Greek and Roman Metrology — 1862

Google

This is a digital copy of a book that was prcscrvod for gcncrations on library shclvcs bcforc it was carefully scannod by Google as pari of a project

to make the world's books discoverablc online.

It has survived long enough for the copyright to expire and the book to enter the public domain. A public domain book is one that was never subject

to Copyright or whose legal Copyright term has expired. Whether a book is in the public domain may vary country to country. Public domain books

are our gateways to the past, representing a wealth of history, cultuie and knowledge that's often difficult to discover.

Marks, notations and other maiginalia present in the original volume will appear in this case - a reminder of this book's long journcy from the

publisher to a library and finally to you.

Usage guidelines

Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to the public and we are merely their custodians. Nevertheless, this work is expensive, so in order to keep providing this resource, we have taken steps to prcvcnt abuse by commercial parties, including placing lechnical restrictions on automated querying. We also ask that you:

+ Make non-commercial use of the files We designed Google Book Search for use by individuals, and we request that you use these files for personal, non-commercial purposes.

+ Refrain fivm automated querying Do not send automated queries of any sort to Google's System: If you are conducting research on machinc translation, optical character recognition or other areas where access to a large amount of text is helpful, please contact us. We encourage the use of public domain materials for these purposes and may be able to help.

+ Maintain attributionTht GoogXt "watermark" you see on each case is essential for informingpcoplcabout this project and hclping them lind additional materials through Google Book Search. Please do not remove it.

+ Keep it legal Whatever your use, remember that you are responsible for ensuring that what you are doing is legal. Don't assume that just Because we believe a book is in the public domain for users in the United States, that the work is also in the public domain for users in other countries. Whether a book is still in Copyright varies from country to country, and we can'l offer guidance on whether any speciflc use of any specific book is allowed. Please do not assume that a book's appearance in Google Book Search mcans it can bc used in any manner anywhere in the world. Copyright infringement liabili^ can be quite severe.

About Google Book Search

Google's mission is to organize the world's information and to make it univcrsally accessible and usable. Google Book Search hclps rcadcrs discover the world's books while hclping authors and publishers rcach ncw audicnccs. You can search through the füll icxi of ihis book on the web

at |http: //books. google.com/l

Google

About this book

This is a digital copy of a book that was stored in library shelves for generations before being published by Google carefully scanned as part of a project to make the world's books available online. The book has survived copyright law and can now be made publicly available. A publicly accessible book is a book that was never subject to copyright or for which the copyright protection period has expired. Whether a book is publicly available can vary from country to country. Publicly accessible books are our gateway to the past and represent a historical, cultural and scientific assets that are often difficult to discover.

Signs of use, annotations and other marginal notes contained in the original volume can also be found in this file - a reminder Remember the long journey the book has taken from the publisher to a library and on to you.

Usage guidelines

Google is proud to partner with libraries to digitize publicly available materials and make them available to the masses to make accessible. Public domain books belong to the public, and we are merely their custodians. This is never the case Labor expensive. In order to continue to provide this resource, we have taken steps to prevent misuse to prevent commercial parties. These include technical limitations for automated queries. We ask that you adhere to the following guidelines:

+ Use of the files for non-commercial purposes We have designed Google Book Search for end users and would like you to use it Use files only for personal, non-commercial purposes.

+ No automated queries Do not send automated queries of any kind to the Google system. If you do research via machine translation, optical character recognition or other areas where access to text in large quantities is useful, please contact us. We encourage the use of publicly available material for these purposes and may provide you may help.

+ Retaining Google brand elementsThe Google "watermark" that you will find on every file is important for information about this project and helps users find additional material via Google Book Search. Please do not remove the watermark.

+ Move within legality Regardless of your intended use, you must be aware of your responsibility, to ensure that your use is legal. Do not assume that a book that we believe is intended for users in the United States is publicly available, is also publicly available to users in other countries. Whether a book is still subject to copyright is varies from country to country. We cannot provide advice as to whether a particular use of a particular book is permitted by law is. Don't assume that the appearance of a book in Google Book Search means that it is available in any form, anywhere on the world can be used. Copyright infringement can have serious consequences.

Via Google Book Search

Google's goal is to organize the world's information and make it widely usable and accessible. Google Book Search helps readers discover the world's books and helps authors and publishers reach new audiences. You can find the entire book text online at |http: //books. Search google .coiril.

Ik^S^fitSl

MB) HBHIKfl!l.SgIE«BBS>

: t « ■ ■ ■ ■ I ■

I ■ ■ ■

.

"l l.l

GREEK AND ROMAN

ETROLOGY

FROM

. » I •.

■■'i ■ ■ «.I .;-.', ... . ■.■•■■■

•.•:!>■ ■.

«S-1 . . ■

FRIEDRICH HÜI/rSCH.

BERLIN,

wp:idmannsche bookstore.

18 62.

-•• • •

••

• • *

9

. •

• • •

W'

« «

• • •

• «

THE LORD

DR. JULIUS LUDWIG KLEE

REGTOK AT THE EREUZ SCHOOL IN DRESDEN

AND

PROFESSOR DR. FRIEDRICH KRANER

DIRECTOR AT ZWICKAU GYMNASIUM KNIGHT OF THE KING. SACHS. ORDER OF MERIT

IN DEFINITE ADVERSATION DEDICATED.

Inbalts directory

Introduction.

§ 1. Task of metrology. Incorporation of the material pp. 1 - 5.

1. General information about measurements and measures. Field of metrology.

2. Division and arrangement of the material. Method of presentation. Attachment. Tables.

§ 2. Sources pp. 5-14.

1. Rulers, hollow gauges, weights, coins. 2. Greek metrological writings. The Heronic Fragments etc. 3. Metro logical writings of the Romans. 4. Some other writings of the ancient world thums, insofar as they serve as sources for metrology.

§ 3. The newer literature pp. 14 - 20.

§ 4. Overview of the most important newer Mafs, weight and coin systems pp. 20-23.

First part.

