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Length in Relation to
Volume and Weight


1. The relation among the units of length can be explained by the ratio 15:16:17:18 among the four fundamental feet and cubits. Before I arrived at this discovery, Decourdemanche and Oxé discovered that the cubes of those units are related according to the conventional specific gravities of oil, water, wheat and barley.

In terms of the logical structure of the ancient system of measures, the organization of the units of length by the ratio 15:16:17:18 precedes that of the units of volume and weight according to the ratio 163:163:173:183. But this ratio of volumes and weights, by which each unit is 1/5 more than the lower one, is the reason why there was introduced the relation 15:16:17:18 among units of length. It was necessary to have units related as 5:6 in order to take into account the specific gravity of what (0.8) in relation to water and that of barley (0.666) in relation to wheat. Hence, it is not surprising that modern scholars came to the realization of the structural relation among units of volume and weight, before my realization of the relation 15:16:17:18 among the units of length.

Having noticed the ratio among the units of length, I can further clarify the scheme presented by Oxé in 1942. fundamental units of weight relate as:

 
 

153 =3375

163 =4096

173 =4913

183 =5832

With small adjustments each unit is 6/5 of the lower one, since

 
 

6/5 3375 = 4030

6/5 4096 =4915

6/5 4913 = 5896

I have determined that, even though the ratio between a volume of water and a volume of wheat is calculated as 5:6 and that between a volume of wheat and a volume of barley is also calculated as 5:6, one aims at keeping the simple relation 2:3 between the volume of water and a volume of barley. Two successive increases by½ should be equal to an increase by½; this can be achieved by introducing the discrepancy leimma or 24:25, since 25/24 x 6/5 x6/5 - 900/600 - 3/2. This is the reason for the existence of this discrepancy by Lehmann-Haupt. The disrcepancy, leimma is usually taken into account in the ratio between volume of water and volume of wheat which is calculated eitheir as 5:6 or 4:5. I have shown that these two types of ratio of water (wine) to wheat units, are still used today in English and American measures. There were some kinds of wheat that had a specific gravity higher than O. 8, but in general one had to calculate by this specific gravity and relate volumes of water and wheat as 4:5. As Oxé has implied, usually it is the water (wine) measures that is reduced of a leimma to a unit netto; the unit of volume for wheat is 5/4 of the water unit netto and 6/5 of the same unit brotto. It is the cube with an edge of 16 natural basic fingers that is usually reduced of½5 .

Oxé has called attention to the circumstance that the shilf from brotto to netto units of volume and weight, allows a shilf from decimal to duodecimal computation, by assuming the equivalence of these two serious:

 
 

24 48 72 96 120 144 288

25 50 75 100 125 150 300

The accurrence of the factor 120 and 150 indicates that both series can be fitted into sexagesimal reckonings. The unit of 150 has the usual relation 6:5 to the unit of 120. In cuneiform documents one uses two minai and two pints related as 6:5, but most commoly the pind, unit of volume , is 6/5 of the mina, unit of weight.

As I have determined, the difference between netto and brotto units results in the distinction between the trimmed and the natural version of the units length, according to the ratio 3Ã24: 3Ã25.

There are as many talents as there are types of foot. This can be expressed by the following table , in which, in order to make comparison easier, I have calculated all figures in cubic fingers of trimmed foot.

netto 

 brutto

Cube of 15 basic fingers

little talent
3375
3515.625

Cube of 16 basic fingers

basic talent
4096
4266.650

Cube of 17 basic fingers

wheat talent
4913
5117.708

Cube of 18 basic fingers

barley talent
5832
6075.000


Most commoly, the basic talent is considered the water (wine) unit and the two highter talents are the corresponding units for wheat and barley. The basic talent brotto (Attic commercial talent) contains 50 basic pinds of 450 c. c. and the basic talent netto (Attic monetary talent, Attic and Roman wine amphora, Roman quadrantal) contains 48 basic pinds.

The relation among the most common talents is presented in the following scheme.

 

netto
brutto

Cube of 15 basic fingers

3375
 
- - -
6:5
 
 
 

Cube of 16 basic fingers

4096
 
- - -
5:6
 
 
 

Cube of 17 basic fingers

4913
4:5 
5117.7

Cube of 18 basic fingers

- - -
2:3 
6075


The calculation of the units of the talents by the cube of feet related as 15:16:17:18, does not fit with absolute perfection with intended proportions among the talents, but the difference is minima. The following are the volumes of the talents , expressed in cubic fingers of trimmed basic foot, adjusted to the intended proportions together with the difference from the cubes of the foot.

little talent

3276
-99

basic talent netto

4096

wheat talent netto

4915.2
+2.0

wheat talent brutto

5120
+2.0

barley talent

6144
+69


The only significant difference concerns the little talent, cube of the trimmed lesser talent. The little talent usually represents the weight of the basic talent filled with wheat. If one reckons beginning from the basic talent nottto, there should be a little talent equal to 4/5 of basic talent netto. This is the reason why there is a doubly trimmed lesser foot of 274.7314 mm.; as indicated by the bar of Nippur, the cube of this foot is a talent of 20.736 c.c. or 48 minai of 432 grams (exactly 4/5 of an Attic monetary talent of 60 minai of 432 grams.)

