From the earliest period of their history the Jews were alive to the necessity of an accurate system of weights and measures, and an honest handling of them. The first legislation in the interest of economic righteousness in general is found in Leviticus 19:35 and Deuteronomy 25:13–16, and the prophets constantly denounced the use of false measures (Amos 8:5; Hos. 12:8; Micah 6:10; see also Prov. 11:1; 16:11; 20:10). Rabbinic legislation went so far as to demand the periodic cleaning of weights, scales, and measures lest their true standard be impaired by dirt (BB 5:10; see also BB 89a-b).
Metrological Systems in the Bible and the Ancient Near East
An authoritative and accepted system of weights for buying and selling, building, measuring areas, and the like is a necessity of civilized life. Therefore even in very ancient periods fixed measurements were established, initially for barter, estimation of distances, etc., and later for more complex needs such as building, the division of land, the digging of canals, and others. For that reason, most of the first measures were natural or common physical phenomena, such as the palm of the hand, a day's journey, seeds of grain, and simple utensils. As time progressed, the measures were improved and made more precise, but they were still called by their ancient names. Various systems of measurement developed in the large cultural centers of Egypt and Mesopotamia from a very early period. There, even complex reckoning was carried out to determine the equivalence between the different categories, that is, to reckon volume in terms of weight or area, and the like.
This type of reckoning is not found in the Bible though it was certainly known in Israel. An allusion to a similar reckoning is found in the Bible in a verse which expresses acreage in terms of volume of seed requirement: "And he made a trench about the altar, as great as would contain two measures of seed" (I Kings 18:32; see also Jer. 27:16; Isa. 5:10b (see *Targum ), and later sources down to modern Palestine Arab usage).
The weights and measures in the Bible are in large part based upon the weights and measures which were accepted by the ancient peoples, the names of the measures also being the same. In Israel, measures of several peoples were used simultaneously: from Mesopotamian measures, the kor, se ʾ ah, shekel, and others; from Egyptian measures, the ephah, hin, and others; and measures whose names were borrowed from the Canaanites such as letekh and kikkar. Apparently the Israelites adopted the measures from the Canaanites, who lived in the land before them, along with the names which were originally Egyptian and Mesopotamian. For this reason Egyptian measures have been found that have Mesopotamian names. Some measures, since they are not found among the neighboring countries, were apparently established in Israel.
In biblical measures, it is customary to distinguish between natural measures (measures established in reference to parts of the human body, utensils, average sizes of burdens loaded on animals, etc.) and between measures established by reckoning which were fixed and precise. In some cases the Bible explains the relationship between measures, but it is difficult today to establish their absolute values because as early as the days of the Second Temple the biblical measures were abolished, and later translators and commentators were inclined to identify them with their contemporary measures without being precise as to their values.
In the metrology practiced in the Ancient Near East, there were measures which differed in their absolute value but were identical in name, for example: in Egypt and Mesopotamia, the short cubit was in use along with the long cubit, and there were also different weights, light and heavy, called by the same name, such as the mina. Double weights of this sort were in use also in Palestine, as has been proven from the Bible and from archaeological finds, and were in use there almost until modern times.
Aside from these, there were measures confined to specific localities. Ancient documents provide evidence of weights named for cities: "Alalakh weight," "Carchemish weight," and the like. This custom, too, was practiced in Palestine. In addition to the already-mentioned difficulties, there is the problem of the durability of these weights, since it is likely that with the passage of time many changes took place in them. The ascertaining of biblical measures and the determination of their values in terms of present-day measures is done mainly on the basis of archaeological finds. In the excavations carried out in Palestine, many weights have been uncovered and also fragments of vessels upon which measurements of volume have been written. Linear measure can be reckoned according to ancient structures whose measurements are marked. In the neighboring countries – mainly Egypt, Syria, and Mesopotamia – actual measuring rods of wood and stone were uncovered, along with weights and economic documents, all of which are valuable aids in determining the biblical measures. However, it still cannot be known whether these measures are identical with biblical measures and which of the various standards the Bible used. The Bible demands the use of correct measures and promises long life to one who is careful in this matter (Deut. 25:13–16; Amos 8:5, et al.).
The units of length mentioned in the Bible, as well as those used by other ancient peoples, are derived from average measures of the length of human limbs. Names of measures based on the limbs of the body are in use in some languages even to this day.
It appears that in the early period it was customary to measure with the limbs themselves: the part of the arm from the elbow to the tip of the middle finger is the "standard cubit [lit. by a man's forearm]" (Deut. 3:11); the span (zeret) was the distance between the tip of the little finger and the tip of the thumb with the fingers straddled. The measurement of the handbreadth was the width of the four fingers, and the fingerbreadth was measured according to the width of the finger. As time progressed, absolute and more precise values and relationships were established for these natural measures, though these were still named according to the parts of the body.
The large measures mentioned in the Bible are based upon crude estimates such as the range of the bowshot (Gen. 21:16), i.e., the distance which the bow is able to shoot the arrow. In several places in the Bible, the expression kivrat ʾ erez, "a short distance," is mentioned (Gen. 35:16; 48:7; II Kings 5:19) which seems to mean a journey of two hours. Greater distances were measured by days' journey (Gen. 30:36; 31:23; et al.).
Among the instruments used for measuring small units of length, the Bible mentions: ḥut, "thread" (Jer. 52:21); ḥevel, "rope" (Amos 7:17); ḥevel middah, "measuring line" (Zech. 2:5 ; kav (qav) ha-middah, "measuring line" (Jer. 31:38 ; petil pishtim… u-qeneh ha-middah, "line of flax… and measuring reed" (Ezek. 40:3). It is likely that all or some of these instruments were used regularly for linear measure and it should be noted that the rope served as a standard measurement of length among several ancient peoples.
Five small units of length are mentioned in the Bible. Their exact length is not explicit but their interrelations are generally established: kaneh (qaneh), "reed"; ʾammah, "cubit"; zeret, "span"; ṭefaḥ/ṭofaḥ, "handbreadth"; and ʾeẓbaʿ, "fingerbreadth." The most important and basic measure was the cubit. It appears that there were two values for the cubit which were in use in different periods: the short cubit is implicit in II Chronicles 3:3 in the description of the Temple, "in cubits of the old standard," and the meaning of the verse is that the measurements of the Temple are given in terms of the ancient cubit and not the longer royal cubit which was in use in this time. In the description of the future sanctuary in Ezekiel 40:5 (see also 48:13), the second or long cubit is mentioned: "and the length of the measuring reed in the man's hand was six long cubits, each being a cubit and a handbreadth in length." The cubit in this description exceeds the normal cubit by one handbreadth and thus contains seven handbreadths and not six like the short cubit. Ezekiel uses the long Persian cubit, which was in use also in Mesopotamia, and which may have come into use in Palestine during the time of the Return. (See Table: Units of Length-Bible.)