The length, area and hollow dimensions.

First section. The Greek[[longitude and

Area dimensions

§ 5. The system of Greek length measurements pp. 27 - 33.

1. General. 2. ^dxrvXog, naXaictxri, am&af^i], 3. novg, nij- Xvg^ 4. nXi^Qov^ arci^tov.

§ 6. Overview of the less common length measurements pp. 33 - 37.

§ 7. The area dimensions p. 37 f.

§ 8, Determination of the Greek length measurements pp. 39 - 47.

1. The question about the unity or diversity of the Greeks

75' iW^

VI CONTENT.

Leogenmafse. 2. Fuss and Elle. Herodotus's fiiiqios Tirj^vg. 3. Sta- dion. Inaccurate determination of distances. 4. The Itinerary« Stadium.

§ 9. Continuation. The Itinerary Stadium pp. 47 - 51.

1. Herodotus' stadium. 2. The Stadium of Xenophon and Era tosthenes. 3. Resume.

§ 10. The Olympic Stadium pp. 51 - 56.

1. Comparison of the stadium with the Roman mile. 2. The atti sche feet. 3. The Ptolemaic Fuss in Cyrenaica. Traces of a common Greek five-meter scale and its gradual reduction gering. The Olympic Stadium.

§ 11. The longer stages of the imperial period pp. 56 - 58.

Second section. The Roman longitude and

Area dimensions

§ 12. Overview of the system pp. 59-64.

1. The foot and its parts. 2. Palmipes, cubitus, ulna. 3. The step. 4. Decempeda and actus.

§ 13. The Wegmafse pp. 65-67.

1. The passage. 2. The Mile. § 14. The area dimensions pp. 67-71.

1. Pes quadratus. 2. j4ctus and iugerum. 3. Division of the Jugerum.

4. The larger area dimensions.

§ 15. Determination of the Roman foot pp. 71 - 77.

1. Foot sticks. Land fines. Derivation of the length measure defn hollow mafs. 2. Determination of the foot from the buildings.

Third section. The hollow mafse.

§ 16. The Attic Hohlmafs pp. 78-87.

1. Difference in measurements for liquid and dry. move denes Hohlmafs in Greece. Requirements for maintenance of correct size and weight. 2. The fluid mass. 3. The Mafse for dry. 4. Determination of the Attic hollow dimension

§ 17. The Roman hollow mafses pp. 87-95.

1. The hollow mafs derived from the length mafs, but according to the important normirt. 2. Quadrantal. 3. The remaining fluids. 4. Duodecimal division of the sextarius and hemina. 5. The Mafse of the dry.

§18. Determination of the Roman hollow mafse pp. 95-99.

1. Determination according to longitude and Farnese CoBgiuSy 2. after the weight.

CONTENTS. VII

Second part.

The weights.

§ 19. The Greek weight tsyslein pp. 103 - 110.

1. The elements of the system. Derivation of the same from the Orient.

2. Talent and its parts. 3. Overview. 4. The Attic Han weight. 5. The little golden talent.

§ 20. The Roman weight system pp. 110-114.

1. Overview of the system. The duodecimal axe of the ace. 2nd time chen for the parts of the ace. 3. Various uses of the Duo* Decimal division of the Ace. 4. The Roman weight system in the Imperial period.

§ 21. Determination of the Roman pound pp. 114 - 119.

1. Determination according to the weights, 2. according to the length and Hohlmafs, 3rd after the coins.

Third part.

Bie coins.

First section. The Greek coinage.

§ 22. Introduction pp. 123-128.

1. The original means of exchange. Creation of the coin. 2. Be- interpretation of the coin stamp. 3. Mutual relationship of value metals.

§ 23. The Persian and Asia Minor coins pp. 128 - 131.

1. Derivation of Greek currencies from Asia. 2. The euboi ian and Babylonian talent. 3. Asia Minor Gold and Silver stater.

§ 24. The Aeginaean coin fox pp. 131 - 138.

1. Derivation of the Aegean currency from silver in Asia Minor stater. 2. Spread of the Aeginean currency. 3. Determination of value tion of the same.

§ 25. The oldest coinage of Athens and the introduction of a new one by Solon pp. 138-146.

1. The original currency of Athens was the Aeginean. 2. The Solonian coinage is the Euboian one. 3. Evidence for it. 4. Origin of the name Euboic. 5. Attic system Currency.

VIII CONTENT.

§ 26. Determination of the normal weight of the Attic coin pp. 146-149. 1. Comparison with Roman weight. 2. Determination according to the coins.

§ 27. The Attic silver coinage pp. 149-162.

1. Nominal. 2. The oldest coat of arms coins. 3. The periods of Attic style. 4. Differences in weight. 5. The embossing of the remaining denominations except the tetradrachmon. 6. Chronological Demarcation of the coinage eras.

§ 28. Gold and copper coinage pp. 162-168.

1. Expansion of Attic gold coinage. 2. The Gold Stater. 3. The younger copper stamping.

§ 29. Determination of the value of the Attic Courant pp. 168 - 173.

1. Silver as the sole Greek courant. 2. The value Mood must be based on normal weight. 3. Subtlety of Attitude schen coins. 4. Analyzes. Definitive determination of the value of the attire chen silver coin.

§ 30. The Curse of Gold pp. 174-177.

1. Ordinary estimate of gold in relation to silver in Greece. 2. Gurs ratios. 3. Determination of the value of gold.

§ 31. The Attic coin base in the Macedonian Empire pp. 177 - 184.

1. Spread of the Attic currency. 2. Introduction of Attic (Persian) gold fox by Philip. 3. Introduction of the Attitude silver coinage by Alexander. 4. Determination of value Macedonian money. 5. Macedonian mints. The embossing after Alexander's death.

§ 32. The Attic currency in the Roman period pp. 184-187.

1. Equality between denarius and drachma. The Greco-Roman Accounting talent. 2. Polybius' equations between Greek and Roman change.

Second section. Roman coinage

Republic.

§ 33. The oldest copper coin pp. 188 - 196.

