Then the scribe gave up the quantity of tin given in the smaller unit, which is 10 gin.

10.4.2.B Extract of a letter.

2 gu2 10 ma-na ku-nu-ku 16 1/2 gin2-ta ku3-babbar pí -šu 7 5/6 ma-na 2 2/3 gin2 '2 gu 10 mana of sealed (tin) At 16 1/2 gin (tin) each (gin of silver); its (value in) silver: 7 5/6 mana 2 2/3 gin'

The operation is the following:

(2 gu + 10 mana)  (16 + 1/2) = (2 gu + 10 mana) × 2/33 = (3 mana + 21/33 mana + 18 gin + 6/33 gin) × 2 = 6 mana + 42/33 mana + 36 gin + 12/33 gin = 7 mana + 52 gin + 24/33 gin = 7 5/6 mana 2 24/33 gin

The result given by the scribe is an approximation, 2/3 gin is the closest fraction known by the Assyrians for 24/33 gin.

As for the previous example, it is possible to reverse the problem: the scribe knows the quantity of silver available and wants to compute how much tin he has to give to obtain this amount of silver, the correct result is 2 gu 9 5/6 mana 9 gin tin. Here, the scribe added 1 gin of tin to reach a quantity expressed only with gu and mana. a) The first is the following:

(1 gu + 52 mana)  7 = 16 mana b)
The second is the following:

1 gu  (7-1/6) = 1 gu  (41/6) = 60 mana × (6/41) = 8 2/3 mana 6 34/41 gin The addition of these two quantities of silver gives 24 2/3 mana 6 34/41 gin. The scribe gave up the fraction of gin from the second result, i.e. 34/41 gin.

c) The third operation is the following:

(1 gu + 1 mana)  7 = 8 mana + 4/7 mana + 8 gin + 4/7 gin = 8 2/3 mana 2 6/7 gin The scribe rounded up 2 6/7 gin to reach 3 gin. When reversing the problem: the scribe knows the quantity of silver available and wants to compute how much tin he has to give to obtain this amount of silver, the correct result is 1 gu 1 mana 1 gin. The scribe then would have rounded down this quantity, giving up 1 gin.

d) The fourth operation is the following:

50 mana  (6 + 1/4) = 50 mana  (25/4) = 50 mana × (4/25) = 8 mana
The result is correct.

General Observations and Clues on Computation Methods

The vast majority of the results of conversion computations are correct, or given with an approximation, including roundings up or down. There are rare cases where the result is incorrect.

 On several occasions, the conversion ratios or the results are given with a subtractive notation. For example, the two first examples concerning the conversion of gold into silver give a conversion ratio with a subtractive notation: In the first case, the conversion ratio is 9 minus 1/3 gin (Text 10.4.2.D.). The quantity of gold to be converted being 1/2 mana 1/4 gin, it would have been easier to multiply this quantity by 8 2/3 gin, thus using an additive notation.  But in the second case, the conversion ratio is 9 la2 1/6 gin (10.4.2.A.). This notation simplifies the computation since the quantity of gold to convert is 1/3 mana 6 1/3 gin, thus expressed with two times a third.

In the samples concerning the conversion of tin, on two occasions we also find a conversion ratio with a subtractive notation:

 In the first case, it is 15 la2 1/6 gin (10.4.2.I.) and the quantity of tin to convert is 2 gu 16 mana. 2 gu, at least, is easily divided by 15, since it corresponds to 2 × 60 mana.  In the second occurrence, the conversion ratio is noted as 7 la2 1/6 gin (10.4.2.G.b). In this case, the operation would have been easier with a conversion ratio given in an additive notation: 6 5/6 gin.

Note that the use of a subtractive notation can be the consequence of the absence of a specific sign to express a fraction. For example, in the computed value of silver in text 10.4.2.C. we find 10 la2 1/4 gin, because there is no sign to express the fraction 3/4.

In many cases, the scribe rounded the result down or up, either by giving up the fraction of the smaller unit:

- It is interesting to see the merchants' hesitation on the way to render the fraction 2/7, the best approximation among the fractions known by the merchants being 1/4. 1/3 is a good approximation for 3/8 and 1/6 is a good approximation for 3/17.

In Table 10.2, which gives the conversions of tin into silver, the second last column proposes the results of the computation of the price in silver (first line) and of the quantity of tin bought with the amount of silver specified in the text (second line). The last column gives both the difference for the price of silver, and below for the quantity of tin computed. When doing the computation on the quantity of tin, the difference is usually small and generally corresponds to an integer or to a known fraction. In some cases, a small quantity of tin has been omitted, to round to the higher unit:

-10 gin (10.4. The difference between the quantity of tin given by the scribe and that computed is between 15 še (0.68 g) and 1 2/3 gin (13.9 g). The quantity 15 še corresponds to the smallest weight recorded at Kültepe. 19 One may note that the quantities of tin bought are never given with a quantity of gin lower than 5 gin, while for silver, we find fractions of gin. This is quite logical since silver is much more expensive than tin. The results computed above suggest that the quantity of tin bought was defined in advance, and the price in silver then computed according to the announced conversion ratio. However, the adjustment was presumably done on the quantity of tin and not on the quantity of silver.

All these observations give clues about the way the Assyrian merchants computed in order to convert the value of one metal into another. They always preferred to use fractions of the higher unit instead of integers of the lower unit. They used a limited number of fractions: 1/6, 1/4, 1/3, 1/2, 2/3, 5/6. They did not know the fraction 1/5 which is attested in contemporaneous Babylonian texts. 20 Such a use of fractions implies that they were carrying out computations with fractions on each measurement unit separately. The fact that in some cases they used a subtractive notation could also suggest that they computed starting from the higher measurement unit and ended their computation with the smallest measurement unit.

A systematic analysis of the computations shows that errors are rare. The variations are usually below 1 gin of tin, or between 1 and 2 gin of tin: most of the time, they correspond to a rounding if we consider that the last adjustments were made on the quantities of tin.

Conclusion

This chapter analysed the computations carried out by merchants when converting the value of a quantity of one metal into another, according to a given conversion ratio. While carrying out such operations, the Assyrians presumably did not use the SPVN system as the Babylonians did in the palace administrations at the same time. Indeed, Babylonian administrators, when carrying out such computations, used first to convert their data into the sexagesimal place value notation (SPVN) using metrological tables. They carried out computations on SPVN numbers and then converted the result back into the correct metrological system with the help of metrological lists. 21 Instead, the Assyrians computed with the metrological values, including fractions, starting with the largest measurement units. Such a hypothesis can only be confirmed by using a much larger sample of texts.

The texts give the baseline data, i.e. the quantity of gold or tin and the conversion ratio, and the result obtained, i.e. the corresponding value in silver. However, there is no trace of the computation, and the steps of the calculation always remain invisible. These intermediary calculation steps could have been written down on another type of media, for example wooden tablets coated with wax. Such a media was already in use during the late third millennium BCE, and there are at least two Old Assyrian texts which refer to writing boards with wax: ina ṭuppim ša iskurim, 'on a wax tablet'(ATK 5 11:21-22), and 1 ṭuppum ša iskurim, '1 wax tablet' (AKT 6b 468:12-13), in an inventory of a private chapel. 22 Another possibility, suggested in earlier publications, is that the merchants used a computing tool. 23 Such an instrument could be either a tool on which the merchants were computing, like an abacus, or a complement to mental computation on which they would reproduce the results 20 Michel (1992).