Table 1. Ratio between the Units of Length in the Bible
reed cubit handbreadth fingerbreadth According to the short cubit reed 1 cubit 6 1 handbreadth 36 6 1 fingerbreadth 144 24 4 1 According to the long cubit reed 1 cubit 6 1 handbreadth 42 7 1 fingerbreadth 168 28 4 1
Attempts have been made to learn the value of the cubit in terms of present-day measures by comparisons with ancient structures whose measurements are noted, such as the tunnel of Siloam dating to the reign of Hezekiah; or on the basis of the measurements of buildings which, in the opinion of their excavators, were built in whole cubits, such as the walls of Hazor, Megiddo, and Gezer from Solomon's time (I Kings 9:15); or by estimating the volume of "the molten sea" which stood in the Temple (I Kings 7:23 – 26; II Chron. 4:2). However, all of these calculations are unreliable. Various scholars (e.g., R.B.Y. Scott) – some on the basis of comparisons with Egyptian and Mesopotamian standards, and some according to parallels from Hellenistic sources – established the values shown in Table: Value of the Cubit.
Table 2. Conjectured Value of the Cubit
long cubit (28 fingerbreadths) – 521.0 mm. short cubit (24 fingerbreadths) – 446.0 mm. handbreadth (4 fingerbreadths) – 74.0 mm. fingerbreadth – 18.6 mm.
These figures probably approximate the actual values of the measures, but they cannot be considered precise.
As was the case with linear measures, human limbs were initially used to measure volume. The small units were: komeẓ (qomeẓ, "handful"; Lev. 2:2; 5:12), which is the measure of the grasp of three fingers and perhaps is the shalish mentioned in Isaiah 40:12; ḥofen (Ex. 9:8, et al.), which is the entire palm of the hand; and ḥofnayim, which is two handfuls. They were also accustomed to measuring with receptacles which the farmer used at home and in the field; the omer (ʿOmer) is a bundle of ears of corn; a quantity of wine in the measure of a skin (jar) is also mentioned (I Sam. 1:24). The values of these measures cannot be established, for it is certain that they were not precise; later on some of them did become fixed, their previous names being preserved. It is likely that various foods used to be prepared in fixed portions, and therefore the Bible notes quantities of food, liquid and dry, in numbers of portions without designating the volume (I Sam. 25:18; II Sam. 16:1, et al.).
The units of volume mentioned in the Bible are the following:
homer (Lev. 27:16; Isa. 5:10; Ezek. 45:11; 13:14; Hos. 3:2);
kor (Ezek. 45:14);
letekh (Hos. 3:2);
ephah (Ex. 16:36; Ezek. 45:11, 13; 46:14, et al.),
bath (Ezek. 45:11, 14; II Chron. 2:9);
se'ah (Gen. 18:6; I Sam. 25:18; I Kings 18:32; II Kings 7:1, 18, et al.);
hin (Ex. 29:40; Ezek. 45:24; 46:11, 14, et al.);
omer (Ex. 16:16, 36; Lev. 23:10 – 14, et al.);
ʿissaron (Ex. 29:40; Lev. 14:21; Num. 15:4, et al.);
qav (II Kings 6:25);
log, which is the small liquid measure (Lev. 14:10, 12, 15, 21, 24).
(See Table 3: Measures of Volume and Their Ratios).
Table 3. Measures of Volume and Their Ratios
Homer – kor letekh ephah – bath seʾah hin omer – ʿissaron qav log homer – kor 1 letekh 2 1 ephah – bath 10 5 1 seʾah 30 15 3 1 hin 60 30 6 2 1 omer – ʿissaron 100 50 10 3 1/2 1 ⅔ 1 qav 180 90 18 6 3 1 ⅘ 1 log 720 360 72 24 12 7 ⅕ 4 1
It is worth noting the mixture of the decimal system which was used in Egypt and the sexagesimal system of Mesopotamia which is most characteristic of the scale of weights and measures in Palestine. Also the names – as was noted – are in part from Egyptian measures and in part from Mesopotamian measures.
If a distinction is made between liquid and dry measures, the following tables can be set up as seen in Table: Dry and Liquid Measures.
Table 4. Distinction between Dry and Liquid Measures
Dry Liquid homer 1 kor 1 letekh 2 bath 10 ephah 10 hin 60 se'ah 30 log 720 omer–ʿissaron 100 qav 180
Scholars no longer attempt – as in previous generations – to equate these measures with Greek and Roman measures and thereby determine their absolute values, because this was based on conjecture only. The only method by which modern scholars can determine the values of these weights is to measure the volume of vessels discovered in excavations in Palestine whose capacity is marked on them, such as fragments of vessels with the words bt, "bath," or bt lmlk, "royal bath," written upon them. According to W.F. Albright's calculations, which are accepted by most scholars today, the "royal bath" has a capacity of 22 liters. (See Table: Scale of Measures of Volume.)
Table 5. Scale of Measures of Volume (Dry and Liquid)
homer-kor 220.0 liters letekh 110.0 liters ephah-bath 22.0 liters seʾah 7.3 liters hin 3.6 liters omer-ʿissaron 2.2 liters qav 1.2 liters log 0.3 liters
Aside from the inscriptions "bath" and "royal bath," some potsherds were discovered during excavations with inscriptions
which in general designate the type of goods and the quantity; however, for the most part, the names of the units of volume are missing from these inscriptions (a common practice in the Bible also; see I Sam. 25:18; II Sam. 16:1). A shard was found at Tell Qasileh bearing the inscription (according to the reading of B. Mazar), "To the king, 1,100 [measures of] oil, from Aḥiyahu." The liquid measure is not explicit: in the opinion of Mazar, the log is intended. Another inscription, discovered in Kadesh-Barnea, reads 51, and according to M. Dothan, it designates five measures of oil and the hin is intended. Also discovered in Samaria were tens of ostraca upon which measures of oil and wine are mentioned by the nbl, "skin" (biblical, nevel, cf. I Sam. 1:24; 25:18; II Sam. 16:1, et al.). The units of volume mentioned in the Elephantine papyri from the fifth century B.C.E. are seʾah and qav, the measure being designated by the first letter only. This way of designating measures continued in Palestine until the end of the Second Temple, as a vessel uncovered in the ruins of Qumran reveals. Upon it is inscribed: "two seʾah and seven log." This vessel has the capacity of 35.65 liters.