1. Original means of exchange. ^it rude, 2. bars with brands, aes signatum, 3rd introduction of the copper coin under the Decem- virn. 4. Weight of the oldest ace; the libral fufs. 5. Minification of copper money.

§ 34. Determination of the value of the liberal copper coin p. 196 - 200.

1. The Roman copper courant is valued according to its current metal determined. 2. Transition from copper to silver currency.

INBAtT. IX

§ 35. The introduction of silver coinage and the first reduction of the As pp. 200-213.

1. Time of the first silver coinage. Value marks and embossing.

2. Normal weight of the oldest denarius. 3. Importance of value sign. The trientaleFufs. 4. Context of the first silver coinage gnng and the asreduction with the Sicilian literary system. 5. Messages from the ancients about the currency of silver coins and the reduction of copper. 6. Minting of copper in the Triene* talfufse. 7. Determination of the value of the coins of this period.

§ 36. The Roman silver currency from the Hannibalic War to End of the Republic pp. 213-225.

1. Reduction of the denarius to -^^ pounds. 2. Expression of the silver coin. The Victoriatus. 3. The further reductions of the copper coin. 4. The Roman sesterce bill. 5. Determination of value Courants of the Republic.

§ 37. The gold coinage of the Roman Republic p. 226--22p.

1. Bullion money in traffic and in the air. Curse of Gold. 2. The Gold coins of the Republic. 3. Caesar's Aureus.

Third section. The coinage of the imperial era.

§ 38. The gold standard from Augustus to Septimius Severus p. 229 to 240.

1. The coinage system of the imperial period. 2. The gold standard in return rate to the previous silver currency. 3. The gold coinage of Caesar except for Caracalla. 4. Formation of silver. Reduction of the Weight and deterioration of the grain since Nero. 5. The copper embossing. 6. Determination of the value of the gold courant.

§ 39. The decline of the coin system in the third century pp. 240 - 245. 1. The gold coin. 2. The Antoninianus. 3. Transition of the silver to the copper coin. 4. Monetary calculation of this period. value determination ments.

§ 40. Constantin's coinage regulations pp. 245 - 253.

1. The return to the balance. The gold pound. The solidus. 2. The Silver coins of Diocletian and the late period The Miliarense. The Siliqua. 3. The copper coin. The Follis. The invoice denarius. 4. Value determinations.

appendix«

I. Orieohenland and the East.

§ 1. Boeotia p. 257. § 2. Aegina p. 258.

X CONTENT.

§ 3. Corinth pp. 258-260.

§ 4. Sparlas. 260 f.

§ 5. Greek Islands pp. 262-265.

1. Aegina. 2. Chios. 3. Eoboea. 4. Crete. 5. Cyprus. 6. Lesbos. 7. Rhodes. 8. Samos.

§ 6. Macedonia pp. 265-267.

§ 7. Asia Minor. 267-271.'

1. Län^enmafs. 2. Minor Aiiatic gold and silver coinage. 3. Ci- stophor currency.

§ 8. Syria p. 271.

§ 9. Palestine pp. 272-274.

§ 10. Persia pp. 274-279.

1. Length measurement 2. Hollow mafs. 3. Weight and coin feet.

§ 11. Egypt. Length, area and hollow dimensions pp. 279 - 285.

1. Egyptian cubit. 2. Phileteric system. 3. Shoinos. 4. Re- Introduction of the Phileteric Measure. 5* area mafs. 6. Hollow mafse.

§12. Egyptian coinage p. 285 f.

§ 13. CyrenaicaS. 286f.

n. Italy and the West.

§ 14. Italy p. 288 f.

§ 15. Sicily pp. 289-293.

1. Area dimensions 2. Hollow mafs. 3. Coinage. The liter system.

§ 16. Hispania p. 293.

§ 17. Gaul p. 293 f.

§18. Germania p. 294.

Tables.

I. The Itinerary Stadium p. 297.

II. Overview of the Greek Langenmafse p. 298. HI. The multiples of the foot, the ulna, the orgyia and the plethron. 299. IV. The Olympic Stadium p. 300.

V. The Greek area measure p. 301. VI. Overview of the Roman longitudes p. 302. VII. The multiples of the foot and the passage p. 303. Vm. The Roman Mile p. 304. IX. The Roman surface measurements p. 304.

X. The Greek hollow mafse p. 305.

CONTENT. XI

XI. The Roman Hoblmafse p. 306. XII. The Attic weights p. 307.

XIII. The Roman weights p. 308.

XIV. Redoction of the Attic drachma and mine p. 309. XV. Rednction of the Attic talent p. 310.

XVI. Rednction of the Attic Gold Stater p. 311. XVII. Rednction of the libral copper ace p. 311.

XVIIT. Rednction of the oldest silver money and the triental ace p. 312. XIX. The silver courant of the Roman Republic and the gold courant of the Imperial period p. 31 3 f.

Supplements.

A. Rednction of Greek and Roman measures, weights and coins zen on the measures, weights and coins of Baden, Bavaria, Hanno- ver, Austria, Saxony, Württemberg pp. 315 - 317.

B. Rednction of some newer measures p. 318.

Introduction.

§ 1. Task of metrology, separation of material,

1. Man is the measure of all things. This often Old Protagoras's saying is also the foundation basic principle for the study of measurements, metrology. All measuring sen is a comparison. A certain size becomes the basis and this is used as a benchmark for all similar sizes. applies. The resulting ratio is the number of measured object. First of all, because it's possible not at all from the concept of human being and we- To separate kens, the spatial dimensions must be measured have been. Naturally, the human body forms here even the base. The width of the hand, the length of the arm, the spread arms, the foot, the step are dimensions on whose body need nature itself to point out to people; they are with about the same for all adults; they can be found almost everywhere easy to put on, and are sufficient for the needs of the first cultivator ture state. The extended length was on the Arable fields to the area size. A hundred feet long, as far as that Plow bulls could be driven in one breath, he pulled plower his furrow, and added as many to it side by side, until the width of the tilled piece was equal to the length. This square of the hundred-five furrow is among the Greeks and Italians the original surface area.