What I have discussed above is the most common pattern, but one finds that any of the talents can be taken as a unit of weight, that is, as a water unit. If the lesser talent is taken as a water unit, the basic talent becames the corresponding wheat volume and what I call the wheat talent became the barley volume. Similar calculations can be made beginning with the wheat talent and the barley talent. For instance, in Attica the barley talent isd used as a unit for wheat, called metretes, with a volume of 72 basic pinds and a weight or 72 monetary minai.

Only occasionally Oxé considered the link of units of volume and weight with units of length; he concentrated his attention on the relations of specific gravity among the several units of volume and weight, but nevertheless he arrived at a pattern similar to mine. The following are the values, expressed in c.c. or grams, of the talents we both consider as fundamental; Oxé’s figures are in parentheses.

 

netto
brutto

15-finger cube little talent

21.600
 (21.744)
- - -
- - -
16-finger cube basic talent
25.920
 (26.028)
27.000
(27.180)
17-finger cube wheat talent
- - -
- - -
32.400
(32.616)
18-finger cubbe barley talent
- - -
- - -
38.800
(39.190)


I general Oxé’s figures are slightly higher than mine, because he does not take into account the discrepancy komma. He evaluates the basic load brutto as 90.600, a value between my two values of 90.000 and 91.125. Accordingly he evaluates the basic sheqel as 9.06 grams . He calculates the Roma libra as 326.16 (instead of 324), the Euboic mina as 407.7(but the value of 405 is proved by the iron bars of the Argive Heraion), the basic mina as 453 (istead of 450), and the basic pind as 543.6 (instead of 540). But it is a matter of minor differences that do not change the value of his general structure. The only point where Oxé’s value distort an important ratio, is when he calculates the artaba as 28.992 (instead of 29.160); the relation 8:9 between talent notto and the artaba is steadily emphasized by economic documents and by metrological texts.

I have taken from Oxé the term little talent. He calls middle talent the talent I call basic. What I call wheat talent, he calls great talent or centenarium (one hundred librae). He does not call talent what I call the barley talent, because this unit seldom is used as a wather unit and hence as a weight; he prefers to call it metretes.

It may be worth comparing my values, which finally are based on acient sample weights and acient lineal measurements, with those of Decourdemanche which are based on Arab units. The following are his four anchor points, with the corresponding values in my computations:

 

foot
talent
foot
talent

319.6mm.
32.640grams
318.75mm.
32 400 grams

II 

308.56
29.376
307.796
29.160

III 

349.0
42.500
350.0
42.875

IV 

277.0
21.250
277.449
21.600

2. Oxé considered that units connected with the specific gravity of oil form a special series, and realized the importance of units conceived as a standard load, but did not connect the two problems. The cube of the basic cubit is considered the amount can be carried by an ass or the amount that can be carried by a man for a short distance. This unit, which I call load, is called imeru, “ass”, in Akkadian; homer in Hobrew, h, r, “sack” in Egyptian; *Ballavtiov, Bastajya, * in Greek; follis in Latin. When the use of the barrel spread from Celtic territory through the Roman Empire, this was the size of the standard barrel and it has remained ever since.

The mathematical aspects of this unit have been clarified by Segre in considering Egyptian units, but his remarks can be extended to all ancient metric systems. He noted that the cube of the trimmed basic cubit (basic load netto) contains 3 3/8 cubes of the trimmed basic foot (basic talents netto); in order to simplify the relation there was introduced the artaba (cube of the artabic foot) of which 3 make a basic load netto. Segre noted also that the cube of the Egyptian royal cubuit is considered equal to 5 artabai. This cube, called the “great measure” in Demotic and Greek documents, is 144.703 c.c.; whereas 5 artabic are 145.800 c.c.

From what precedes, it is apparent that the load is a weight (water) unit, and that there must be correspondent volumes for wheat and barley.