21 Proust (2008, 2010).

22

First published by Barjamovic and Larsen (2008) as Kt 94/k 670.

23

of the intermediary steps. Since they computed with integers and fractions, such an instrument would allow both to be represented. It is interesting to note that such a computing instrument, the nikkassū, is mentioned just before the tablet coated with wax in the inventory of the private chapel quoted above (AKT 6b 468:12). 24

  4 ma[na of go]ld of [li]qtum quality at [5 1/2 gin (of silver) eac]h (gin of gold) its (value in) silver: 1 gu 17 mana' With the restitutions given in the broken parts of the tablet, the result is correct. The operation is the following: (14) mana × (5+1/2) = 70 mana + 7 mana = 1 gu 17 mana 10.3.1.C 10 ma-na ku3-gi za-ki-um 5 1/2 gin2-ta ku3-bi4 55 ma-na '10 mana of pure gold at 5 1/2 gin (of silver) each (gin of gold) its (value in) silver: 55 mana' The result is correct. The operation is the following: (10) mana × (5+1/2) = 50 mana + 5 mana = 55 mana 10.3.1.D «MAŠ (or 1/2)» 10 ma-na ku3-gi za-ki-um 5 1/2 gin2-ta ku3-babbar[ áp -šu] 55 ma-na '10 mana of pure gold at 5 1/2 gin (of silver) each (gin of gold) its (value in) silver: 55 mana'

  10.3.2.B Extract of a letter2 gu2 10 ma-na ku-nu-ku 16 1/2 gin2-ta ku3-babbar-bi-šu 7 5/6 ma-na 2 2/3 gin2 '2 gu 10 mana of (tin under) seal at 16 1/2 gin (of tin) each (gin of silver) its (value) in silver: 7 5/6 mana 2 2/3 gin'

  Extract of a letter. Photo Cécile Michel, ©Archaeological mission of Kültepe[1] 1/3 ma-na ku3-gi E-na-A-šùr ub-lam 8 gin2-ta ni-dí-šuku3-[b]i 10 2/3 ma-na 1 gin2'[1] 1/3 mana gold Enna-Aššur brought here. We sold it at 8 gin (silver) each (gin of gold); its value in silver: 10 2/3 mana 1 gin'The operation is the following: (1+1/3 mana) × 8 gin = 10 2/3 mana The scribe curiously added 1 gin to the resultwas he distracted? gin (of silver) each (gin of gold); its value in silver: 5 mana 10 minus 1/4 gin'

  Extract of a letter. Photo Cécile Michel, ©Archaeological mission of Kültepe 5 gu2 3 ma-na an-/na 17 gin2-ta ku3-bi 17 5/6 ma-na '5 gu 3 mana tin at 17 gin (tin) each (gin of silver) ; its (value in) silver : 17 5/6 mana'

  Extract of a letter. 8 gu2 40 ma-na an-na ku-nu-ki-ni 50 ma-na an-na ak qa2-tim 16 gin2-ta ku3-bi 35 2/3 ma-na '8 gu 40 mana tin under our seal 50 mana hand tin at 16 gin (tin) each (gin of silver); its (value in) silver: 35 2/3 mana' The operation is the following: (8 gu + 40 mana + 50 mana)  16 = (9 gu + 30 mana)  16 = 35 mana + 5/8 mana = 35 mana + 37 1/2 gin = 35 1/2 mana 7 1/2 gin This letter shows several operations.

Table 10 .

 10

	Provenance Preservation	Inventory No.	Publication	No. in the
					present chapter
	Aššur	Vorderasiatisches	A 1001 = Ass	Donbaz (1985)
		Museum, Berlin	14479
			(too damaged)
	Aššur	Vorderasiatisches	Ass 13058e =	Donbaz (1985: 16)	10.3.1.C
		Museum, Berlin	13058i
	Aššur	Vorderasiatisches	Ass 13058f	Donbaz (1985: 5, 16)	10.3.1.A
		Museum, Berlin
	Aššur	Vorderasiatisches	Ass 13058g	Donbaz (1985: 16)	10.3.1.B
		Museum, Berlin
	Aššur	Vorderasiatisches	Ass 13058k	Donbaz (1985: 16)	10.3.1.F
		Museum, Berlin
	Aššur	Vorderasiatisches	Ass 13058l	unpublished
		Museum, Berlin
	Aššur	Vorderasiatisches	Ass 13058m	unpublished
		Museum, Berlin
	Aššur	Vorderasiatisches	Ass 13058n	unpublished
		Museum, Berlin
	Aššur	Vorderasiatisches	Ass 13058o	unpublished
		Museum, Berlin
	Aššur	Vorderasiatisches	Ass 13058p	unpublished
		Museum, Berlin
	Kaneš	Anadolu Medeniyetleri	Kt a/k 178	Hecker (1996)	10.3.1.D
		Müzesi, Ankara
	Kaneš	Anadolu Medeniyetleri	Kt 84/k 3	Donbaz (1985:, 7; no	10.3.1.E
		Müzesi, Ankara		copy)
	Kaneš	Anadolu Medeniyetleri	Several, unknown unpublished
		Müzesi, Ankara

1 Old Assyrian conversion school exercises

Table 10

 10

	No. in the	Inventory no.	Publication	Provenance Preservation
	present chapter
	10.3.2.A	AO 8264	TC 3, 43:6-7	Kaneš	Musée du Louvre, Paris
			copied by Julius Lewy
	10.3.2.B	BM 113286	CCT 3, 5a:4-6	Kaneš	British Museum, London
			copied by Sidney Smith

.2 Old Assyrian texts analysed in section 10.3.2 10.3.2.A Extract of a letter 1 1/2 ma-na ku3-gi 8 1/4 gin2-ta ni-dí-/in ku3-bi 12 1/3 ma-na 2 1/2 gin2 '1 1/2 mana of gold at 8 1/4 gin (of silver) each (gin of gold) we sold, its (value in silver): 12 1/3 mana 2 1/2 gin'