It was only a small step from the natural dimensions on the use of artificial and precisely standardized measuring rods. Architecture cannot be imagined without it, hence the which we find among the Aegyptians, the oldest builders on earth, also the oldest precisely standardized measuring sticks (Appendix § 11, 1); and

Hultsch, metrology. \

2 TASK OF METROLOGY. UNITHEILUN6 OF THE MATERIAL. S1.

the same people, like the ancients, had Herodotus at their head, emphasize many times, first of all the art of precise measurement of the country i). The Nile flooded it every year fertile farmland and covered it with its mud Marks of the property, every year was therefore through precise Surveying gave the owners what was theirs again, an income direction that is at least as old as the Egyptian one in general. cal culture.

Not as easy as the yardstick for length and Based on the area expansion, measurements for the volume were obtained and for the heaviness of the bodies. The hollow mafse would have can be easily derived from the length measure; alone like that- As far as we know, it was the Romans who first discovered it, and in relatively A moderately later time I tried to put her hollow mafs on it Length ftifs must be based (§ 17, 1). Originally the jug, in which oil or wine was kept, the greater or smaller container into which the grain was poured Mafs dispensed for liquid and dry. A more precise standard The information could not be anything other than arbitrary, which is why From time immemorial there has been a much greater diversity in the Uohl- dimensions than in the length and area dimensions It was similar with the weight. The burden that the man carries who picks up the work from the floor and in his hands or is not even remotely one such a certain size as the members of the human body. This burden also represents a very large weight; there- On the other hand, there is not enough capacity for the smaller weights immediate destination. Because if ÖQaximj corresponds to the original In a high sense of the word it means something like wrapping your hand around grasp, or lihra as much as you hold floating in your hand, like that We recognize that the first attempts have a smaller weight to form, but a firm determination was not possible afterwards. So the weight had to be created artificially. The development The origin of the same is lost in the oldest oriental times culture; what concerns the peoples of classical antiquity is the same For now we only want to state that the Romans had their weight according to the Greek standard, and that the Greeks for their part the load to be placed on the scale, the raAavroy, as the oldest weight had, but the actual system of weights came from the Orient

1) Herod. 2, 109, Strabo 16 p. 787, Heron Fragm. 2, 1 and others.

.-V, ^

t.

1. 2. TASK OF METROLOGY. ICE HEALING OF THE SUBSTANCE. ö

borrowed, and the fixed approaches for this in connection with the minting of the coins.

This leads us naturally to the most important one for traffic Application that advances the art of the chariot human culture has found on the coins. Above all other means of exchange that the peoples share on the first level served their development, the noble metals gained early early advantage because they, although actually only one Commodity, but better than any other object of possession suitable for general value measurement. The valuable metal became originally weighed, but then in pieces of precisely determined with the right weight under the guarantee of the state and therefore made into a coin, rather the essence of it becomes will be discussed in more detail below (§ 22, 2); enough here it just to point out that with the appearance of the coin To a certain extent, a new, independent measure emerges from the weight develops. The coin is no longer just a piece of value metal of a certain weight, rather it becomes the measure for all W^erth estimate, which is why they also, the further trade and Traffic develops more frequently through mere credit symbol is represented. Of course, by its nature it is not completely unchangeable scale, but at least the one on at least the wavering ones that were able to produce themselves. In this sense Metrology also has to deal with the coinage of ancient peoples. act. Above all, it has to determine the coin base, the normal determine the painting weight and the fineness of the metal and then the value of the coin in relation to today's money determine. The field of numismatics only comes close to that to touch where the mint of the coins, be it the style of the Images or the symbols and inscriptions can be used to provide information about the time of minting.

2. From the suggestions given about the area of Metrology results in the division and arrangement at the same time of the substance. The purpose of this manual is to: To give an outline of Greek and Roman metrology. It It is understood that the treatment is not in the way can be separated, that first the Greek metrology for itself and then the Roman one is abolished. Both peoples have in everything that concerns mafse and coins, multiple bills of exchange flow exerted on each other. First it was the Romans who... Mafs and weight according to the Greek standard, and later the Greek masses and especially the coins felt this

N

4 TASK DEK HBTROLOUTE. EmTSCILATION OF THE KTOFF. i I, I.

Influence of Roman volition. There must be the egg The reason for the division is the previously discussed Ilauplarten of the necks form. We therefore treat in the first part the lengths gene and area margin in addition to the Iloblniarsen, which has theirs fixed determination only achieved through the weight, but as Dimensions of spatial extent do not depend on the previously mentioned were allowed to be separated. Then follow in the second part Weights, in the third the coins. Both can be The course of the investigation cannot be separated because of our knowledge The Greek weight is based almost exclusively on the Coins and also the Roman can only be secured through this determine - in the presentation alone they have to provide an overview - to be divorced for reasons of convenience, which is also the advantage It is clear that the emphasis is primarily on the presentation of the system is taken into account, so this is the case anyway circumstance, the depiction of the coinage system was assumed to be known. can be set. Within the individual parts give the According to historical sequence, the Greeks preceded the HOmein, although in the investigation very often the Greek ones Must first be based on the Roman ones, which we mostly know about who are informed, could be determined.

In general, caution and consideration are important easy to use, the guiding aspects of J The manual was written. That's why this difficult i and endless investigation into the derivation of the dimensions is not a- M been gone. The I is not even remotely located here enough material. We still have to do a lot better about Diel Measures of ancient Egypt and the Asian civilizations under-'T the method of comparative metrology must still be 1 stated quite differently and especially from the arbitrarinesses French scholars who have sinned a lot here, purified'l the investigation will be started againa f can. It is also sufficient to use the sources carefully, dtel focus on the own area of Greek and Roman Me-' trology limit, perfect for determining the b6-| appropriate measures, without emerging from the fog of Egyptian and Ba- Bylonian prehistory the explanation would have to be obtained. moreover, as with the Egyptian Ellenmafse or with the per~.J siscb-Asia Minor coin feet, secure documents are available, is^ the support provided by this was readily drawn upon. ■!