The load exists in several types. The largest of all is the cube of the artabic foot , 98.4151 grams. The typical load is the cube of the basic foot, which gives abasic load brutto of 91.125 gramas and a basic load netto of 87.480 grams (3 artabi). These units can be calculated as 3 1/3 basic talents, instead of 3 3/8, so that , by a discrepancy komma, they became 90.000 grams (10.000 basic sheqels) and 86.400 grams. The later unit is practically equal to cubes of the hybrid foot of 350 mm., each of 42.875. For a short distance a man can carry two jars of about 1½ talent (one at each end of a carrying yoke), whereas an ass is usually loaded with two packs of half a load, one on each side (*kavjniov*); the cube of the hybrid foot corresponds to this half load. There are loads conceived as 3 basic talents: 3 basic talents brutto are 871.000 grams, and 3 basic talents netto are 77.760 grams.

The corresponding units of volume are the cubes of the two feet called royal. I have already cosidered the cube of the Egyptian royal cubit, the cube of the barley cubit (Babylonian royal cubit) is called koros (gur in Sumerian, kurru in Akkadian, kor in Hebrew). A koros bruto is 129,746 c.c. and a koros netto is 124.557 c. c. The koros brutto is practically equal to 5 basic talents netto, 129.600 c.c.

The Egyptian “great measure” and the koros, typical Mesopotamia, were conceived as barley volumes according to a relation 5:3 to the load. This reckoning is mentioned in the Rhind Mathematical Papyrus, where the 5/3 of the cubit cubit are the sack. The koros was considered the wheat volume in relation to the load equal to the cube of the artabic foot.

The existence of a load conceived as 3 basic talents, instead of 3 1/3 or 3 3/8, gives origin to units reduced of 1/10. There is a reduced mina of 405 grams and a reduced pint of 486 c.c. The great advantage of the reduced pint is that 60 make an rataba and 180 make a basic load. Furthermore, 250 reduced pints make a koros, with a small adjustement that I shall discuss in dealing with the metrics of Mesopotamia, and 300 make a “great measure” or cube of the Egyptian royal cubit. There is a practical advantage in having the artaba equal to 60 reduced pints, since the daily ration of weat for an adult male is 2 pints, an artaba is exactly the ration, if one reckons by reduced pints (the ration of an artaba a month is most common in Greek papyri). The actual ration can remain the same, if the wheat in the pint is shaken (mensure conferta, ** Even today in commercial practice one calculates that shaking increases the contents of a grain measures by about 10%

The reduced mina of 450 grams has the great advantage that it can be calculated directly with all precision as a cube with an edge of 4 fingers by the trimmed basic cubit. This reckoning allows greater exactitutde in determing the small units than a calculation that divides the talent .

The existence of reduced pint and a reduced mina was explained by assuming that the basic talent was filled with oil, instead of water (wine). This gives origin to a series units calculated pondo olei, intead of pondo vini. The reckoning according to the specific gravity of oil, was extremely important exports of Egypt was medicated oil. Egypt was the center of the ancient chemical industry; medicated oil, in sealed jars, usually of the size of a hin (reduced mina or pint) was paid for at high prices and at times at fabulous prices, as medicinals are today. Because of its insignificant bulk, economic historians have neglected this most important item of ancient international trade. Medicated oil was the only protection against insects, parasites, skin diseases, an similar afflictions of societies with low sanitary standards. The high cost of smearing oil was a social problem in Greece, as inscriptions indicate. Many medications and cosmetics took the form of spiced oil. Units smaller than the mina and the pint are they are connected with the pint of oil. Almost all the metrological tables, published by Hultsch in MS, that concern small units, are derived from medical treatises and stress the density of oil in relation to wine. With the revival of learning in Europe the first metrological investigation are found in medical treatises, beginning with the shool of Salerno.

It was in line with this tradition that the physician Jean Francois Fernel, the Modern Galen, performed the first mensuration of the length of the degree of latitude, after the ancient ones. In the Middle Ages the standards of small units were usually kept by the guild of the apothecaries. Still today the English apothecaries’ dram is 3.888 grams, that is, exactly 9/10 of the Attic monetary drachma of 4.320 grams. This proves with which perfection monetary standards have been preserved through the millennia. The Attic monetary drachma is the netto variety (24/25) of half the Egyptian kite of 9 grams (basic shequel ) In Greco-Roman economy, oil untis were important , because wine and oil were the main items of export and the same jar could be filled with wine and with oil; in the secod case the weight is calculated as 9/10.

The following table indicates how the reduced pint and mina can be easily related to most of the cubit units.

Volume in c.c.
Weight in grams

Pint
486

Mina
405
Unit of
length
in mm.