Table 10 .7

 10 Samples for the conversion of tin into silver arranged according to a decreasing conversion ratio

	Text	Amount of tin Conversion	Equivalent in	Correct result	Difference
			ratio	silver
	10.4.2.A	5 gu 3 mana	17 gin	17 5/6 mana	Correct value: 17 mana 49	+ 10/17 gin
					7/17 gin	rounding up
					The amount of silver	-10 gin tin
					corresponds to: 5 gu 3 mana
					10 gin tin
	10.4.2.B	2 gu 10 mana	16 1/2 gin	7 5/6 mana 2 2/3	Correct value: 7 5/6 mana 2	Approx.
				gin	24/33 gin
					The amount of silver	+ 1 gin tin
					corresponds to: 2 gu 9 5/6
					mana 9 gin tin
	10.4.2.C	9 1/2 gu	16 gin	35 2/3 mana	Correct value: 35 1/2 mana 7	+ 2 1/2 gin
					1/2 gin	rounding up
					The amount of silver
					corresponds to: 9 1/2 gu 2/3	-2/3 gin tin
					gin tin
	10.4.2.H	2 gu 20 mana	15 gin	9 1/3 mana	yes
	10.4.2.I	2 gu 16 mana	15 la2 1/6 gin 9 mana 10 gin	Correct value: 9 mana 10	-10/89 gin
					10/89 gin	rounding
					The amount of silver	down
					corresponds to: 2 gu 15 5/6	+ 1 2/3 gin
					mana 8 1/3 gin tin	tin
	10.4.2.J	3 gu 37 1/2	14 1/2 gin	15 mana	yes
		mana
	10.4.2.K	9 gu 30 mana	14 1/4 gin	40 mana	yes
	10.4.2.L	2 gu 10 mana	14 gin	9 mana 17 gin	Correct value: 9 mana 17 1/7	-1/7 gin
					gin	rounding
					The amount of silver	down
					corresponds to: 2 gu 9 5/6	+ 2 gin tin
					mana 8 gin tin
	10.4.2.M	2 gu	14 gin	8 1/2 mana 4 1/4	Correct value: 8 1/2 mana 4	Approx.
				gin	2/7 gin
					The amount of silver
					corresponds to: 1 5/6 gu 9	+ 1/2 gin tin
					5/6 mana 9 1/2 gin tin
	10.4.2.N	2 gu 10 mana +	14 gin	9 5/6 mana 6 la2	Correct value: 9 5/6 mana 6	Approx.
		9 mana		1/6 gin	minus 2/7 gin
					The amount of silver	-1 2/3 gin tin
					corresponds to: 2 gu 19
					mana 1 2/3 gin tin
	10.4.2.D	1 gu 5 mana	14 gin	4 1/2 mana 7 gin Correct value: 4 1/2 mana 8 -	1 4/7 gin
					4/7 gin	error
					The amount of silver	+ 22 gin tin
					corresponds to: 1 gu 4 1/2
					mana 8 gin tin
	10.4.2.O	15 mana	14 gin	1 mana 4 1/3 gin Correct value: 1 mana 4 2/7	Approx.
					gin	-2/3 gin tin
					The amount of silver
					corresponds to: 15 mana 2/3
					gin tin
	10.4.2.P	6 gu 58 2/3	13 2/3 gin	30 1/2 mana 8 gin Correct value: 30 1/2 mana 8	-2/41
		mana			2/41 gin	rounding
					The amount of silver	down
					corresponds to: 6 gu 58 1/2	+ 2/3 gin tin
					mana 9 1/3 gin tin
	10.4.2.Q	21 mana	13 1/2 gin	1 1/2 mana 3 1/2	Correct value:	Error 1/2 for
				gin	1 1/2 mana 3 1/3 gin	1/3 gin
						+ 1/6 gin tin

For general studies on the Old Assyrian archives see[START_REF] Veenhof | Archives of Old Assyrian traders In Archives and Archival Tradition. Concepts of Record-Keeping in the Ancient World[END_REF];[START_REF] Veenhof | The archives of Old Assyrian traders: their nature, functions and use. In Archives and archival documents in ancient societies: Legal documents in ancient societies IV[END_REF], Michel (forthcoming a).

 Veenhof (2008a);Veenhof (2010a);[START_REF] Larsen | Ancient Kanesh. A merchant colony in Bronze Age Anatolia[END_REF].

For a detailed inventory of the Old Assyrian archives and a complete bibliography of this corpus, see[START_REF] Michel | Old Assyrian Bibliography of Cuneiform Texts, Bullae, Seals and the Results of the Excavations at Assur, Kültepe/Kanis, Acemhöyük, Alishar and Bogazköy[END_REF]Michel ( , 2006a[START_REF] Michel | Old Assyrian bibliography 2 (August 2006[END_REF]Michel ( , 2015)).

Michel (forthcoming b).

[START_REF] Michel | Les fractions dans les tablettes économiques du début du second millénaire en Assyrie et en Babylonie[END_REF];Michel (2008b)

For the weight of the top-pack (elītum), seeVeenhof (1972: 13, 25-27).

 Dercksen (1996: 159).

Michel (forthcoming b).

Michel (2006bMichel ( , 2008bMichel ( , 2010b)). It has been proposed that such calculating instruments could take the form of the objects identified as game boards with 61 holes, of which several exemplars, dating to the first half of the second millennium BCE have been discovered. On such a tool, we could imagine that the inner row of holes could have served to note fractions, while the exterior row would have been devoted to integers.

The research leading to these results was supported by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement n. 269804, 'Mathematical Sciences in the Ancient World (SAW)'. I warmly thank F. Kulakoğlu, Director of the Kültepe-Kaneš excavations, for his permission to work on the tablets excavated in 1993 at Kültepe.

The result given by the scribe is rounded up: he added 2 1/2 gin to reach 40 gin, i.e. 2/3 mana.

When reversing the problem: the scribe knows the quantity of silver available and wants to compute how much tin he has to obtain this amount of silver, the correct result is 9 1/2 gu 2/3 gin tin. Here, the scribe gave up the fraction of gin (2/3) in order to have a quantity expressed only with gu. The operation is the following:

(1 gu + 15 mana)  14 = 5 mana + 5/14 mana = 5 mana + 21 gin + 3/7 gin = 5 1/3 mana 1 3/7 gin The scribe made an error in his computation, the result is incorrect. The result given by the scribe is an approximation, 1/6 gin is the closest fraction known by the Assyrian merchants for 3/17 gin.

When reversing the problem: the scribe knows the quantity of silver available and wants to compute how much tin he has to give to obtain this amount of silver, the correct result is 52 1/2 mana 4 5/6 gin 15 še tin. Here, the scribe added 15 še of tin to reach a quantity expressed only in mana and gin. The operation is the following:

(5 mana + 15 gin)  8 = 37 gin + 1/2 gin + 1 gin + 7/8 gin = 1/2 mana 9 3/8 gin

The result given by the scribe is an approximation, 1/3 gin is the closest fraction known by the Assyrians for 3/8 gin. When reversing the problem: the scribe knows the quantity of silver available and wants to compute how much tin he has to give to obtain this amount of silver, the correct result is 5 mana 14 2/3 gin tin. The scribe would have then rounded up adding 1/3 gin tin to reach 15 gin tin.

10.4.2.G Extract of a letter. Photo Cécile Michel, ©Archaeological mission of Kültepe 1 gu2 52 ma-na 7 gin2-ta ta-di2-in 1 gu2 7 la2 1/6 gin2-ta ta-di2-in : ku3-babbar pa 2-šu 24 2/3 ma-na 6 gin2 … [1] gu2 1 ma-na 7 gin2-ta ta-di2-in : ku3-bi 8 2/3 ma-na 3 gin2 50 ma-na 6 1/4 gin2-ta ta-di2-/in ku3-bi 8 ma-na '1 gu 52 mana (tin) at 7 gin (tin) each (gin silver) was sold, 1 gu (tin) at 7 minus 1/6 gin (tin) each (gin silver) was sold; its (value in) silver: 24 2/3 mana 6 gin. (…) [1] gu 1 mana was sold at 7 gin (tin) each (gin silver); its (value in) silver: 8 2/3 mana 3 gin. 50 mana at 6 1/4 gin (tin) each (gin silver); its (value in) silver: 8 mana'.


Cécile Michel
email: cecile.michel@cnrs.fr.

0. Making clay envelopes in the Old Assyrian period

The Old Assyrian private archives excavated at Kültepe contain mainly letters and legal texts. These were originally wrapped in clay envelopes on which the sender(s), of the letters, or the witnesses and parties, for legal texts, would imprint their personal cylinder or stamp seals. These envelopes were meant to protect the letter during its transport or to give its legal value to a contract. Fragments of envelopes are numerous among the archives, and some complete envelopes with their tablet still preserved inside have also been found. However, except for their seal impressions, envelopes have often been neglected because any text on them might not be seen to be primarily important.