This was due to consideration of practical needs leads to the course of the ongoing presentation only the general

§ 9, 1. SOURCES. 5

my valid, to a certain extent the xoivrj of the Greek and Roman mix Mafse to record. This is the Greeks' at- tic system, which is therefore taken into account almost exclusively has been. Only with coins is this the case with good reason the Persian, Asia Minor and the Aeginean currencies advanced been provided. What else about measurements and currencies? either had only temporary and limited validity, or as foreign only in their contact with the Greek and Roman come into consideration, it was worth mentioning, that is everything has been referred to in the appendix, where the geographical arrangement was to be applied as the only appropriate one. Only may In order to prevent misunderstandings, it is not expected that that in this appendix all municipal and provincial coins currencies (the dimensions are not an issue here), from which we have knowledge through received coins have been made, making the appendix a numismatic card Talog would have been similar. Rather, the norm was only what was learned from Greek and Roman writers is mentioned, and here too only the most important things are included.

In keeping with the character of a dogmatic manual is a clear division into paragraphs and smaller ones sections have been carried out, which at the same time makes it possible ability to refer to the following was offered.

The conclusion is formed by the tables, which show the reduction of the Measures and weights in French and Prussian measures and Weight, as well as the coins on the Dreifsigthalerfufs included. The documents for the tables are in the course of the investigation found in the individual sections, and it is there too, what is often desired for practical needs, the ver- equation with the newer dimensions in rounds and therefore lighter Amounts to be remembered have been given. About the newer ones Measures, weights and currencies will be discussed in a special way Sections (§ 4) are spoken.

§2. sources,

1. The immediate sources for the metrology of the ancients Peoples are the measuring rods, hollow measuring rods, weights and coins zen that are still preserved. This is what stands out at first glance a great difference in the eyes. Measuring rods, hollow measuring rods and weights only perish in very small numbers

6 SOURCES. § 2.

the old world survives i), while the coins are extremely provide plenty of material *). In the same situation also the importance that these sources have for us. The few discovered Roman footholds - Greek are completely missing - do not provide a reliable measure of the Roman Fusses; even less can be learned from the preserved measuring vessels a precise determination of the Roman and Greek hollow determine measurements. The pieces of weight are quite numerous rich, but of very variable amounts. You just need to consider that all these dimensions and weights cannot be measured with thematic accuracy are standardized, but only for intended for practical use, only approximately correct Provide a picture of the normal condition. And like it still is today, anyway that we are much more precise in this would be impossible from the The standard scale used in trade and change is the standard scale to be restored with absolute accuracy, that is still the case much less to be expected with the old measurements, where the ratios nits are even more unfavorable. So here is the un- to attribute only a limited value to indirect sources. Quite The situation is different with coins. They are actually ours only source for determining the old currencies, because the Information from the ancients gives us information about its origins and that mutual relationship between them, but not about their amount Pulp. Furthermore, they are present in such abundance that... they provide a complete picture of the most important influences of the age to present thums. It is also in the nature of things Even in ancient times, the precision in production was greater was than with measures and weights, and this increases Care with the value of the metal, it is with gold coins the largest and these therefore form the most reliable basis. However, here too research must be carried out with the greatest caution procedure. The wear and tear on the pieces we received, initially could be asserted is of less importance. We

1) There is a lack of works that are similar to the nuniismatic catalogues. loge to compile what has been preserved in this field. The material is in age metrological works, reports from the academies and elsewhere scattered.

2) This is not the place to find the extensive literature that belongs here. to perform rature. What is necessary will be discussed in detail during the treatment of Attic and Roman coinage. By the way is based on the list of sources in Mommsen, History of the Roman Coinage. p. XXI ff.

1. 8. SOURCES. 7

have numerous of the most important coinages, especially in gold rich pieces that are still as intact as they were from the mint came, others are so well preserved that the wear and tear also shows cannot be valued at the minimum appreciable amount; In most cases it is therefore not necessary to calculate to become dependent on the worn pieces. But still is Determining the weight of the coins is still difficult enough. Average calculations, such as the French in particular These are usually inadmissible; they just can have meaning where it can be assumed that there are about as many over- coins as under-minted pieces of the type in question. And yet it is natural that the latter are usually far are more numerous, so the average is too low. It So the weight is usually from the highest pieces determine. But that is just the effective weight and on top of that who often still have to go back to normal weight. Because the mouth The state's influence usually disappeared very quickly slightly lower than the normal weight, and yet this alone, if it can be determined otherwise, the document for the determination position of the currency. This is where research and... Criticism goes its own way for each individual currency, general points of view cannot be established.

This is how the coins enable us to firmly determine the old currencies, they also give us the exact description carry the weights, and in turn you can rely on the weight the most approximate determination of the given circumstances Give hollow mafses. For the length mafs form the most reliable Basis the old buildings. The old builders have us here their yardstick, which was probably more accurate than any other others used in ordinary traffic, in hundreds of dimensions, and with due caution From these monuments the old length measure can be at least at least as accurately as the ancients themselves had.

2. We now come to the written sources and initially to the metrological methods preserved from antiquity ian writings. The oldest proven mention of metro logical writers can be found in Galen, from whom o\ Tvegl tüv oxad^i-iiov TLal juergcov ygccipavTcg mentioned several times be^). A writing by Dardanos tvsqI OTad^fxcov is

3) De compos. med. p. gen. 5 p. 789 (Bold). Compare 6 p. 893: ol

•

I

8 tlDELLEK.

mentioned by LydoB*), in which the information was contained the vors oloni see Attic talent^). Another writer on this Gehifite, Diodoros, is cilirated by Suidas^). He has ehenfalis wrote a writing tib^I ara&fmv and in it the description Stimaiiing of the talent and its skills is given. more details, we don't know about him.