The main measure of area in the Bible is the ẓemed (I Sam. 14:14; Isa. 5:10), which refers to the area which a pair of oxen can plow in one day. This method of measuring area persists into the Mishnah and the Talmud Ancient Near East and later passed on to the Romans. In Rome the unit of area used was called jugerum from jugum, "yoke" (Pliny, Naturalis Historia, 18:9), while the modern measures feddan and acre have similar meanings. These measures, which in the beginning were not precise, in time became more clearly defined.
There was also another system of measuring area mentioned in the Bible, based upon the quantity of seeds sown in it (Lev. 27:16; I Kings 18:32; Isa. 5:10b (see *Targum )); and, needless to say, this measurement was not precise. This system was especially prevalent in Mesopotamia, and a formulation of this measure there reads: bīt 1 imēru, "property measuring one homer." This method of measuring area persists into the Mishnah and the Talmud (BB 7:1; 2:5, et al.) and is also attested in a deed from the time of the Bar Kokhba revolt. The Bible uses more precise measurement in its description of a rectangular area, noting the measure of the length and width in cubits or parts of cubits, and also adds the adjective ravuʿa, "square" (Ex. 27:1; 28:16, et al.). Ezekiel also notes the areas of the entire complex of buildings in the Temple in cubits (Ezek. 40).
WEIGHT IN THE BIBLE. The verb shql ("to weigh") is shared by all Semitic languages; and generally the system of weights used by Semitic peoples is the same. Weights, for the most part, were made of stone, hence the Bible refers to weights generally as "stones" (ʾeven). In Akkadian, weights are called also aban kīsi, "stones from the bag," which consist of stones placed in a cloth bag (Micah 6:11; Prov. 16:11, et al.). In Ugaritic too the word ʾ a bn, "stone," signified weights; but there have also been found many cast metal weights from the biblical period. During the Persian period, the metal weight became a coin and indication of this process can be seen in the Septuagint where the word for shekel, σίκλος, is changed to the word for the coin didrachm, δίδραχμον. Similarly they translated beka (beqaʿ), δραχμή, and gerah, ὸβολὸς.
In some ancient countries, especially in Mesopotamia, the old unit of weight was a seed of grain. Although the Bible used the names of early Mesopotamian weights, it does not mention this particular weight since the reciprocal relationship between Israel and Mesopotamia in weights, as in measures of volume, appears only in a relatively late period (apparently the Neo-Babylonian; see below).
Seven weights are mentioned in the Bible: talent, mina, shekel, beka, gerah, pim, and kesiṭah. A scale of the relationships between the first five weights mentioned can be established on the basis of the Bible and other sources; the absolute and relative value of the pim can be determined from archaeological finds (see below). The seventh weight, the kesiṭah (Gen. 33:19; Josh. 24:32; Job 42:11), seems to be an archaic weight and the origin of its name and its metrological value are not known. (Some believe it means rather "a sheep or goat.")
The basis of the biblical system of weights becomes clear by investigating the interrelationships of the three most important weights, the talent, shekel, and gerah.
The talent (kikkar), was the largest unit of weight in the Bible, and was already known by the same name in Ugaritic. In Ugaritic it was pronounced kakaru, as has been shown from Akkadian documents from Ugarit and Alalakh where the Canaanite name appears in the forms qaq (q) aru (m), kakaru (m). The very name kikkar testifies to the round shape of the weights. The relation between the talent and the shekel becomes clear in Exodus 38:25–26. The half shekel brought by 603,550 men amounted to 100 talents and 1,775 shekels. Thus the following calculations can be made as seen in Table: Shekel and the Talent.
Table 6. Relation between the Shekel and the Talent
603,550 half-shekels = 300,000 + 1775 shekels 300,000 shekels = 100 talents 3,000 shekels = 1 talent
This system of dividing the talent into 3,000 shekels differs from the Mesopotamian system which divides the talent into 3,600 parts, and is the same as the Ugaritic system where the talent is also divided into 3,000 shekels. From this it follows that the biblical division is based upon an ancient Canaanite tradition.
The shekel (Akk. šiqlu; Ugaritic, ṯ~ql; early Aram. shql; late Aram. tql) is the most basic weight, as its name, which means simply weight, testifies. Since the shekel is the definite weight, an expression such as "1,000 silver" (Gen. 20:16) can be explained as 1,000 shekels of silver, and the name of the weight is omitted since it is self-explanatory. Abbreviations
like these are also found in other Semitic languages. The fundamental nature of the shekel can also be seen in the fact that all weights which the Bible explains are explained only in terms of the shekel.
The gerah is known in Akkadian as girû. The basic meaning of the Akkadian word is a grain of carob seed. The value of the gerah is the 20th part of a shekel (Ex. 30:13), unlike the Akkadian girû which is the 24th part of a šiqlu. S.E. Loewenstamm noted that the ratio 24:20 is identical with the ratio 3,600:3,000, and therefore he holds that the division of the shekel into 20 gerah is based upon the same ancient Canaanite tradition according to which the talent was divided into 3,000 shekels.