Textual data linked to the enclosing of a tablet in an envelope, and applying a seal on it, document the circumstances and the actors involved in closing of a letter or the certification of a legal document. This study of Old Assyrian envelopes is based on the corpus excavated during the 1993 season at Kültepe, in the house of Ali-ahum and his son Aššur-taklāku. The presence of envelopes and envelope fragments in this archive will be tentatively explained. A detailed study of the materiality of the envelopes will then be made in order to understand their manufacture. Descriptions here of hands-on experiments allow a better understanding of the techniques used to wrap tablets in envelopes, and the constraints while making them.

Encasing a tablet in the Old Assyrian texts

The Old Assyrian terminology linked to tablets' envelopes and to the making of an envelope is limited to the verbal root, harāmum, with the meaning 'to cover', and more specifically 'to cover a clay tablet with a clay envelope.' 1 Similarly, we often find the verbal adjective harmum referring to a tablet in an envelope, a 'cased tablet'. 2 The corpus of available texts contains more than two hundred occurrences of these words. The great majority of these attestations refers to loans. 3 The acting party, who inserts the tablet in an envelope, is usually the creditor, who normally kept the loan contract in his archives to assert his rights at a later date:

"We borrowed for you each 13 minas 16 ½ shekels of fine silver, with an interest of 1 shekel per (mina), and they enclosed our tablet in an envelope." 4 This is shown by direct evidence of loans still preserved in their envelopes, but also by the many mention of memoranda (tahsistum) which consist of copies (mehrum) of loan contracts referred to as ṭuppum harmum, as in AKT 7a, 13a:16-20, ta-ah-sí-is-tum, a-ni-tum me-eh-ra-at, ṭup-pì-im ha-ar-mì-im, ša hu-bu-ul Li-pá-a, dumu Ú-zu-a-a, "this memorandum is a copy of the cased tablet of the debt of Lipaya, son of Uzua." See the many more examples given in the volume: AKT 7a, 1; 2; 14; 24; 25; 26; 32; 38, etc. 4 ATHE 28:18-23, 13 ma-na 16 1/2 gín-ta kù-babbar, ṣa-ru-pá-am 1 gín-ta a-na, ṣí-ib-tim : ni-il5-qé-a-kum-/ma, ṭup-pí-ni ih-ri-mu. A memorandum, which is a copy of a loan cased tablet ("this memorandum is the copy of the debt (tablet) of Aššur-bēl-awātum, son of Šu-Anum") starts with the mention "Seal of the owner of the cased (tablet)," AKT 7a, 43:1 kišib be-el ha-ar-mì-im. This would perhaps suggest that the creditor would have exceptionally sealed the loan contract.

Cécile Michel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History of Kültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203. Apart from debts, a variety of other types of legal texts were placed in an envelope. There are, for example, other types of contractual agreements (payment by working capital, joint-stock companies), verdicts of authorities, oaths or other documents sealed by the authorities: 5 "This memorandum is a copy of the cased tablet concerning the working capital of Ennānum." 6 "This memorandum is a copy of the cased tablet concerning the joint-stock company of Anah-ilī." 7 "I hold an cased tablet with a verdict of the judges of the temple." 8 "We enclosed in an envelope the tablet containing the oath of Ikūnum." 9 "This memorandum is a copy of the cased tablet with the seal of the kārum Kaneš." 10 The act of enclosing a tablet in an envelope had a clear legal value and was so important that it was sometimes done at the Gate of the God where testimonies were given under oath. 11 Once a legal text was enclosed in its envelope, a copy or a summary of the text was written on the envelope, and one or more people -parties and witnesses -stamped or rolled their seal on it, making it legally valid. 12 The verb harāmum is sometimes used in elliptic sentences with witnesses as object, suggesting that these witnesses made a deposition under oath and impressed their seals on the envelope of the record of their deposition: "(Write the names of) all the witnesses (on a tablet and) enclosed (it) in an envelope." 13 "Enclose in an envelope the tablet with the (names of) witnesses." 14 "Let him enclose in an envelope (a tablet with the names of) your witnesses." 15 Thus, beyond enclosing a tablet in an envelope, the verb harāmum also suggests the presence of one or more seal impressions on the envelope: 16 "Whether one collected outstanding claims for the other, either (on the basis of) a cased tablet with their seals or (on the basis of) witnesses (…)."

These seal impressions on the envelope certified the legal value of the document. 17 It was normally impossible to create a fake document enclosed in an envelope bearing seal impressions. Some contracts however envisage the possibility that such a fake could be presented: 18 "Any cased tablet of Suen-nādā's debt that may appear will be considered as fake."

5

For a definition of legal texts, see Hertel 2013, 135: "The general features that set the analytical category of 'legal documents' apart from other types of texts are in general that the former specifically served as legal instruments in substantive and procedural legal matters, and that they were sealed by those who asserted or acknowledged a legal action, right or obligation." For a typology of Old Assyrian legal texts see Hertel 2013, 137. Note that the transport contract TPAK 1, 144:19 ends with the superfluous mention "harmu". 7a, 95:14-19, ta-ah-sí-is-tum, a-ni-tum, me-eh-ra-at ṭup-pì-im, ha-ar-mì-im, ša be-ú-lá-at, En-na-nim; see also AKT 7a, 131 and 150. 7 AKT 7a, 54:11-15, ta-ah-sí-is-tum, a-ni-tum me-eh-ra-at, ṭup-pì-im ha-ar-mì-im, ša na-ru-uq, A-na-ah-ì-lí. 8 EL 325 (Tübingen 1): 31-32, [ṭup-pá-am ha-ar]-ma-am ša dí-in, da-a-a-ni ša bi-tim ú-kà-al; for another example of a cased tablet sealed by judges, see AKT 7a, 21:25-28. 9 BIN 6, 29:26-27, ṭup-pá-am, ša ma-mì-it I-ku-nim ni-ih-ri-im. 10 AKT 7a, 82:13-18, ta-ah-sí-is-tum, a-ni-tum, me-eh-ra-at ṭup-pì-im, ha-ar-mì-im, ša ku-nu-uk, kà-ri-im Kà-né-eš. See also AKT 7a, 119:12-17, ta-ah-sí-is-tum, a-ni-tum me-eh-ra-at, ṭup-pì-im ha-ar-mì-im, ša ku-nu-uk kà-ri-im, Kà-ni-iš ša ar-ni-šu, ša Šu-Ištar, "This memorandum is a copy of the tablet 'in an envelope' with the seal of the kārum Kaneš, concerning the penalty of Šu-Ištar."

6

AKT

11

Hertel 2013, 141. See for example Prag I 446:29, ká dingir ih-ri-mu.

12 See for example CCT 3 22b-23a:27-28 (Michel 2001, no. 245), ù ṭup-pu-šu ha-ar-ma-am, ša ku-nu-ki-šu, "And his cased tablet bearing his seal. " Veenhof 2008, n. 194. Several examples are given in the CAD A, 229-230 sub. arāmu, "to place a tablet in a clay case". 13 TC 3, 62 (Michel 2001, no. 212):21-23, ší-bé-e, a-ni-ú-tim ú a-ni-ú-tim, hi-ir-ma-ma. 14 BIN 6, 96:14-15, ṭup-pá-am ša ší-bi, hi-ir-ma. 15 CCT 5, 2:19-20, ší-be-kà : li-ih-ri-ma. See also ATHE 47:13, ki-ma ši-be ta-ha-ri-ma-ni. 16 The valid legal text, enclosed in an envelope bearing the seal impressions of witnesses could replace the presence of these witnesses: 19 "If Asqudum does not produce either a cased tablet or witnesses for Edinaya, Asqudum will pay Edinaya threefold for that silver, if he can produce either a (cased) tablet or witnesses, Edinaya is considered paid his silver."