Unit of volume or weight

21.160

40
 

277.5

Cube of trimmed lesser foot
 little talent netto

25.920

 

64

296.0

Cube of trimmed basic foot
 basic talent netto

29.160

60
72
307.8
Cube of artabic foot
artaba

32.400

 

80

318.75

Cube of natural wheat foot
 wheat talent brutto

36.450

75

90

333

Cube of trimmed barley foot
 barley talent netto

38.880

80

96

337.5

Cube of natural barley foot
 barley talent brutto

72.900

150

180

416.25

Cube of natural lesser cubit
 2 barley talents netto

77.760

160

192

421.9

Cube of natural lesser cubit
 2 barley talents netto

87.480

 
180
444
Cube of natural lesser cubit
 basic load netto—3artabai

97.200

200

240

462

Cube of artabic cubit
 3 wheat talents brutto

129.600

 

320

506.25

Cube of natural barley cubit
 koros brotto

145.800

300

360

525

Cube of Egyptian royal cubit
 great measure


3. The amount of information available for the study of Hellenistic, Roman and Byzantine history was immensely increased by the discovery of Greek papyri in Egypt. This material is so vast that there has been developed a special discipline called papyrology. The systematic interest in Greek papyri began when Petrie, in occasion of his excavation of Gurob in the winter of 1889/1890, began to unravel the cartooning of mummies, which often had been made of discarded fragments of papyrus (Petrie Papyri), and when B.P Grenfell and A. S. Hunt, in the first archeological campaign dedicated to search for papyri, in the winter 1896/1897 uncovered the huge mass of papyri of Oxyrrhynchos. Greek papyri extend our knowledge in all areas of ancient life, but even though their study has opened new horizons in areas such as religion and literature, most papyri concern economic transactions. Because of this fact the special areaof legal papyrology has received an enormous development; but those who trained me in legal papyrology, Fritz Pringsheim; and Pietro de Francisci, would readily admit that, even though the number of papyri available exceeds the number of scholars capable of dealing with them, papyri provide even far more information in the area of metrology. It is obvious that for each papyrus containing a formal legal transaction , there are many more papyri containing simple accounts of goods or properties with their measures. Hence, one would have expected that the study of papyri would help to solve the open questions in the area of ancient metrics. But papyri began to be studied when the new school of metrology was asserting itself; they seized them as an argument to contend that the ancients did not set measures by any systematic principle and that in each small area and each period there were different and unrelated units. It was known from the earlier studies of metrology that usually the same unit has many different names in different areas and at different times and that, conversely, the same name can be given to different units; this is the reason why, in order to avoid confusion, I have preferred to give purely conventional names to most of the units. The number of metric documents provided by papyri is so great that the number of names mentioned is far greater than those that were known before. Segrè, who has specialized in the study of the typical artaba in the Greek papyri, notes that this unit is referred by at least six different names; he applies the name of artaba to one specific unit (and I follow him in this ), but observes that the same is applied to all units of the range of the talent. The name artaba, which in Persian means the “great” unit, defined in general the cube of the foot. The typical artaba is the cube of the artabic foot, the official unit of the Persian Empire.

Far from being careless about measures, the writers of papyri usually specify the particular sample used as reference. In this respect the terminology is as complicated as that of medieval documents; but the fact that in Paris, for instance, one spoke of a Toise de l’Ecritoire, a Toise du Châtelet, and a Toise de St. Leufroy, does not imply that we are dealing with three different units, and even less that these were purely “local” units which had no mathematical relation with the other units of France or of Europe. It is a matter of a foot equal to 11/10 Roman feet, a unit used in pre-Roman Gaul and well-documented in ancient Athens. But according to contentions of the new school, we should say that in Paris, each section of the city used a standard of different length. In London one spoke of the foot of Guild Hall, of the Exchequer and of the Tower, and so on , but the length of the English foot is most precise and stable. It has been objected to my work by a professor an American history who received his training in ancient history from W. S. Ferguson, that in Brooklyn, N.Y., in the last century, there were used three different feet, one of them called the Foot of the Twenty-sixth Ward; I am not surprised by this fact, but I am most skeptical about the contention that the difference among the feet was such that some pieces of land did not exist according to the tax registers. I cannot explain what was the situation in Brooklyn, because it proved that the statement was based on the information of a book that does not mention sources; but I suspect that it was merely a matter of slightly different standards of the English foot, for which in the United States there was no national definition up to 1928, and for which the Shuckburgh rule, longer than the Bird rule, was authoritative in the first part of the nineteenth century and continued to be used after the official adoption of the Bird rule by the British Parliament in 1824. Until action was taken by the Senate of the United States in 1830., the difference between the standards used by different custom houses was sufficiently great as to cause some to raise the issue that the clause of the constitution guaranteeing equal taxation throughout the United States had been violated. Standard yards were distributed to the custom houses in 1837.