The mina (Heb. maneh; Sum. mana; Akk. man –; Ugaritic, mn), which designates a weight of approximately 50 or 60 shekels (see below), is found in the Bible primarily in the late books (Ezek. 45:12; Ezra 2:69; Neh. 7:70, 71). In the period preceding the destruction of the First Temple, the mina is mentioned only once, in the verse about Solomon's shields (I Kings 10:17). From this it is reasonable to assume that in ancient times in Israel reckoning was done in shekels and talents only, and the mina was not used except in unusual situations. It appears that this practice too had its roots in an ancient Canaanite tradition, for in Ugaritic writings many calculations are found involving shekels and talents and very few involving the mina. The value of the mina is defined in Ezekiel 45:12. From this verse it follows that the mina is equivalent to 60 shekels like the Akkadian man –. However, there is reason to assume that Ezekiel's definition was influenced by his Mesopotamian environment, and that the Canaanite-Israelite mina was equivalent to only 50 shekels. First, it appears that there are two systems intertwined in Ezekiel's words. Portions of 15 and 20 shekels are appropriate for a mina of 60 shekels, as they equal a fourth and a third of it. Not so a portion of 25 shekels which is appropriate only for a mina of 50 shekels, of which it would comprise half. F. Thureau-Dangin found support for the existence of a Canaanite mina of 50 shekels in Ugaritic weights which contain 50 Ugaritic shekels. He regarded these as weights of a mina. According to this, the ratio of the Mesopotamian weight to the Canaanite weight would be 60:50, like the ratios 3600:3000 and 24:20 which were dealt with above. Support for this system can also be found in the passages which speak of payment of 50 or 100 shekels (Deut. 22:19, 29, et al.), which probably refer to payments of one or two minas. Moreover, there are signs that the Mesopotamian system of Ezekiel did not succeed in supplanting the Canaanite system. The Septuagint (LXXA) reads for Ezekiel 45:12: "five shekels shall be five shekels, and ten shekels shall be ten shekels, and your mina shall be fifty shekels"; and although Borrois advanced proofs to show that this version should not be preferred over the Masoretic Text, this version is significant. It provides evidence that at the time of the translation, the mina consisted of 50 shekels.
The beka is mentioned twice in the Bible (Gen. 24:22; Ex. 38:26) and its value is explicitly determined as one-half a shekel. Its name is derived from the root bqʿ, "to break, to divide," and its basic meaning is "a part." According to the reckoning of a mina as 50 shekels, the Table: Weight and their Ratios 1 may be set up:
Table 7. Measures of Weight and Their Ratios (mina = 50 shekels)
talent mina shekel beka gerah talent talent 1 mina 60 1 shekel 3,000 50 1 beka 6,000 100 2 1 gerah 60,000 1,000 20 10 1
However, on the basis of Ezekiel 45:12 according to which the mina contains 60 shekels and on the assumption that Ezekiel divided the talent (kikkar) into 60 minas, the Table: Weight and their Ratios 2 may be set up.
Table 8. Measures of Weight and Their Ratios (mina=60 shekels)
talent mina shekel beka gerahtalent talent 1 mina 60 1 shekel 3,600 60 1 beka 7,200 120 2 1 gerah 72,000 1,200 20 10 1
This table is arranged according to the Mesopotamian system and contains nothing from the Canaanite-Israelite system except the division of the shekel into 20 gerah instead of 24.
In addition to being divided into the beka and gerah, the shekel is also divided into a fourth and a third (I Sam. 9:8; Neh. 10:33). There is support for this division both inside and outside Palestine. From Assyrian documents found at Calah it is evident that the shekel was very often divided there into many more subunits, but there is no proof that this was so in Israel as well.
Also mentioned in the Bible is the peres (Dan. 5:25, 28), and C. Clermont-Ganneau has suggested that it is half a mina. This weight is mentioned also among bilingual weights (Akkadian-Aramaic) from the Persian period and its written form is פרש. The peres is also mentioned in the Mishnah (Pe'ah 8:5; Ḥul. 11:2) and its value there is half a zuz.
In establishing the value of the shekel there is an additional complication in that the Bible mentions at least three kinds of shekels: in Genesis 23:16, a shekel of silver "at the going merchant's rate [ʿover la-soḥer]," which is similar to the Akkadian expression ina manê ša tamkari, "in the merchant's mina"; in Exodus 30:13, "shekel by the sanctuary weight [ha-qodesh]"; and in II Samuel 14:26, "shekels by the king's weight [be-ʾeven ha-melekh]," that is, shekels stamped by the royal treasury as proof that they are perfect. Also in the Elephantine papyri from the Persian period it is said "royal weight" (באבני המלכא or במתקלת מלכא). It cannot be determined whether these shekels were equivalent in value, but
on the basis of evidence from external sources, it appears that there were differences between them.
ARCHAEOLOGICAL FINDS. In excavations carried out in Palestine many weights have been uncovered – some with the weight marked on them, but most without any notation. The shape of the weights, for the most part, is semicircular (dome-shaped). There are also some cast metal weights that are rectangular and cube-shaped, and some that are oval or in the shape of animals. Most of the weights found in Palestine are from the end of the period of the monarchy (the seventh to sixth centuries B.C.E.).
Very few weights and inscriptions with the word shekel written explicitly have been found in strata from the Israelite period. A bronze weight in the shape of a turtle was found in the coastal plain; on its reverse side it bears the inscription (according to the reading of A. Reifenberg) פלג שקל, and on the front, פלג רבעית, and its weight is 2.63 gm. And in fact, a weight of this sort (one-quarter shekel) is mentioned in I Samuel 9:8. Another bronze weight from Samaria, also in the shape of a turtle, bears the inscription חמש ("five"), and this has been interpreted to mean five gerahs, that is one-quarter of a shekel, and its weight is 2.49 gm. Another weight from Samaria is marked on one side ל[ק]רבע ש and on the other רבע נצף, and its weight is 2.54 gm. (see below). At Tell Qasileh an ostracon was found with the following inscription engraved upon it: ז]הב אפל לבית חרן] and here too, B. Mazar interprets the letter sin to mean shekels. Two ostraca containing calculations in shekels were also found in Yavneh-Yam. Many weights found in excavations bear a special mark in the form of
ש, with another sign next to it which in general designates the number of units. These weights have for some time been considered shekels. They were discovered for the most part at localities in the Kingdom of Judah, in the following places: Gibeon, Jerusalem, Ramat-Raḥel, Gezer, Tel Zechariah, Tell Jedideh, Lachish, En-Gedi, Tel Malḥatah, and Arad; and others in the coastal plain; Tel Jemmeh, Nebi Rubin, Yavneh-Yam, and Ashdod. Only one weight of this type is known from the area of Samaria, and it was discovered at Shechem. Many others of unknown provenance are in private collections.
Scholars have been greatly divided as to the interpretation of the sign X which appears on the weights. Thompson thought that this sign was taken from the Egyptian nb ("gold") weight which weighs approximately 12 gm. On the basis of a bronze weight of 12.28 gm. which was discovered at Gezer and upon which is written the number two and next to it lmlk, Diringer and Borrois maintain that the purpose of this sign is to designate the royal shekel which was fixed at 11.3 gm.; and this was the accepted opinion among scholars in the past. Recently the debate was revived when R.B.Y. Scott suggested that the sign be interpreted as a schematic drawing symbolizing the word ẓeror, that is, a cloth bag, tied at the top, in which precious metals were wrapped. Y. Yadin, basing his opinion on these weights from Gezer and upon the image of a scarab found in the Elephantine Papyri upon which the word למלך, lmlk, also appears, maintains that this sign is merely a schematic drawing of the well-known royal scarab which is found on common lmlk seals. In his opinion, in every case where this sign is written, it serves as a recognized sign designating the word lmlk, that is, the official royal standard.