Legal texts enclosed in clay envelopes were usually stored together in the archives; several bullae, which were used to close and tag the tablet containers, indicate that such legal texts were kept together; this is also corroborated by the observations of the archaeologist, as well as mentions in the texts: 20 "Enter Nuhšatum's house and let her place all containers with encased tablets of our father before you." "I left you the containers with the cased tablets of Aššur-rabi."

Legal tablets enclosed in envelopes covered with seal impressions could be sent to Aššur when a legal case was brought to court or for the division of a succession: "All this (represent) the debt of Adada, the scribe; his encased tablets will travel to the City (of Aššur)." 21 "We will have the tablets enclosed in a case (…) and we will send (them) to you." 22 Tablets, enclosed in an envelope, are referred to as 'encased tablet' (ṭuppum harmum); ṭuppum is a generic term in Old Assyrian, which corresponds both to the materiality of the object and its content, whether it is a "legal text" or it is a "letter". Several of the examples given above refer to memoranda (tahsistum) which are copies of a legal text. 23 Such private records, were preserved in the merchants' archives and were useful to keep track of their transactions; they had no legal value. They were easily accessible, meaning that they were not enclosed in an envelope. 24 However, we do find exceptional mentions of memoranda enclosed in an envelope or sealed: 25 "Encase a memorandum in an envelope stating that my deposit will go for three years and that the silver cannot be claimed (by another)."

But this remains unusual because normally, such memoranda, considered as "open", are opposed to encased tablets whose text is hidden: 26 "He had placed it among the open memoranda and the cased tablets of his father."

19 BIN 4, 147:11-20, šu-ma, ṭup-pá-am ha-ar-ma-am, ú-lá ší-bi4 a-na, E-dí-na-a Ás-qú-dum, lá uš-té-li a-na, kù-babbar, a-nim šu-šál-šum, Ás-qú-dum a-na E-dí-na-a, i-ša-qal šu-ma ṭup-pá-am, ú ! -lá ší-bi4 uš-té-li, kù-babbar, Ás-qú-dum šabu. 20 Özgüç N. -Tunca 2001;Özgüç T. 1994, 369, concerning the description of the archive discovered in the house of Elamma, brother of Ali-ahum; Michel 2018, 63-64. TPAK 1, 63:1015, [a]-ṣé-er Nu-ùh-ša-tim, e-er-ba-ma mì-ma, ta-malá-ki, ša ṭup-pé-e ha-ru-mu-tim, ša a-bi4-ni i-na igi-ku-nu, lu ta-áš-ku-ma; AKT 3 106:11-14, ta-ma-lá-ki, ša ṭup-pé-e, ha-ru-mu-tim, ša A-šùr-gal e-zi-ba-ki-ni. 21 AKT 3 27:20-24, mì-ma a-nim hu-bu-lúm, ša A-da-da <dub>-sar, ṭup-pu-šu ha-ru-mu-tum, a-na A-lim ki <e-tí-qú>.

22

BIN 6, 73:25, 30, ṭup-pè-e nu-ha-ra-ma (…) nu-šé-ba-lá-kum. See also AKT 4, 25:55-56, šu-nign 14 ṭup-pu-ú ! ha-rumu-tum, gán lúm e-tí-qú. Note that usually, merchant preferred sending copies of encased: TC 3, 213:45-47, me-eh-ru-um ša ṭup-pè-e, ha-ru-mu-tim gán lam , e-ti-qú; CCT 1, 4:47-48, me-eh-ru-um ša ṭup-pè-e, ha-ru-mu-tim gán lam e-tí-qú; VS 26, 119:49-50, me-eh-ru-um, ša ṭup-pè-e ha-ru-mu-tim gán lam e-tí-qú.

23

The archive unearthed in 1988 and partly published by Bayram -Kuzuoğlu 2014 (AKT 7a) contains more than a hundred of memoranda which are copies of legal documents originally preserved in envelopes (see comments Bayram -Kuzuoğlu 2014, 60-61). Note that CCT 2, 17:3-5, makes a distinction between encased tablets, copies and memoranda: lu ṭup-pu, ha-ru-mu-tum lu me-eh-ru, lu ta-ah-sí-sà-tum. 24 For this type of texts, see Veenhof 2013, 43-44. 25 BIN 4, 32:31-35, ša 3 ša-na-at, ma-šu-kà-tí i-lu-ku-ma, kù-babbar lá i-ṣa-bu-tù, ta ! -ah-sí-is-tám, hi-ir-ma-ma. For other examples of memoranda placed under seal, see CAD T, 53b and Veenhof 2013, 43-44. This suggests that tahsistum could exceptionally have a legal value. For such a meaning, see the unpublished tablet Kt 93/k 543: 12-13, 17-19, ta-ah-sí-[is]

- /tá[m], ba-lu-um : A-lim ki [ù l]á ni-du-a-ak (…) li-mu-um : ta-ah-sí-is-/tám, a-[na] A-lim ki : ú-bi4-il5-ma : ta-ah-sí-is-tám, igi A-lim ki : i-sí-ú-ma, "
We will not cancel the tahsistum without (the authorisation) of the City (of Aššur) (…) the eponym brought the tahsistum t[o] the City (of Aššur), and they invoked the tahsistum in front of the City (of Aššur)." CCT 1, 13a:20-24, iš-tù : ta-ah-sí-sà-tim, pá-tí-a-tim : ṭup-pè-e, ha-ru-mu-tim ša a-bi4 ! -šu ! , iš-ta-kà-šu. Veenhof 2013, 43-44 notes the expression "open memorandum" (tahsistum patîtum) in AKT 6b, 375:11 and AKT 6b, 446:19-20, by contrast to the loan contract enclosed in its envelope.

Cécile Michel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History of Kültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203. Letters were also encased in a clay envelope on which the name of the recipient(s) was indicated, as well as the indication "sealed by (the sender)." The latter rolled his cylinder seal over the envelope several times. Such an envelope protected the confidentiality of the content of the letter and the integrity of the tablet during its transport. 27 The seal impression(s) of the sender on the envelope authenticated the message. 28 Letters are referred to in texts by the words ṭuppum or našpertum ('message', 'shipment'). None of the examples recorded of an encased tablet (ṭuppum harmum) concerns a letter, although they were in fact also encased, and the verb harāmum is never used referring to a letter. Therefore, harāmum clearly does not refer to a technical gesture but rather to a legal act. For this reason, Old Assyrian specialists usually translate this verb as : 'to validate, to certify a tablet' and the adjective harmum as 'a certified tablet, a valid tablet'. 29 The certification of the tablet is done with the addition of seal impressions on the surface of its envelope.

Texts do not provide many insights into the actual enclosing of a tablet in an envelope. Thus, the following sections will focus on the envelopes themselves and their materiality. The archive excavated in 1993 at Kültepe will serve as a case study.