If the contention of the new school for the metrics of papyri were to be applied to medieval metrics, the weight of the Paris livre would have no relation with the Roman libra and all those writers, beginning with Budé in 1514, who connected the length of the pied de roi with the weight of the livre, did not know in which world they were living. As a result of the contentions of the new school, today the metrics of Greek papyri are considered as impenetrable as the swamps of the Nile Delta in which outlaws used to take refuge In spite of this, there has been developed a school of economic historians much concerned with the problem of prices, but dealing with this most enlightening source of historical information without serious investigation of the units to which the prices refer. The elaborate theory of Larsen about fluctuations of prices in Greece during the Hellenistic age evaporates into thin air if one questions his gratuitous evaluations of the units of measure. For any normally-thinking person it should be self-evident that prices do not mean anything, if the corresponding measures are not defined. The issue of measures is even more vital in ancient economic history, because it was common practice to keep prices stable by changing the measures.

Hultsch considered that the discovery of a new and rich source of metric information provided the solution for problems with which he had been concerned all his life. It was on the basis of the first publications of collections of papyri that in 1903 he wrote his most comprehensive work in which he integrates all his earlier researches; most of it appeared in the second yearly issue of the new review Archiv für Papyruskunde. This work is intended to present a general structure of the metrics of Greek papyri, but it throws light on all ancient metrics systems in general. He had reached that tragic moment in a man’s life when the power comprehension is at the maximum, but the physical energies are beginning to fail One evidence of this last point is that the key unit is the cube of the natural basic cubit of 450 mm., but its value is steadily computed as 91.185 c.c. instead of 91.125.

Hultsch stated that the study of the metrology of Greek papyri must start from the units of length. He considered as fundamental the Egytptian foot of 300 mm. (natural basic foot) and the artabic foot. The cube of the cubit of the first foot is a unit of 91.125 c.c. and the cube of the artabic cubit is a unit of 98,480 c.c. (98,415.1 c.c. by my reckoning). The talent type units (artabai in the terminology of the papyri) are fractions of these two units. In concluding his analysis, Hultsch lists the following fundamental talents:

I Medimnos of 48 choinikes

43.770 c.c.

II Metrhrh” dwdekaxou”
Ptolemaic artaba = Attic metretes

39.390

III Old Egyptian artaba

36.470

IV Artaba mevtrw Qhsaurikw’/

29.180

V Metrhth” ojktacou”, kepavmion oi[nou
Greek amphoreus, Roman quadrantal

26.620
VI Artaba of 24 choinikes
21.880

One can see that Hultsch has set scheme of fumdamental talents most similar to the one I have adopted. His unit V is a wine unit as in my scheme, and the corresponding unit III, unit V increased as by half, is my barley unit. His unit III is the corresponding unit netto; Hultsch himself observes that this unit it the cube of a foot of 332. mm., which he properly identifies with the typical foot of Mesopotamia and with the pes drusianus (about which he wrote the entry of RE). Unit VI is the cube of the double trimmed lesser foot in my scheme.

My only disagreement, and it is minor one, concerns unit I. He considered it a double unit, since he called it medimnos (a medimnos is a double talent), and it is in fact the double of unit VI. Hultsch included it in his scheme, because he knew that there must be a unit of 48 choinikes. Up to that time papyri mentioning this unit had not been discovered, but already in his Metrologie (p.625) he had brilliantly inferred its existence. Having concluded that the major unit of the talent type had a volume of 48 choinikes, Hultsch tried to determine the volume of the choinix. He considered evidence (Archiv., p. 624) suggesting that the choinix is equal to 827 c. c. (in my computation 810 c.c., that is, two reduced minai of 450 grams), but rejected this value with the argument that the choinix is equal to the daily ration of wheat and that 827 c.c. is too small a ration For this reason he made the choinix equal to two Alexandrine sextarii or reduced pints of 486 c.c. (this is my value; Hultsch’s value for the choinix is 873 c.c. and hence almost identical with my value of 872 c.c. for two reduced pints). But the publication of the metrological table of Dioskoros in 1917 (London Pap. V, 1718) proves that Hulsch was correct in his first calculation; this text makes clear that there is an artaba of 48 choinikes and that it is equal to unit II of Hultsch. I accept Hultsch’ scheme , with the correction of identifying the artaba of 48 choinikes (barley talent brutto) with his unit II.