Alongside this sign is usually written an additional sign which all scholars interpret as a number which notes the quantity of royal shekels contained in each weight. By examining the average weight of all the weights of this kind which have been discovered up till now, it becomes evident that they were clearly divided into weights of one unit (11:3 gm.); two units (22.6 gm.); four units (45.5 gm.); eight units (91.2 gm.); 16 units (188.5 gm.), and 24 units (268.24 gm.). In line with this, Yadin assumes that the numerical signs are Hebrew and signify parallel units (that is, they designate the numbers 1, 2, 4, 8, etc.). Against this, Aharoni, following Scott, conjectures that these numbers are actually Egyptian-hieratic which were copied on weights of the Judahite kingdom and stand for the values 5, 10, 20, and 30. The contradiction between the division of the weights into units of 4, 8, 16, and 24 and the values of the Egyptian numbers he explains by saying that the basic weight, that of eight shekels, is identified with the Egyptian dbn which was chosen by Josiah for international trade. Since the dbn weight is divided into 10 qdt, it means that Judahite weights of 4, 8, 16, and 24 units are equivalent to 5, 10, 20, and 30 qdt. The hypothesis of Scott and Aharoni that the signs on the large units are Egyptian is reasonable, all the more so since much important evidence has been gathered concerning the use of hieratic numbers in Israel during this period (from an ostracon from Arad, among other sources). However, in spite of this, it is difficult to assume that the Egyptian system itself was adopted in Israel, since the basic unit in the shekel system – as Aharoni also notes – is a weight of eight shekels. This division, different from that practiced in Egypt (division by tenths) or Mesopotamia (division by sixths), and which is evidence of Phoenician-Israelite local distinctiveness, is the same phenomenon which was found in the biblical system of weights. Likewise, it is difficult to imagine that they used one system for weighing and actually meant a different system (an uncommon situation in the metrological systems of the Ancient Near East). Another suggestion which Aharoni himself raised, and then rejected, is more reasonable; it is that the Egyptian numbers were carved on the weights because of their simple form (it is difficult to carve complex numbers on small stone weights) without paying attention to their original values, and that the Egyptian number five was understood to be four in Israel. Support for this interpretation is found on an ostracon from Yavneh-Yamon which, according to the reading of J. Naveh, is inscribed "the weight of four [shekels of] silver" and next to it is the common sign for the unit of four shekels, which is to say that they did not read this number five and intend four, but rather also read the number as four.
Weights with Designations Discovered in Israel. Three other types of weights, also from the end of the Kingdom of Judah,
have been discovered in Israel and their names are inscribed on them in full: nẓp, pym, and bqʿ.
The word nẓp does not appear in the Bible and is known only from the inscriptions on these Hebrew weights, and also from Ugaritic. The word nẓp is explained on the basis of the Arabic nisf, "half." If this interpretation is accepted, the weight of the nẓp unit is half of 19.75 gm. since the average weight of the nẓp is 9.8 gm. This unit of weight is not known in Israel. In R. de Vaux's opinion, the nẓp is half the weight of the Ugaritic shekel, which is known as the "heavy shekel" and weighs from 18.7 to 23.4 gm. It is also possible that the nẓp does not belong at all to the metrological system based on the shekel but rather to a different and unknown system. At least one weight which is a subunit of the nẓp was found in Samaria. On it is written רבע נצף, "one quarter," and it weighs 2.54 gm. According to this, the whole nẓp weighs 10.16 gm. However, on the second side of the weight is written ל[ק]רבע ש, "one-quarter shekel," and some see this as additional proof that two standards existed side by side in Israel, and one weight could be at the same time one-half shekel according to one standard and a whole shekel according to the other. Seventeen nẓp weights have been discovered.
The pim is mentioned once in the Bible (I Sam. 13:21). Pim (pym) weights which were uncovered in excavations helped to clarify the obscure verse I Samuel 13:21, but not to explain the name. Several scholars tried, unsuccessfully, to explain it. Clermont-Ganneau suggested: pi (shenayi) m (according to Zech. 13:8), that is two portions, i.e., two-thirds. E.A. Speiser held that its source is from the Akkadian šinipu, that it means two-thirds (of a shekel), and that in Canaan they borrowed the last part of the word from Mesopotamia, interpreted it as a third, and made it dual. Diringer and Borrois also think that the pim is two-thirds of a standard shekel but that Speiser is correct that the source of the word is foreign and that it has no meaning in Hebrew. Twelve such weights have been discovered, and their average weight is 7.8 gm.
The beka is the one unit of weight mentioned in the Bible whose value has been determined. It is half a shekel (see above). However, this value does not correspond to the beka (bqʿ) weights found in excavations. In Israel, seven weights have been found with the name beka written on them. On some the name is written in full, and on some only the letter ב (beth) appears. Their average weight is 6.03 gm. more than the value of the half-shekel of 11.3 gm. The heaviest one is 6.65 gm. and the lightest 5.55 gm. Petrie believes that the beka is an extremely ancient unit of weight which was used in Egypt and has been discovered in pre-dynastic graves of the Amration period (the fourth millennium B.C.E.). In his opinion, the beka was the common weight used in Egypt for gold and its weight was 12.28–13.90 gm. If Petrie's opinion is accepted the Israel beka would be half the weight of the Egyptian weight which Petrie established as the Egyptian beka. Reifenberg publicized a coin from the Persian period bearing the inscription beka; its weight is 3.88 gm. Weights Marked with Numbers. In addition to the aforementioned weights, some 20 weights marked with numbers (either letters or numerals) have been uncovered in excavations, and their weights range from 1.52 to 7.05 gm. Recently, Scott has gathered all the above-mentioned finds, sorted them into groups, and tried to determine their precise relationships to the perfect weights mentioned above. However, all attempts – those of Scott as well as his predecessors – to determine the exact value of these small weights, are very unreliable since there are no written sources about the detailed division of the Israelite shekel into small subunits.