The envelopes in the '1993 archive'

Inventory of the envelopes

In 1993, the Kültepe archaeological team, under the direction of Tahsin Özgüc, excavated two badly damaged houses (or, perhaps, one large house), which contained 954 tablets, envelopes and fragments, 30 and 37 bullae that had been used to label and seal various types of containers. This large archive belonged to three generations of a family of merchants whose main members were Ali-ahum, his son Aššur-taklāku and his daughter Tariša. The brother of Ali-ahum, Elamma, whose archives have been published by Klaas Veenhof in AKT 8 (2017), lived across the street.

The '1993 archive' includes an important number of letters, 40 % of the archive. Legal documents correspond to 28 %, a little less than half of these are loan contracts. Thus, almost 70 % of the texts belonging to this archive could originally have been protected by an envelope. I was led to work on the envelopes because they represented almost 20 % of the archive: There are 185 envelopes, mainly envelope fragments, and a few intact envelopes with the tablet still preserved inside. It was possible to match some forty envelope fragments with their respective tablets (see below). In eight cases, more than one fragment has been identified for a given tablet. 31 Of the total number of envelopes and envelope fragments, 57 of them originally protected letters, with five envelopes being still intact with the letter inside. A letter's envelope usually has a very short text -for Old Assyrian envelopes, the name of the recipient(s) and a short notice identifying the seal of the sender(s) (kišib PN) 32 -and the sender(s) seal impression(s) which can be repeated several times on both sides and on the four edges. 33 Thus, though fragments of envelopes are often anepigraphic, in some cases one or more seal impressions are partly visible on their surface. When such a fragment corresponds more or less to one side of the envelope, has one or two seal impressions, often from the same seal, and is empty of text, it most probably is the reverse of a letter envelope. Indeed, envelopes of legal documents were covered with text -the copy of the text on the tablet or a summary of it -, and had the seal impressions of the parties and the witnesses. Using this reasoning,

32

Note that Old Babylonian letter envelopes have only the name of the recipient(s) preceded by ana; exceptionally, a mention is added with the name of the sender with the expression ṭuppi PN, 'letter of PN', see Sallaberger 1999, 26-28; Charpin 2013, 57, n. 62. 33 For seal substitutes, see Ricetti 2015.

Cécile Michel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History of Kültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203. 191 26 of the envelope fragments probably protected letters. Two more fragments show on their inner side the negative imprint of a second page. Old Assyrian letters could sometimes be extended on a small tablet of flat lenticular shape, written on one side only (see below). So, all together 46 % of the 185 envelopes and fragments are letter envelopes, which corresponds to a surprisingly high percentage.

Only 17 envelopes and fragments (9 % of the total) have been identified as covering legal texts. Among these, seven concerned loans, six of them are completely preserved with the tablet is still inside. At last, 83 envelope fragments (45 % of the total) remain unidentified.

Presence of envelopes in the archive

The important number of envelopes and envelope fragments found in the '1993 archive' needs an explanation.

The existence of joins that have been made between fragments of envelopes suggest that these envelopes were kept untouched in the archive, the tablet still inside, and broke when the building collapse.

Envelopes that gave a legal value to a contract or a judicial document presumably remained intact in the merchants' archives, and one would expect that there were many of them. Four of the loan contracts that are still preserved in their complete envelope belong to the last owner of the archive, Aššur-taklāku, son of Ali-ahum, as creditor; the corresponding debts, due by Anatolians, have never been paid back, or Aššur-taklāku issued a receipt to the debtors at the time of the repayment; therefore their envelopes remained intact. 34 It is most probable that these documents were kept together in the archive. 35 Logically, the envelopes of letters should be exceptional in the archive, since the recipient was obliged to break the envelope to read the letter. The envelopes and envelope fragments that were found in the excavated house were either opened in Antiquity and not cleaned away from the archive, or more likely broken when the buildings fell apart. The discovery of intact envelopes still containing their letter can only be explained if the letter has never reached its recipient: either it was not sentwhether a copy or an original -or the letter was never delivered to its recipient; it arrived while he was absent from Kaneš or he had died. One third of the 57 well-identified envelopes that protected letters was addressed to the grand-father Iddin-Suen; this ancestor is moreover represented in the archive only by letters. The presence of these envelopes could suggest that Iddin-Suen received these letters as he was no longer there, either dead or retired at Aššur. 36 The second important group of letter envelopes (23 %) concerns the last owner of the archive, Aššur-taklāku, son of Ali-ahum and grand-son of Iddin-Suen. Three of these letters were sent by Aššur-taklāku, two of them addressed to his wife among other recipients. 37 There is a great probability that she read the letters from her husband and that pieces of the envelopes were not cleaned out and remained in the archive room. Aššur-taklāku is the sender of the third letter, together with his father, to a group of colleagues; the envelope has never been opened and remained intact (Kt 93/k 144). Thus this letter has never left the house. Among the ten letters addressed to Aššur-taklāku and for which fragments of envelopes were found in his house, one was sent by his father (Kt 93/k 374), and two others were sent by her sister, alone (Kt 93/k 372+380) or with other persons (Kt 93/k 143b). All the other letters were addressed solely to Aššur-taklāku. This merchant traveled a lot; he had long periods away from Kaneš, and spent a year or more in jail. 38 Either he read these letters and left pieces of their envelopes in the room, or he never opened them, and they broke at the fall of the building. Five of the letters have evidently never been opened since they are still preserved intact in their envelopes. Besides the letter Kt 93/k 144 written by Ali-ahum and his son Aššur-taklāku (see above), one letter envelope was sealed by Aššur-taklāku and Šamaš-abi and was addressed to two other merchants (Kt 93/k 211); again, this message has presumably never been sent. Another letter was addressed first to an anonymous tamkārum, 'creditor', who could be one of the family members living in the house (Kt 93/k 944). The individuals mentioned in the headings of the last two encased letters do not belong to the family living in the house. There is no clue about the presence of these two encased letters in the archive (Kt 93/k 97; Kt 93/k 379); their recipients might not have a house in Kaneš, and were receiving their mail in the house excavated in 1993. 39 In any case, the large number of letter envelope fragments found in this house remains a mystery; it is hard to believe that the inhabitants read their letters leaving all these pieces of envelopes without cleaning them away. Thus, many of these fragments might have belonged to complete envelopes, which fell apart with the destruction of the building.

The Materiality of Envelopes and Envelope Fragments

The tablet and its Envelope

The Old Assyrian tablets are usually small in size, the average corresponding more or less to the palm of the hand. The writing is small and tight, which makes it possible to write a lot of text on a small surface. For example, several letters sent by Aššur-taklāku, the last owner of the '1993 archive', are written with a very tiny script: Kt 93/k 526 measures 4,9 × 6,7 cm and has 53 lines (Fig. 1), including 7 lines on the left edge. 40 This small size facilitates the making of an envelope. The envelope protected the letter during its transportation, both the object itself and the intimate character of the text content. The obverse of the envelope contains the name or the names of the addressees, sometimes with their patronyms, and the name of the sender, whether one or several, with the indication that he has or they rolled his or their seal on the surface of the envelope; the corresponding seal impressions are visible on both sides and over all the edges (Fig. 2). The owner(s) or user(s) of the seal(s), often anepigraphic, can therefore be identified more easily. In a few cases, two or three lines of text are added, prompting the reader to carefully read the content of the message. The reverse of the envelope with its two seal impressions, with a blank space in between, is usually 39 For such a situation of a group of texts preserved in someone's else house see Michel -Garelli 1997 (TPAK), introduction: the archive of Šumi-abiya contained some 25 letters of Aššur-mūtappil, some still in their unopened envelopes, but no loan contracts.