The objection raised to his own reckoning by Hultsch was removed by Segrè when he observed that the choinix of the Ptolemaic period was equal to two hin or Alexandrine sextarii, but added that in Egypt the hin was identified with the mina and that one treated the same units as units of volume and of weight (Metrologia, p. 17, 23). Is is unfortunate that Segrè, having established this principle in the introductory part of his treatise, did not carry it through in the main part of this treatise in which he had to conform to De Sanctis presuppositions. I have determied that, whereas in Greece one distinguished the pint and mina, taking as mina the weight of the pint filled with water, in Mesopotamia one both the reduced pint of 486 c.c. and the corresponding reduced mina of 405 grams, as units both of volume and weight (qu and mina). In Egypt the hin had all the volumes and weights of the Mesopotamian qu and mina. Hence the difficulty of Hultsch can be so explained; it is true that the choinix is in principle the daily ration of wheat and that it is certain that the daily ration of wheat in Egypt was two reduced pints (1/30 of artaba); but one called choinix also the weight of this choinix, and then, by the process described by Segrè, one used this weight unit as a unit of volume. The term choinix in Greek papyri refers to units equal to two Egyptian hin, assuming the two main values of the hin, that is 405 and 486 c.c. In the terminology of the papyri, however, one follows the Greeek practice of distinguishing pint (xevsth”) from the mina (called), but the term livtra but the term i[nion remains ambiguous.

In my opinion the scheme of Hultsch still stands after more than half a century of investigations of papyri. But this work was treated with great scorn by the new school of metrology. Unfortunately Grenfell and Hunt were influenced by the metrological ideas of Petrie and joined the position of the new school; immediately they dismissed the work of the “veteran metrologist” by asserting that he had not been able to adapt his old metrology to the new science of papyrology. No further evidence beyond this statement was ever submitted by Grenfell and Hunt, but the assumption was that, since the science of papyrology was new, metrology had also to be new. Against Hultsch there was used the argument that he reached the age of seventy; at that time the argument of old age was used to attack Mommsen and Oppert. Typical of this approach was that of Beloch, who exploited the rhetoric of the German Jugendbewegung and introduced into classical studies the term Abschreiber, translated into Italian as scimmione. In this spirit Hultsch could be looked at just as one the members of the zoo of the philological school and relegated to a cage. But old age is something we are all bound to reach, if we are fortunate. Many years later W. S. Ferguson and Larsen, in defending the dogmas of the new school of metrology, replied to my plea for specific evidence that I should trust their judgement, acquired through long experience . When I met Ferguson he could still claim that Mommsen was a pedant spending his life filing useless data, but he could not use the argument of the heroic days of Beloch and De Sanctis that the Abschreiber were doomed because youth is always right.

The vitality of Hultsch’ classification is proved by the circumstance that the Papyrological Primer of M. David and B. A. von Groningen (3rd ed., Leyden, 1952, 35) sums it up without quoting it; the reference given is Segrè’s Metrologia which being the only work of Segrè conforming in some way to the new school, is the only one that can be mentioned within the bounds of academic respectability. Papyrologists condemn Hultsch’ scheme on30 principle, but since nothing has been offered by the new school, they follow it, even where it is in need of revision.

4. If one can object that Hultsch was not a specialist of papyrology and that the greatest mass of papyri was published after his death, the same argument cannot be used against Segrè. The latter began his scholarly activity in the field of legal papyrology and shifted his interest to metrology, partly under the influence of his war service as a cryptologist. In 1918 he began the ten-year work which concluded with publication of his Metrologia. The peculiarity of Segrè’s approach is that he centered the research on ancient metrology on the evidence of Greek papyri. In 1920, in the first yearly issue of the new review of papyrology, Aegyptus, he presented his conclusions about the metrics of Greek papyri. In this masterly piece of scholarship he set most clearly the important points; the only shortcoming is that he too was not yet acquainted with the metrological table of Dioskoros (the fifth volume of the London Papyri bears a date of 1917).

Whereas Hultsch anchored his figures on two units of length, Segrè added the trimmed basic foot to the Egyptian royal cubit (septenary multiple of the natural basic foot) and the artabic foot. He linked them together in a tight construction, by which the cube of the trimmed basic cubit (basic load netto in my terminology) is equal to 3 artabai (cubes of the artabic foot) and to 3½ or 3 3/8 (discrepancy komma) cubes of the trimmed basic foot; the cube of the Egyptian royal cubit is equal to 5 artabai.