A large number of weights have been discovered which contain no inscription, no number, and no sign whatsoever. Examination of these weights has not led, in general, to sufficient clarification. Among them, it is worth noting in particular two weights. One was found at Tell Beit Mirsim, weighing 4,565 gm., and in W.F. Albright's opinion has the value of eight minas of 50 shekels each (that is, the weight of 400 shekels). The second is a basalt stone weight from the area around Taanach which weighs 4,780 gm. This weight is decorated with the relief of a winged lion and in addition bears the personal name Šmʿ. In N. Avigad's opinion, the value of this weight is eight minas of 50 shekels, that is, 400 shekels, which, he believes, is a standard weight (compare "four hundred shekels of silver at the going merchant's rate," Gen. 23:16). Scott's explanation as noted above is that the shekel weights were established according to the Egyptian standard and interprets the unit of 400 shekels as 50 dbn. In his opinion, that is the reason for the special Israelite system of weights which contains only 50 shekels in a mina. However, we have already found this division at Canaanite Ugaritic and it is more plausible that the special Israelite system was based upon the ancient Canaanite system and not the Egyptian system.
[Eliezer Bashan (Sternberg)]
In the Talmud
After a long and complex development (cf. Jos., Ant., 14:105; 3:144), the talmudic system emerges. In it the Italian mina was equated with 100 denarii (TJ, Shek. 2:4, 46d; mina = litra = Roman libra originally; TJ, Ter. 10:7b), thus equaling 1 1/24 Roman pounds (Tanḥ. B., Ex. 109). However, the Talmud mentions yet another maneh of 40 shekels (160 denarii; Ḥul. 137b–138a), and there were also regional variations (Ḥul. 12b). The biblical gerah was identified with the current me'ah ("obol" = ⅙ drachma; Bek. 50a). The syncretist system was linked to the Tyrian standard and conveniently dovetailed with the monetary system. (See Table: Syncretist System in the Talmud.)
Besides the rough and ready measures, e.g., komeẓ ("three-fingers full"; Lev. 2:2), or ḥofen ("handful"; Ex. 9:8, etc.), a carefully graduated system, primarily of Mesopotamian origin, was used from earliest times both for dry and liquid measures. The relationships between the various denominations are amply attested, revealing the system. (See Table: Measures of Volume in the Talmud.)
Table 9. Syncretist System of Weights and Measures in the Talmud
Kikkar ("talent") mina Italian mina tartimar (=⅓) Unkiyyah "uncia") sela ("hetra-drachm") Shekel ("biblicalshekel") zuz ("denar-ius") Kikkar ("talent") 1 37 60 120 750 1,500 3,000 6,000 mina 1 1/2 1 ⅖ 3 ⅕ 20 40 80 160 Italian mina 1 2 12 1/2 25 50 100 tartimar 1 6 1/4 12 1/2 25 50 Unkiyyah ("uncia") 1 2 4 8 sela ("hetra-drachm") 1 2 4 Shekel (" 1/2 biblical shekel") 1 2 zuz ("denar-ius") 1
Table 10. Measures of Volume (Dry and Liquid) in the Talmud
1 2 3 4 5 6 7 8 A. Dry homer letekh ephah seʾah - omer qav - B. Liquid kor - bath - hin ʿissaron - log 1 homer kor 1 2 10 30 60 100 180 720 2 letekh - 1 5 15 30 50 90 360 3 ephah bath 1 3 6 10 18 72 4 seʾah - 1 2 3 1/2 6 24 5 - hin 1 1 ⅔ 3 12 6 omer ʿissaron 1 1 ⅘ 7 ⅕ 7 qav - 1 4 8 - log 1
The table shows the influence of the sexagesimal system with a parallel decimal subdivision, while philological analysis shows the terms to be derived from Mesopotamian (e.g., 1AB, 4), Egyptian (3A, 5B), and Canaanite (2) sources. In rabbinic times the log was further subdivided as follows: 1 log = 2 toman = 4 revi'it = 6 beiẓah ukl a = 36 mesurah = 64 kurtov. According to Eruvin 83a there were at least three standards current (with a 30% variation; cf. Jos., Ant., 3:197, 321; 8:57; 9:86), but the basic standard was probably linked to the Roman one (Kelim 17:11), so that the log equaled the sextarius (Gr. xestes), giving a se'ah of 1½ modii -16 sext. = 1 mod. -(but cf. TJ,
Ter. 5:1, 43c). For cubic equivalents see TJ, Pesaḥim 10:1, 37c, where 1 revi'it = 7⅓ cu. eẓba ("digit"), while Eruvin 14b states that a mikveh containing 40 se'ah is 3 cu. ammah. However, in view of the differing standards of length (see below), it is difficult to reach any absolute value for these measures.
Alongside this developed system of exact measures, the rabbis introduced a series of "rule of thumb" measures, readily recognizable by all. Thus one was punishable for eating (most) forbidden foods only after having had an amount equal to a medium-sized olive (ke-zayit). The standard for (transgressing the stricture on) leavened bread on the Passover and for eating on the Day of Atonement was a (large) kotevet (a certain species of date), while that for carrying on the Sabbath was a gerogeret ("dried fig"). These measures bore no easy relationship to the established metrological system. They themselves were at most ready and approximate, and their relationship to the exact measures likewise. Thus the ke-zayit was probably about half a beiẓah, the gerogeret larger than the ke-zayit but smaller than the kotevet, and the kotevet larger than the gerogeret but still smaller than a beiẓah. In recent years the size of these measures has been the subject of considerable controversy.
Length. The most common metrical denominations are measures of length derived from parts of the human body: the finger-breadth (digit), handbreadth or palm, cubit (from cubitum, elbow) or length of the forearm. It is this latter, in Hebrew ammah, which appears to be the basic unit of the Palestinian system (Kelim 17:9–10). Normally the ammah consisted of handbreadths (tefaḥ, pl. tefaḥim); however, Ezekiel 40:5 and 43:13 suggest that there was also an ammah of seven tefaḥim. This seems to be paralleled by the Egyptian system, which had a "short" cubit of six handbreadths, and a "royal" one of seven. The Mishnah too tells of different ammot (Kelim, ibid.). There is considerable discussion as to the precise length of the ammah (or ammot), as different sources yield varying results, and much has been written on the subject. All that can be stated with real certainty are the relationships between the different units:
1 ammah = 3 zeret = 6 tefaḥ = 24 eẓba. The only multiple of the ammah mentioned in the Bible is the kaneh ("reed") of Ezekiel 40:5, which according to Menaḥot 97a equals six ammot. Longer measures were approximate, e.g., a bowshot (Gen. 27:16), day's journey (Gen. 30:36, etc.; see also Gen. 35:16). In the Greco-Roman period there was a syncretistic system for the longer measures, in which the mil (Roman mile, milion in Matt. 5:41) of 2000 ammah was reckoned at 7½ stadia (Heb.
ris, Yoma 6:4), giving a convenient division of the parasang (Heb. parsah) into 30 stadia.