40

The remarkable letter sent by Ummī-Išhara to her sister Šalimma, AKT 8, 206, measures 5 × 5,5 cm and contains 49 lines; photos of the tablet are published in Veenhof 2017 (AKT 8), pl. 40, enlarged by 62%.

Cécile Michel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History of Kültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203. 193 uninscribed. Thus, when we deal with a fragment of the reverse, it is very difficult to match it with its corresponding tablet. For documents of legal value, the text is often repeated in its entirety on the envelope, so that one could read it without actually opening the envelope. The seal impressions on every side of the envelope belonged to the parties and witnesses. The persons who sealed the envelope are mentioned at the beginning of the text, on the obverse of the envelope, in the form 'kišib PN' with their fathers' names (Fig. 3). In general, on the envelope, one finds first the names of the witnesses followed by those primarily concerned by the contract, as for example the debtor for a loan contract. The order of enumeration of those who have sealed the envelope does not respect the seal impressions' order. Since the seals are generally uninscribed, it is then difficult to identify the owners or users of seals. The existence of the envelope with the seal impressions of witnesses and parties certifies the validity of the document and protects it against fraud. In the event of a dispute, the envelope was opened and the text of the tablet checked. If the envelope was broken, the document was no longer valid. As discussed above, it has been assumed by default that most of the uninscribed envelope fragments are reverse of letter envelopes, since envelopes of legal texts are inscribed on both sides.

There does not seem to have been a systematic rule for the orientation of the envelope with respect to the tablet. 41 The text written on the envelope has often the same orientation of that of the tablet. 42 A little less than half of the time, the text on the envelope appears as perpendicular to the text on the tablet. 43 Both orientations can apply to letters as well as to legal texts. Note however that the perpendicular orientation is a little more frequent with rectangular tablets; this allowed to unroll the cylinder seal on a longer surface, and thus, to be sure to have the complete scene (Fig. 4). The seals were usually first impressed on the envelope before the text was written; thus some wedges overlap regularly the feet or the heads of the figures of the seal's scene (Fig. 5). D. Charpin noted that for Old Babylonian legal texts, the envelope was covering the tablet head to tail so that, if one side of the document was broken, the text remained complete between tablet en envelope, Charpin 2002, 496, n. 54. 42 This is the case, for example, of the following Kt 93/k envelopes: 62+108, 93+101, 134+251 (head to tail), 217+239, 225, 227, 229+238, 272+380, 369, 379, 554, 555, 694+839, 817, 819, 836, 841, 844, 857+886, 943 (head to tail), 945 (head to tail), 946, 974. 43 This is the case, for example, of the following Kt 93/k envelopes: 136+220+232, 143, 211, 222, 223, 230, 383, 552, 673+852, 823, 824+828, 837, 845, 861, 867. Cécile Michel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History of Kültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203. 195 On letter envelopes, the seal impression of the sender was repeated twice on the obverse, the few lines of text positioned with the same orientation in-between, and twice on the reverse (Fig. 5). It was also reproduced on all the edges. In the case of legal texts, the number of seal impressions on the obverse and the reverse depended on the number of witnesses and the length of the text to write. On the envelope, there is no ruling separating the lines of text contrary to the systematic ruling on the tablet, even in the case of legal documents on which the text is quite long. The text is written with the same orientation as the seal impressions, but in some instances, some seal impressions may appear upside down (Fig. 6). The letters sent by the king of Aššur which transmit to the Kaneš Assyrian authorities a verdict of the City assembly constitute a special case: the king's cylinder seal is unrolled in a direction perpendicular to the text of the envelope (Fig. 7). 44

Matching Tablet and Envelope

Many envelopes of the '1993 archive' show, on their inner side, negative imprints of the cuneiform signs of the corresponding tablet which is the consequence of clay retraction during the drying process (Fig. 8). Imprints of wedges are more or less marked according to whether the clay of the envelope has much retracted or not when drying; in some cases, the inner side of the envelope is completely smooth. A systematic reading of these negative mirror imprints of signs allowed the matching of 22 % of the fragments of envelopes with their corresponding tablets (Fig. 9).

Second 'Pages'

The inner side of some envelope fragments have a circular depression indicating that the letter originally contained two 'pages' enclosed in the same envelope (Fig. 10). The second 'page', referred to in the texts as ṣibat ṭuppim, 'tablet supplement', is usually a flat oval or lenticular piece of clay written only on one side and placed over the obverse or the reverse of the main tablet, with the text facing the envelope. 45 When the envelope was open, the two pages of a letter were separated and there is no indication in the text helping to match them again. To connect them again, the identification of the corresponding envelope is of great help. When the envelope has remained intact, a bulge on one of its faces indicates the presence of a small second page (Fig. 10). There are several such small tablet supplement in the '1993 archive', some remained seldom. Cécile Michel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History of Kültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203. 198

Indications Concerning the Making of the Envelope

Analyzing further the inner side of the envelopes, several observations can be made that give clues about how they were shaped. The envelope was made of a thin layer of clay folded around the tablet and over itself so that it's both ends overlapped. The envelope was more or less thick, often thinner on the edges than on the obverse or on the reverse where the clay overlapped. Different layers of clay can be sometimes distinguished (Fig. 11). 46 Indeed, inside some of the envelope fragments, we observe a completely smooth part, suggesting that, either on the obverse or on the reverse, the layers of clay of the envelope superimposed allowing to close it. When broken, the superimposed layers have been occasionally detached leaving a more or less flat surface, along the zone with negative imprints of cuneiform signs (Fig. 11). Several inner sides of envelope fragments show imprints of textiles and fibers; in such cases, the negative imprints of the tablet's signs are less visible. Such textile imprints were already observed on some tablets, and it was suggested that these tablets had been enclosed in their envelope before being completely dry. 47 In such a case, a fine textile was used to wrap the tablet before applying the envelope in order to avoid the clay of the tablet from sticking to the envelope. 48 When there was enough time to let the tablet be completely air dry, then there was no need to use a textile, the addition of a new and fresh layer of clay would not stick to it. At last, before closing the envelope, it is necessary to leave a lot of free space between the tablet and the envelope, because during the drying process, the clay retracts a lot and thus can easily split or even break itself by retracting on the tablet. This explains why many envelope fragments have impressions of positive cuneiform signs, as the envelope by retracting took on the shape or even stuck to the tablet. Of the first envelopes made, one envelope out of two cracked after one day, and some even broke after two days. The envelope did not adhere to the tablet, and it was possible to make a replacement envelope after removing the remains of the broken envelope. If, when closing the envelope over the tablet there is too much free space, then it becomes very difficult to write on the envelope and to unroll the cylinder seals. It is therefore very important to find the best possible balance to adjust the clay envelope around the tablet.

*

The Old Assyrian archives excavated at Kültepe include an important number of envelope fragments and a few complete envelopes with the tablet still preserved inside. These envelopes were a material protection for the tablets they contained, and they ensured the confidentiality of letters, and with the seals impressions they had on their surface, they gave their legal character to contracts and judicial texts. The terminology linked to the enclosing of a tablet in an envelope refers to the certification of legal texts.