What else we know about metrological writings, We would like to thank the various fragments about measures and techniques important things that are still with us. That at the time of writing According to the oldest, the small one is probably in the analects of the Be- nedictiner published the piece Tteqi fUrgtav x.ai ataO-fiwv xal Tüiv dijAotivFwv ai!i« arjfiäzMv'''), because appears here nor the reduction of the denarius to -^^ pounds, so it has to happen Nero must be taken care of ^). We quote the anonymous author Böckli as the Benedictine metrologist. Far more comprehensive are the fragments handed down under Heron's name. The Investigation about the author and especially about the time It was written with great enthusiasm by various scholars has been listed, but still cannot be considered obsolete be considered. Because despite the extensive works Le- 1 tronne's and Marlin's*), which have recently addressed this question is, and Irotz of the contributions, which by German scholars b^ especially Böckh '■ °) delivered on this is still a certain result not achieved. The main difficulty is that there are different which Heron gave. The first is the well-known mathematician he and mechanic, the pupil of Ctesihius, who was at Alexandria

4) De

council I

lensibus 4, 9 p. 160 HoetI it). Ausderdaselbiitvorki

schlieraen, dafa Dardmos nk

len p. 791.

^ilpäüvio! in jläpdavo; xu ideo mention; of Miljarense r CoDfitnutin written hnt,

!ü § 25, 1 ADm. b.

I opuscula Graeca huctenus nou edita.

see Benedictidi. Paris 16SS. The he-

re «Bffio 32S4 entoomiDeti uud p. 393—393

efg. num. 2§ 10. Compare i

6y Under iiilnrrov.

7} Aaalecta Gra Ex MSS. codLcibu9 . said Fragment iat ex codice printed.

8) See below § 26 note 3 i. E., § 36, 1.

9) Letmnne, rechercbes critiqnei bistoriqnes et geograpbiqae fragments d'Hcran d'Atejisndrie oa du Systeme melrique E|ryptien, After 1 of the author «Death hnpaosgeeben by A. J. H. Vincent Paris IT' *

11 Martin, researches aar In vie et tes onvrsges d'Heron d'AJpxnndrii

l^^_ tons lea nuvragFS mathematiques Grecs qoi nnl öln ntlribne il nn ^^^^L Dnmme Rurnn. In Memiiires presentea par divcra BBvants a l'Ai ^^m Inscr.seriel. tnme IV, Paris 1S54. ^^H lU) Metrol. (Jäters. S. S— II.

\ SOURCES. 9^

probably in the second half of the second century V. C. lived ^ ^ ). A second Heron becomes Proclus' teacher stated, from which it follows that he also went to Alexandria, namely lived around the first half of the fifth century AD ^^). Finally, the third Heron is not written by any writer, However, there are writings by him on geodesy and military science shaft received 13). From a place in his geodesy, the one contains astronomical information, it turns out that this Heron z^ At the beginning of the seventh century AD, i^), i.e., flourished was probably a Byzantine. JNow we have under He- ron's name various fragments, all of which a larger, lost work on geodesy - go ^s). This work, which perhaps yewfxexQOvixsva headline was^^^), contained a full discussion about the practical geometry or the art of field measurement. Also There was an explanation and overview of the dimensions, according to which the taxes were levied; these must be the ones from Eutokius quoted (to be Heron's LiergiTid, and that's where it comes from). the three very important metrological fragments, which Heron's bear names. The first contains those at compiler time valid length measurements, the second the older ones were no longer there at the time common. In this second table we have the complete constant representation of the Egyptian measuring system, as shown below Formed by the Ptolemies under the influence of Greek forces and later under Roman rule by a few more Roman ones Mafse was enriched (Appendix § 11). The third table is the first parallel, but contains many different provisions.

11) According to Böckh p. 8 and Letronoe p. 26 under the government of Ptole maeos VII (Euergetes IT). Martin is looking, admittedly for no real reason, It seems likely that he lived until the first century B.C. C. ge- lived.

12) Proclus was born in 412 AD and studied in Alexandria, So Heron must have taught it around 430. Letronne p. 27.

13) Letronne p.29if., which is to be compared in more detail, leads from him to the writings published in Latin by Barocci (Venice 1572) ten de geodaesia and de machüiis belltcis, further TiaQtxßoXal ix rüiv aiqu- TTjyixtiiv naguTtt^stov et al.

14) Letronne p. 31 - 34. Even later, in the beginning of the tenth Century places it according to the same astronomical determination Ideler, treatise. derBerL Akad. 1812-13 p. 198.

15) Letronne p. 73.

16) The first fragment at Letronne p. 36 begins in"llQ(ovog do/ij T(ov y€(üfXiTQOvfiiv(oVj the second section of the same has the heading "ffgojvoe efaayioyal rtov yiiOfxexQovfji^ymv,

10 SOURCES. S8.

The first two fragments are first found in the Analecten Published by Benedictines and recently published by Letronne from the Manuscripts from the Paris library along with the third fragment been published ^ '^). Now back to determining the time to return to the original Heronic work As expected, you end up between all three Heron. The most recent indefs, although also the author of a geodesy decidedly in no way related to the work in question ^ ^). Letronne chose the second Heron, but without this to be able to justify it properly. Martin i^) finally answers the question mente goes back to a work by the older Heron. After his arrival view that essentially seems to deserve approval is the Elder Heron the original author of geodesy and the been metrics; from this work are at different times various excerpts, including the tables about the Mafse emerged, but the later customary measures were incorporated into this been worn. All of these later compilations still carry the name Heron^s to refer back to the original work. sen. What remains worrying, however, is that even the content of the second fragment, which contains the oldest provisions, in the period after the incorporation of Egypt into the Roman Empire Rich, and therefore considerably, to be placed after the older Heron; So this table should also xard xrjv TtaXaidv ex&eüiv already available in revised form.