Surface. In biblical times the concept of area was expressed by squaring the length, i.e., "x ammot squared" (ravu'a, passive participle from arba, "four"). In the Mishnah it is expressed in the form "x ammot by [al] × ammot." In antiquity two methods were used to measure land:
(a) a standard was based on the area plowed by a yoke of oxen in a given time (cf. Roman jugum, jugerum);
(ii) an area was judged by the amount of seed required to sow it (a method of Mesopotamian origin).
Both methods were known and practiced in biblical times, the former being alluded to in Isaiah 5:10, the latter in I Kings 18:32 (cf. Lev. 27:16). In the Mishnah the size of a field is uniformly calculated by the second method. The whole series of dry measures (see above) was employed in this system. The size of these surface measures may be in terms of ammot from certain talmudic equations. Thus from Eruvin 96a it emerges that a "beit se'atayim" (2 se'ah plot) equaled the area of the Tabernacle's court, 5,000 sq. ammot. Hence, a "beit se'ah" = 2,500 sq. ammot (BB 26b). The obscure ma'anah of I Samuel 14:14 is identified with a four se'ah plot (= beit haperas; Oho. 17:1), and said to be 10,000 sq. ammot. (See Table: Measures of Surface.)
The ammah varied between the approximate limits of 45.75 and 53.34 cm. (18 and 21 in.), but the upper limit may be even higher (21½ in., for example). The beit se'ah, which was 2,500 sq. ammot would therefore be equal to 1,143 – 1,333.5 sq. m. However, the variation in se'ah measures would affect this calculation.
The basic measure of capacity is the log:
1 log midbarit = 503.5 cc. = grm (= 30.7 cu. in.)
1 log yerushal mit = 699.4 cc. = grm (= 39.6 cu. in.)
1 log sepphorit = 777.4 cc. = grm (=47.4 cu. in.)
The basic weights were the sela = 224 grains and the mina (40 selas) = 8,960 grains. All other measures may be calculated from these, according to the ratios given. However, the resultant calculations will only have a "probability truth-value," as the range of variation grows in the higher multiples.
As measures (shi'urim) are of great halakhic importance, there were throughout the ages constant attempts to reevaluate them in current terms. There has thus grown up over the years a considerable body of halakhic material dealing with metrology, which affords much valuable information.
Criminal Law. The biblical injunction, "You shall not have in your pouch alternate weights, larger and smaller; you shall not have in your house alternate measures, a larger and a smaller; you must have completely honest weights and completely honest measures" (Deut. 25:13–15) was interpreted not as prohibiting any fraud by means of false weights and measures (which is dealt with in Lev. 19:35–36), but as applying to the manufacture or possession of any weights or measures, including utensils (such as pots or pitchers), which might be used for weighing or measuring and cause false weighing or measuring (BB 89b; Maim. Yad, Genevah 7:3; Sh. Ar., ḤM 231:3). While the manufacture of false weights and measures may be punishable with *flogging , the mere possession thereof is not, the violation of a negative injunction being so punishable only where an act is committed, as distinguished from the omission to get rid of the prohibited utensils. In order effectively to enforce the prohibition, courts in talmudical times appointed market inspectors charged with the control of all weights and measures even in private houses (BB 89a). There are detailed provisions for the manner in and the materials with which weights and measures are to be manufactured or repaired so as to be and remain accurate (Maim. Yad, Genevah, 8:4–11; Sh. Ar., ḤM 231:4–11). It is said that the crime of false measures is graver than even those crimes (like incest) which are punishable with karet ( *Divine Punishment ); the latter can be expiated by repentance and flogging, whereas in the case of the former repentance is of no avail, since neither the damage caused or the persons to whom restitution has to be made can be ascertained (BB 88b and Rashi ad loc., Maim. Yad. Genevah 7:11).
[Haim Hermann Cohn]
The Approach in Jewish Law
The dominant approach in Jewish law to the subject of weights and measures is the insistence that any doubt be resolved by the merchant in favor of the customer. Where the price is established by weight according to a scale, the merchant compares the two sides of the scale – the weight as opposed to the merchandise. However, if it is difficult to be certain of the comparison, the merchant must make his estimation in favor of the customer. Where the custom was not to make such a
Table 11. Measures of Surface and Their Ratios
beit-kor beit-letekh beit-peras beit-zemed beit-se'ah beit-kav beit-rova square ammot beit-kor 1 2 7 1/2 10 30 180 720 75,000 beit-letekh 1 3 3/4 5 15 90 360 37,500 beit-peras 1 1 ⅓ 4 24 96 10,000 beit-zemed 1 3 18 72 7,500 beit-se'ah 1 6 24 2,500 beit-kav 1 4 416 ⅔ beit-rova 1 104 ⅙ square ammot 1
determination, the merchant must add an additional amount of merchandise for which he does not charge, and there is also a minimum amount that is required to be added. This law is derived from the verse in Deuteronomy 25:15: "A perfect and just weight…" and, as explicated in the Talmud, "'just' – [take] of yours and give him" (BB 88b; Sh. Ar., ḤM, 231:14). Due to the stringency of the requirements, the question arises as to whether imprecision in weights and measures may be pardoned. Tosefta BB 5:4 states: "…one sells to another one log [liquid measure or dry measure] and a half [log], a quarter [log], an eighth [log]: when he calculates the bill he may not say fill up this measure and say, sell me this (kortov) (1/64 portion) for the science of measures is not dependent on people, and it is God who has set his name upon them, because the verse ends with 'I am the Lord your God' [Lev 19:36]." Some commentators are of the opinion that agreeing to pardoning inexactitude is not effective, insofar as it may mislead people into thinking that this is the local custom, from which they will learn to cheat. Others are of the opinion that pardoning is effective, based on the Mishna in BB 7:2 (BB 103b), regarding one who sells a bet kor (area of land in which one can sew a particular amount of produce) and says to the buyer that the measure is "more or less." Even if he sold less or more, up to a certain percentage of the quantity a deviation of certain amount is permitted, and the transaction is valid (see Sh. Ar., ḤM 231:1 and Kesef Kedoshim; ibid; 209.1, Sh. Ar., ḤM 209:1; Teḥumin 3, p. 338).