I have repeatedly stated how much importance I attach to this interpretation, and it is clear that I have exploited it to the full. In his essays of 1920 Segrè accepted completely the principles of the old school and derived all units from the units of length. He further stated:

In general I believe that the measures of the Egyptians are part of a metric system conceived architecturally.so as the produce simple relations among the several units.... This proves the skill and care which the ancients and the Egyptians in particular, applied to this practical branch of their geometry. It is most likely that Egyptian metric systems, particularly in the Roman period, were not historical formations, but the product of highly intelligent individuals who had succeeded in assimilating many foreign elements into the indigenous metric system. In my opinion, the old Egyptian metric system takes its start from theoretical presupposotions. It is immutable: the measures are preserved in temples and are connected by simple numerical links....

In the treatise Metrologia, which appeared eight years later, the principles of the old school are restated in the introductory pages, but they are not followed in the main body of the text. Segrè accepted to have his work thoroughly edited by De Sanctis who had been one of the champions of the new school. As a result the work is chaotic and full of material errors; the best contributions to scholarship are in some footnotes which are not in total agrement with the text. In this confusion of ideas the insight of Segrè did not progress beyond what he had achieved in 1920. The greatest obscurity veils the parts that were of particular concern to De Santis: Greek metrology and the metric reforms of Solon in particular. The plight of Segrè is revealed by his act of allegiance to the theories of De Sanctis and Beloch about Solon’s reforms. These texts, badly interpreted up to now, have been exactly understood by De Sanctis, followed by Beloch” (p.153). A footnote stresses that their interpretations are against “the common thesis of metrologists and numismatists” ; what Segrè should have said is that the contentions of De Sanctis and Beloch are in flat contradiction with the textual evidence. The old school of metrology had indicated that there were at least two main types of mina, linked by a simple mathematical relation 4:5 or 5:6, and Lehmann-Haupt had implemented this conclusion by introducing the theory of increased norms which I have developed into the system of discrepancies. The text of Aristotle, discovered in 1891, confirms textually the existence of units related as 24:25, as Lehmann-Haupt had assumed, and confirms that the Attic pre-Solonian mina was identical with the Aiginetic mina. De Sanctis, identifying himself with the opponents of Lehmann-Haupt, proclaimed that in Greece there was only one kind of mina. Since this was the cornerstone of De Sanctis’ argument, Segrè was in a most difficult position. In the page following the quoted approval of the general interpretation of Solon’s reforms by De Sanctis and Beloch, Segrè states that he accepts the theory that there is only one mina, but adds “This assertion, according to me, is exact only in part, in that the existence of an Aiginatic mina is by now beyond dispute.” Hence, the position of De Santis can be accepted as correct, provided one grants that the opposite opinion is absolutely valid

But except for this expression of veiled disagreement, Segrè fell into line. This is particularly evident in his treatment of the ejpikatallaghv in the Delphian accounts; Segrè certainly had the mathematical mind to see that these accounts support Lehmann-Haupt’s theory of increased norms, but he presented the Delphian accounts as being without any strict metrological principle and introducing arbitrarily percentage changes in the rates of exchange. This had unfortunate consequences for me, because I started my study of metrology by considering the Solonian reforms and proceeded from there to a study of Greek inscriptions regulating rates of exchange; on the basis of the authority of De Sanctis and Segrè, Greek historians and Greek epigraphists to whom I submitted my work objected that any attempt to interpret the texts according to strict metrological reckonings is preposterous and that the Greeks fixed rates of exchange according to expediency. They introduce a concept of money as having a value at the discretion of the ruler, that appears only in the Roman Empire; they deny the Greek conception of nomos as being objectively right and similar to the nomos of the natural sciences

As the new school affirmed that there was only one mina in Greece, it affirmed also that there was only one choinix in the metrics of Greek papyri. In 1912 Ulrich Wilcken, in his classical introduction to papyrology, accepted from the new school the contention that there was only one choinix, but stated that the texts clearly indicate that there are artabai related as 24:25 (p. LXIX). But the existnece of units related as 24:25 was the main contention of Lehmann-Haupt, and the issue on which he had been attacked by Weissbach, Viedebantt, De Sanctis, and Beloch. Hence, Segrè had to deny the existence of this relation. together with asserting that there is only one choinix. But in his essays of 1920 he had stated that in Hellenistic Egypt one used the cube of the trimmed basic foot and the cube of the natural basic foot, two units that relate as 24:25, as do the same units in the Solonian system.

The article of 1931 by Segrè on artabai marks the nadir of his metrological research (Studi di filologia classica, 1931, 111-115). He claims that there were 18 types of artaba, not related by any mathematical principle; but if one examines his list, one can see immediatly that some of the units are related as 24:25, that is, are the netto and the brutto variety of the same artaba. If one assumes the existence of two types of choinix related as 5:6, a relation much stressed by Hultsch, one can easily fit Segrè’s eighteen artabas into Hultsch’s scheme, as I have had occasion to do in the part dealing with units of volume and weight.