They are on the same level as the Heron Excerpts Tables of the length measurements, which are in the under the Alexandrian Didymo's name is recorded in writing /u^r^a juaQfnaQCov xal TtavToicüv ^vlwv^^) are included. The second one can be found here Heronic fragment again without significant changes ^i), and a subsequent shorter table on the €v&v/d€TQtxd eidtj again agrees almost word for word with the text of a Heron

17) Anal. Benedict, p. 308 ff., Letronne p. 42 f. 47-50. 59-61. The The above count of the fragments differs from Letronne's, all of them Heron's fragments had to be taken into account. But she agrees with that von Fenneberg in his studies on length, field and Wegmafse p. 44 ff. given print. So I quote below briefly Heron, Fragm. 1 etc.

18) Letronne p. 75.

19) Research p. lOOf. 223.

20) Edited by A. Mai in Iliadis fragmenta et picturae, Mai- country 1819 p. 153 ff.

21) Cap. 14-16.

2. SOURCES. 1 1

Manuscripts agree*^). But in these two tables previous overview of the calculation of the square and Kubikraafse^^) there is the important deviation that instead of the Philetary foot of the Ptolemaic, instead of the Italian is called the Roman, where the secure key for the knowledge of the entire Philetary system (App. §11.2).

Only through confusion in younger manuscripts is it possible Didymus' writing includes a short fragment about weights. laid, which can also be found in a Heron manuscript det. It has no connection with Heron other than that it is included in the geometric collection on which he- ron's name had been inherited, was recorded^^). We citi ren the author, who must have lived after Nero, with Momm- sen as the anonymous Alexandrian.

A fairly extensive collection of metrological questions Mention can be found appended to the end of Galen's works. They all refer to hollow dimensions and weights and are probably with the practical needs of the people in mind Doctors who give the medication partly according to the hollow measure prescribed, compiled according to weight. That's why especially the reduction of the hollow dimensions on the weight of the wine or oil or other liquids contained therein made, a point that Galen himself made several times in his works come to speak. Also those in the tables guided comparison of different dimensions and weights, especially the Attic, Alexandrian and Roman Galen several times because in his various source writings also found different dimensions and weights. The first part of the Fragments are headed Falijvov tov aocpcovccTov tcbqI fiSTQcov y,ai OTad-fjLCJv öiöaGxalia, then follows an excerpt m Twv KleoTtazQag xoaiurjTiKWv tieqI OTad^jucüv zal jtieTQCov, So originally a compilation of measures and weights for ointments and fragrant oils; then a table comes over Measures and weights of the Rofs doctors and finally a fragment

22) V. Fenneberg p. 72.

23) Cap. 12 f.

24) Martin p. 191. 212. Mommsen p. 30 (where for Fincent Martin to read).

25) Tom. XIX of the edition of Kühn p. 748 ff. ; in something different those, less complete redaction also in Stephani Appendix evil- lorum ad thes. ling. Gr. pertin. p. 214 ff.

12 SOURCES. § S

^loanogidov nsQi fiivQOiv xat arad'/itaiv. The draft documents* time of the older plays under Cleopatra's and Dioscorides' names can be dated to the end of the first century AD, the younger ren Galenische be moved to the exit of the second.

The Bishop Cpiphani OS of Salamis on Cyprus wrote In 392 in Alexandria a writing neQi ihbtqwv aal azaS'- i4iüv^^), which are particularly affected by the hollow mafses, especially the biblical, briefly about weights and coins, also with chronological and other discussions gets busy. There are also two fragments, the first above some weights and hollow dimensions, the second about the length mafse^*^). In any case, both are from the aforementioned writing Epiphanios undressed; but since they contain provisions that missing from the writing as it now stands before us, it follows that we only have the latter in a mutilated form.

3. We only have Latin metrological works received very little. The most excellent is the VolusiusMae- ci a n u s , who died in 175 AD, distrihutio partium, a small one carefully written script, which depends on the names and designations gen of the parts of the As and of the Roman fraction calculation acts*^). The gromatist Baibus, who worked under Trajan and Hadrian was alive and wrote a letter to his friend Celsus probably under the title expositio et ratio omnium menr- mrarum'^^). We have two pieces from this, at least both of them in the extract, received. The first, eocpositio et ratio omnium for- marum^^), after the introduction, contains an overview of the red

26) Reprinted io Epiphanil opera ed. Petav. Tom. II (1682) p. 158 to 184, the second half also in Le Moyoe, Varia sacra (1685) p. 470 to 489. Heber place, time and autheolicity of the writing cf. Mommsen P. 791.

27) Both fragments are io the ^'ExXsxrd riviov raiv naXaimv TTfQi Tcav vnox(ifj^i'ü)v arax^fjKüV 'Eßgatiov at Le Moyne p. 498-503. The first is headed tov ayCov ^Enitf^avCov Kvttqov, the second TifQi nrjlixoTrjTog fjtijQOJV. Because this second fragment also belongs to the Epiphanios is to be attributed, although his name is not explicitly mentioned leads, both his position speaks immediately after the other question- mente, as well as the fact that the length measurements are in the original writing of the Epiphany could not have been missing.

28) Published by Böcking in 1831 and more recently by Mommseo into the Abhandi. the Saxon Society the science B. 3 p. 281 ff.

29) prefer the age of Baibus see Larhmann, writings of the Roman. Feldmesser 11 p. 135, about the presumed title of his work diesel- ben p. 134.

30) In the Gromatici by Lachmann p. 91 ff.

3. 4. SOURCES. 13

mix length and area measurements, the other, de asse minur- tisque eitus portiuncults ^ ^ ), gives a short compilation the parts of the ace.

There is a short discussion about the weights Grammarian Priscian in his writing de figuris numero- rum^^). The same is true, at least according to the authority of some Manuscripts, including the author of the didactic poem deponderibus et menmris^^), which is an uncritically written but overall reliable representation of the Greek and Roman contains hollow dimensions and weights.

Three small ones also deal with the ace and its parts Poems in the Latin Anthologies^).

Various metrological tables, all without special their value can still be found in the collection of grom- ian writings ^ 5). There is also the section from Isidore's etymologies, which deals with the fields and paths, taken n^).