Beyond the use and significance of envelopes, a thorough observation of envelope fragments as well as experiments allow a better understanding to their mode of production. This is an ongoing project which is carried in collaboration with physicists at Hamburg within the frame of the Centre for the Study of Manuscript Cultures. 52 The goal is to set up a procedure using a tomographic scanner to be able to read the tablets still enclosed in their envelopes without opening them. The first tests carried out on tablets and envelopes produced as part of the experiments gave satisfactory results. 53

52

The tests have been done by Maik Kahnt, under the supervision of Christian Schroer (DESY). The project is carried first within the frame of the SFB 950 and soon within the Excellence Cluster Understanding Written Artefacts (dir. M. Friedrich).

53

Similar experiments have been very recently carried by the staff of the Delft University of Technology on samples of the Böhl collection, Leiden: http://www.nino-leiden.nl/message/seeing-through-clay-4000-year-old-tablets-inhypermodern-ct-scanner page consulted on August 31, 2018.

Cécile Michel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History of Kültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203.

  translations given by Veenhof 2017 (AKT 8): 'valid record / sealed debt-note / valid debt-note.' 30 There are 891 tablets and fragments excavated in 1993, 61 pieces discovered in 1994 and 2 more tablets found during the cleaning of the area in 1998. For a general presentation of the archives, see Michel 2008b. 31 Michel 2008b, 56.

34

  Kt 93/k 550 is a debt of Šakdunua, son of Šarpa; Kt 93/k 941 is a debt of Šarabunua, Tamuriya and Hapuala; Kt 93/k 942 is a debt of Kabašunuwa, son of Kēna-Aššur; Kt 93/k 946 is a debt of Hašuahšu, the alahhinnum. 35 Michel 2018, 61-64. 36 Michel 2018, 65. 37 The letters are Kt 93/k 852 and Kt 93/k 863; for Lušitiya, wife of Aššur-taklāku, see Michel 2015.

Fig. 1 :

 1 Fig. 1: Letter to Rabi-Aššur, Ataya, Puzur-Aššur, Šu-Ištar, Šamaš-abi, Anina, Amārum, and Tariša from Aššur-taklāku; Kt 93/k 526 (4,9x6,7 cm), left edge, obverse and reverse.

Fig. 2 :

 2 Fig. 2: Envelope of a letter from Ah-šalim to Ištar-bāni, Kurub-Ištar and Hattiya; Kt 93/k 379 (5 × 4,6 cm).

Fig. 3 :

 3 Fig. 3: Envelope of a loan contract belonging to Aššur-taklāku, the debtor is Kabašunuwa, son of Kēna-Aššur Kt 93/k 942 (4,6 × 5,1 cm).

Fig. 4a :

 4a Fig. 4a: Letter, Kt 93/k 239+217 (tablet 5,5 × 6,4). The text on the envelope is written parallel to the one on the tablet.

Fig. 4b :

 4b Fig. 4b: Contract, Kt 93/k 945 (5,3x5,7 cm). The text on the envelope is written parallel to the one on the tablet, but head to tail.

Fig 4c :

 4c Fig 4c: Letter Kt 93/k 143 (env. 6,5 × 9,5 cm). The text on the envelope is written perpendicular to the one on the tablet.

  41

Fig. 5 :

 5 Fig. 5: Two seal impression of Tariša's seal on the envelope Kt 93/k 372+380 (5 x 4.8 cm)

Fig. 6 :

 6 Fig. 6: Contract, Kt 93k 215a (4,7x4,2 cm)

Fig. 8 :

 8 Fig. 8: Inside of the envelope Kt 93/k 865

Fig. 9 :

 9 Fig. 9: Join between envelope fragments Kt 93/k 865Kt 93/k 232+136 + 220

45

  Michel 2008, 123. The study of Old Assyrian second 'pages' is ongoing within the frame of the Center for the Study of Manuscript Culture (Hamburg).

Fig 11 :

 11 Fig 11: Insides of envelope fragments. Kt 93/k 552, Kt 93/k 228, Kt 93/k 117, Kt 93/k 142

Fig. 14 :

 14 Fig. 14: The different steps in the manufacture of an envelope.

CécileMichel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History ofKültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203.

Acknowledgements

I heartedly thank the two successor directors of Kültepe excavations, Tahsin Özgüç and Firki Kulakoğlu who entrusted me the publication of this large archive. I wish to thank the directors of the Anadolu Medeniyetleri Müzesi in Ankara who allowed me to work on the collection of tablets, as well as all the staff of the Tablet seksyonu for their kind help, with a special mention to Şerife Yılmaz. All my thanks go also to Philippe Abrahami who kindly read this article and to Arch Naylor who corrected the English language.

, and the Center for the Study of Manuscript Cultures (SFB 950), Hamburg.

Michel 2008b.

Cécile Michel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History of Kültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203. Taylor -Cartwright 2011, 299. 47 Andersson Strand -Breniquet -Michel 2017, p. 98-99. 48 Cartwright -Taylor 2011, 68 propose another explanation: "(The presence of fax fibers on tablets) could indicate wrapping of the tablets in a protective linen cloth to keep them moist or to protect the inscribed surfaces or results from resting the tablet on a cloth used as part of the sealing process." A list of tablets from other periods showing imprints of textiles suggesting that they have been wrapped in textiles is given by Garcia-Ventura -López- Bertran 2014, 195-196; these authors interpret the wrapping of objects in textiles as rituals (201-206).

Cécile Michel, Making Clay Envelopes in the Old Assyrian Period, in F. Kulakoğlu, C. Michel & G. Öztürk (eds.), Integrative Approaches to the Archaeology and History of Kültepe-Kanesh, Kültepe, 4-7 August, 2017, Kültepe International Meetings 3, SUBARTU XLV, Turnhout: Brepols, p. 187-203. 199 In a unique case up to now, tiny pieces of a textile remained fossilized on the tablet Kt 94/k 487. This tablet looks brand new, as if just out of its envelope. No analyses have yet been carried on these textile remains. 49 Thus, the practice of wrapping tablets in a thin textile before shaping the envelope must have been quite regular in the Old Assyrian period; this was necessary when the authors of letters or writers of legal texts could not wait for two days before enclosing their tablet in an envelope. A white powder, which could correspond to decomposed textile fibers, remained inside some uncleaned envelope fragments. 50 Starting from these different observations, I carried out some experiments to understand how the envelopes of tablets were fashioned in antiquity. 51 The problems encountered in the manufacture of the envelopes are presented here step by step.

It is necessary to obtain a thin layer of clay whose surface is very flat. For this, unlike for the tablet, specific tools are needed. To flattened the clay into a 'sheet' with a regular thickness, one needs a flat surface and some kind of cylinder which could be made in wood, stone or even clay to roll it on the clay like a rolling pin. Another solution is to flatten the clay directly on a cone or a cylinder to obtain this 'sheet' of clay. However, the tests point to the first solution. It is also necessary to find a way to prevent the tool sticking to the clay sheet. Envelope tools must have been found in excavations, but if so none has been so far identified.

Then we must think about the shape of the thin layer of clay destined to form the envelope. A square or rectangular shape, when folding around the tablet, leaves too much clay for the edges, which result in protuberances. This is due to the influx of clay when the thin layer is folded to close it. On original envelopes, the thickness of clay is equal or even smaller on the edges compared to obverse and reverse. In order to avoid such an influx of clay on the edges a solution consists in pre-cutting the 'sheet' of clay with a shape of a cardboard box that would have been opened and unfolded. Thus, when folded, the envelope has a regular thickness on all sides except on the side where the two layers of clay close.

Abbreviations