If was at that point that I met with Segrè and that he caused me to become interested in metrology. Even though then I was only in my last yerar of my secondary classical education and in the following years I was a beginner in the field of legal papyrology under Pringshein, the fact that Segrè had found one person who could follow a serious technical argument of metrology may have contributed to increase bis self-confidence. In the meanwhile De Sanctis, after the death of his intimate friend Beloch in 1928, became much more amenable to reasonable argument. In 1940, at the age of seventy, De Sanctis, printed in his Storia dei Greci (I, 458) a declaration to the effect that the Solonian system of measures was a “closed system” and that “such systems had been already used for millennia in the Orient.” This declaration means the total denial of all the contentions of the new school: the contention of Eduard Meyer and of Ridgeway, accepted by almost all ancient scholars, that the linking of length with volume and weight is the product of modern science is denied by somebody who cannot be accused of being interested in spreading Jacobin ideas. It is not surprising that De Sanctis is not consequential in applying to the Solonian reform his acceptance of the old school, because this would imply a revision of his general interpretation of Greek culture.

De Sanctis still claimed that in Greece there was only one kind of mina, but he understood that he could not defend this position, except by claiming that in Greece there was only one kind of foot. In order to defend this peculiar contention, he has to reject the evidence afforded by Greek buildings; following one of the dogmas of the new school, he reject the validity of Newton’s method. Most strange is the statement that the Attic foot is not the same unit as the Roman foot. One can hardly expect a consistent position in a retraction of one of the main products of a style of scholarhip for which De Sanctis had been one of the major spokesmen. One must rather admire De Sanctis, because he proved more flexible than his pupils, and followers who make it an issue of school pride to defend to the last the dogmas of the new school.

It is unfortunate that De Sanctis’ retraction came too late; my teachers at Harvard, as followers of De Sanctis, could consider the matter closed by his Atthis. When Segrè came to the United States, he considered that the effort to start a new academic life could represent a new lease on life, and reexamined metrological problems according to the strictly mathematical analysis used in his essays of 1920.

The article “A Documentary Analysis of Ancient Palestinian Measures,” which appeared with a noticeable delay is, in spite of the title, a general survey of the principle of organization of Egyptian, Hebrew and Hellenistic measures, stressing the strict connection between the units of length and the units volume and weight.* There are many specific points on which I disagree with the statements contained in this most rich and highly compact article, but methodologically I am in complete agreement. It is important to notice that in the last page Segrè restates the basic scheme of his essays of 1920. He completed the general revision of the premises of ancient metrology, in a second article on “Babylonian, Assyrian and Persian Measures” which presents a point of view I completely follow in my reconstruction of Mesopotamian metrics.** He revived the doctrine of Lehmann-Haupt that the qa of stereometric texts (doubly reduced pint) is a cube with an edge of 6 sexagesimal fingers. Segrè properly saw in the Mesopotamian qa the equivalent of the Persian unit of which 60 make an artaba and the antecedent of the Alexandrine sextarius. He calculated the typical Mesopotamian cubit as 501 mm., whereas I calculate it as 499.407 mm. when trimmed.

These studies reviving the best in the method of the old school brought upon Segrè’s head the wrath of the American academic world, with the result that he found himself excluded from any academic connection and treated in some specific cases with personal rudeness. He was discouraged from continuing in the line of research which he had initiated with renewed enthusiasm and with positive succeses from the point of view of scientific knowledge. Being obstacled even in the access to the means of research, Segrè abandoned metrological studies. About his one case one could quote the epitaph of Hadrian VI: Proh dolor; Quantum refert in quae tempora vel optimi cuiusque virtus incidat.

Sachs in the refutation of Segrè declared that his position “cannot be taken seriously” but in fact it is Sach’s argument that is indefensible, so much that the Preface to MCT by Neugebauer and Sachs contains an acceptance of one of the main tenets of the old school. In the following year Sachs published two Neo-Babylonian metrological tables, on the basis of which he must grant what followers of the old school had claimed for a long time: that the unit petqa, “obol,” can be both 1/8 and 1/6, or 1/12 of sheqel.* This indicates that the mina can be both single and double, which Sachs had strenuously denied; it also supports the contention that there is a mina of 540 grams next to a mina of 405. The petqa is probably a unit of 1.125 grams (1/8 of a basic sheqel of 9 grams). Up to that moment Sachs had denied the validity of the equivalent evidence afforded by economic documents with the argument that they contain “errors and approximations; “errors and approximation are introduced by the new school to explain what the old school explains as fractional adjustments (discrepancies by my interpretation).


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