The question arises today in the context of factories requesting a certain acceptance of imprecision on their part. The term for this is "scale tolerance." For example, a factory packages a line of products on a production line; each box or bag is stopped at a particular point on the line for a predetermined number of seconds, is filled with a predetermined amount from a container that is poured into it, is automatically closed, and continues on the line. The manufacturers claim that on occasion, unpredictably, the measurements in this process will be imprecise, as in the case where some of the product is spilled or the bag's progress is off schedule on the production line by a second more or less. They therefore demand that they not be checked on the basis of a single bag, but rather according to the average of a number of bags. The European Market has approved this arrangement – one which seems to require an act of pardoning imprecision in advance. If, on the other hand, we were to require the manufacturers to take into consideration the "determination" in favor of the consumer, they would raise the price of the product accordingly. It may be that an arrangement could be used whereby the labeling states that the package contains 98 to 102 tea bags, as in the case of the declaration of "more or less" cited above, or perhaps 98 to 103 tea bags, in order to fulfill the obligation of the determination in favor of the customer (see Tehumin 3, supra).
[Itamar Warhaftig (2nd ed.)]
GENERAL BIBLIOGRAPHY: G. Cardascia, Les Archives des Murash – (1951), 199; S. Moscati, Epigrafia ebraica antica (1935–50), 83–98; A.E. Berriman, Historical Metrology (1953); D.J. Wiseman, Alalakh Tablets (1953), 14–15; A. Goetze, The Laws of Eshnunna (1956), 186; C.F. Nims, in: Journal of Egyptian Archaeology, 44 (1958), 56–65; J.B. Pritchard, Hebrew Inscriptions and Stamps from Gibeon (1959), 29–30; R.B.Y. Scott, in: BA, 22 (1959), 22–40. MEASURES OF LENGTH: Clarke-Engelbach, Ancient Egyptian Masonry (1930), S.V. measurements; C.L. Wodley, Ur of the Chaldees (1954), pl. 10b; R.B.Y. Scott, in: JBL, 77 (1958), 205–14. VOLUME MEASUREMENTS: K. Sethe, in: Zeitschrift fuer aegyptische Sprache und Altertumskunde, 62 (1926), 61; F. Thureau-Dangin, in: Revue d'assyrologie et d'archéologie, 25 (1928), 115–8;27 (1930), 65–71;28 (1931), 109–19; 29 (1932), 189–92; 32 (1935); 1ff.; 34 (1937), 80–86; C.H. Gordon, in: BASOR, 78 (1940), 10–11; E.L. Sukenik, in: Kedem, 1 (1942), 32–36; H. Lewy, in: JAOS, 64 (1944), 65–73; D. Diringer, in: BA, 12 (1949), 76 86; N. Avigad, in; IEJ, 3 (1953), 121–2; V.R. Grace, in: S. Weinberg (ed.), The Aegean and the Near East (1956), 86–109; R.T. Hallock, in: JNES, 16 (1957), 204–6; B. Parker, in: Iraq, 19 (1957), 125–38; J.T. Milik, in: Biblica, 40 (1959), 985ff.; P.W. Lapp, in: BASOR, 158 (1960), 11–12. AREA MEASUREMENTS: K. Baer, in: JNES, 15 (1956), 113ff.; S.E. Loewenstamm, in: IEJ, 6 (1956), 221–2. WEIGHTS: Cowley, Aramaic; F. Thureau-Dangin, in: Revue d'assyrologie …, 24 (1927), 68–75; A. Reifenberg, in: JPOS, 16 (1936), 39; idem, in: Matbe'ot ha-Yehudim (1948); 7–10; idem, in Yedi'ot, 15 (1950), 70; M. Narkiss, Matbe'ot ha-Yehudim (1936); A.S. Hemmy, in: JEA, 23 (1937), 39ff; D. Diringer, in: PEQ, 74 (1942), 82–103; J. Friedrich, in: Wiener Zeitschrift fuer die Kunde des Morgenlandes, 49 (1942), 17–9; A.J. Sachs, in: BASOR, 96 (1944), 29–39; idem, in: JCS, 1 (1947), 67–71; H. Lewy, in: BASOR, 98 (1945), 25; W.F. Albright, ibid., 110 (1948), 74, n. 21; S.R.F. Glanville, The Legacy of Egypt (1953), s.v. weights; E.G. Kraeling, The Brooklyn Museum Aramaic Papyri (1953); J.J. Finkelstein, in: Anatolian Studies, 7 (1957), 137; N. Glueck, in: BASOR, 153 (1959), 35–38; R.B.Y. Scott, ibid., 32–35; Y. Yadin, in: Scripta Hierosolymitana, 8 (1960), 1–17; J. Naveh, in: IEJ, 12 (1962), 27–32. IN THE TALMUD: ET, 1 (1951), 343, S.V. Eifah ve-Eifah; EM, (1950), 272f., S.V. Eifah ve-Eifah; 4 (1962), 846–78, S.V. Middot u-Mishkalot; M. Bloch, Das mosaisch-talmudische Polizeirecht (1879), 35ff.; Y. Gilat, Mishnato shel R. Eliezer b. Hyrcanus (1968), 11–20; idem, in: Tarbiz, 28 (1958/59), 230ff.; A. Segré, Metrologia (It., 1928), 55–93; S. Ganzfried, Kiẓẓur Shulḥan Arukh, ed. by D. Feldman (1927), 169–208 (second pagin.); A. Naeh, Shi'urei Torah (1947); B, Naeh, in: Shanah be-Shanah (1962), 89–99; Sperber, in: Journal of the Economic and Social History of the Orient, 8 (1965), 266–71. ADD. BIBLIOGRAPHY: M. Elon, Ha-Mishpat ha-Ivri (1988), 1:558, 560, 567, 584, 592, 610ff., 701, 821; 2:846, 879, 881, 1000, 1223; idem, Jewish Law (1994), 2:679, 681, 689, 719, 732, 754ff., 865, 1006; 3:1034, 1074, 1210, 1465; I. Wahrhaftig, Haganat ha-Ẓarkhan le-Or ha-Halakhah, Teḥumin, 3 (1982), 334–82.
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