4. Of course, all the others are also available as sources Writings of antiquity, insofar as they contain information about measurements, weights and coins included. Here you have to Criticism examines the value of communication in each individual case. fen. Herodotus is particularly well versed in this area, especially in The length measurement is not exactly reliable, it can be left to him that demonstrate the most certain inaccuracies and mix-ups sen. But more or less the whole of Greece shares this error. chenvolk with him. The habit of calculating in round numbers to take the measurements only according to their approximate amount, similar to equate the dimensions of different peoples and distances could only be determined after an imprecise estimate. common. One should also not forget that most of the

31) Published by Gronov, de sestertiis p. 883 ff. and by Böckin; zasammeo with Volasius Maecianas.

32) In coups p. 1345 ff., in Keil p. 408 ff.

33) Werosdorf, poetic Lat. minores V pars I p. 494 ff. In the oldest The author's name is missing from the manuscript, others mention Priscian. Under It is now generally cited by his name, and his authorship is unknown. at least better founded than that of Rhemnius Fannius Paiaemon, who has long been considered the author. Compare ßernhardy, Grundrifs der rb'm. Lit. p. 457.

34) Anthol. Lat. ed. Meyer II n. 1066-68.

35) GromU. ed. Lachmann p. 245. 371 ff. 407.

36) P. 366 ff. aas Isidore. Orig. 15, 13-16.

14 RECENT LITERATURE. § 3.

tizeD only occasionally used when treating other objects there will be, and that newer writers in such Don't be afraid to strive for absolute accuracy in cases. Under The later Saniinel writers take first place Pol- lux, who is in the section of his onomastics where he talks about the coins and weights deals 3^), good sources, especially Aristotle used. With great caution the lexical graphs and ancient commentators, such as Eustathios, need. Some of them have extremely valuable news from old, good sources, but also a lot of inaccurate and erroneous liche; There is also often information that relates to very different things Times and circumstances relate, undivided next to each other. Among the Romans is the gromatist Hyginus, from whom Unfortunately, only a few notes about length and area measurements were made. are a completely reliable source of information. From un- Unfortunately, our main source, Pliny's collection, can not be praised the same. The uncritical way he does uses his sources, has to be discovered precisely in relation to the dimensions astonishing inaccuracies, mix-ups and errors led. This applies to Festus and Paul's excerpts the same as by the Greek lexicographers.

The inscriptions “offer extremely little on metrology regarding. The most important is the Attic inscription that legal regulations regarding hollow dimensions and weights contains (§. 16, 1).

§ 3. Recent literature.

The earlier metrological literature of modern times is now completely antiquated. Indefs can be from a compilation of the main works, as they are sometimes still due to individual information must be cited and most of them at least from historiographical are of commercial interest, cannot probably be ignored i).

1. Not long after the reawakening of science Then the Frenchman Bude published his extensive work about the ace:

37) 9, 51 — 87 {n^Qi vo/jirtfLinTcov).

1) Compare the overview in Hussey, essay p. 1 — 9. A compilation position of the literature up to around 1670, admittedly very imprecise and highly clumsy arrangement, says Labbe in his Bibiiotheca nummaria. The Bibiotheca, which dates back to the end of the 18th century, is better nummaria by Lipsius ^ Leipzig 1801.

^ECEBE UTEAATCB. 15

Gol. Badaei ParisicBsis 4e asse et partibes tims libri V. Paris 1514^ tor Behrmais repeats '). The preface is dated Idibu Martü A. D. M. D. XJllI.

He collected the stencils of the ancients and combined them into one to simplify the system. One of his main purposes was to represent ment of the sesterce calculation, which was still a mystery at the time. He insures gold and silver coins with the greatest care to have weighed, but without causing errors like ror that of equality between the mine and the Roman pound to become*).

Uncertain what year, probably soon after Bude's work, published

LeoDardi de Portis de sestertio pecuniis ponderibns et seasnis aatiqnis libri doo ^). Repeated in 1524 aod more times (printed in the The- saar. GronoT. vol. IX p. 1433 ff.).

He didn't know the pound any other way than ad prindpia naturalia, quae stahilia sunt, namely after siliquae, Schotenkomem, to determine. He also believed in the measure of length to have to take away the natural measure; yes he heard the sound of a footmafs in the gardens of the Angelus Colotius (§15 note 5) was preserved and thereafter a measure was passed the staff of half a Roman foot. Names will be announced soon

George. Agricolae libri qoinqne de meosoris et pooderibns: ia qaibns

pleraqoe a Bndaeo et Portio panim aoimadversa diligenter excotiontar.

BasU. 1533. Lac.' Paeti de meosoris et ponderibas Romanis et Graecis com bis qnae

bodie Romae sunt coliatis libri qnioqne. Veoet. 1573 (printed in

Tbesaor. Graev. vol. XI).

Paetus first attempted to precisely determine the Roman Pounds by weight, with the correct value came very close (§21 note 6).

2) Lipsins p. 60. I used the one provided by the author himself Edition from 1550.

3) P. 122: hoc est enim capot eins rei quam agimus, here cardo totius operis, haec deoiqae alea aocipitis iocepti, ot ostendere aggrediamur vei demoDstrare potias quid inter sestertia ceotum et sestertium ceuties iotersite.

4) P. 159. 163.

5) The year of publication is not specified. The page numbers missing. The name of the author, different from the title, is in the Preface written by another hand by Porti'us ^ as he intended is called. According to Agricola, Portius' work appeared only after Bnde'schen, but the former apparently has no knowledge of the latter.

16 NEUERB LITERATURE. S8-

I. B. Villalpandi de Roraanis Graecis Hebraeisqae ponderibns atque Dninismatis, secuodae partis apparatus About secundus, in H. Pradi et I. B. Villalpaodi io Ezechieiem explanattones et apparatus urbis ac templi Hierosol. vol. III Rome. 1604 p. 329-500.

He measured the Farnesian Context first described by Paetus. gius (§ 18, 1) and tried to use this to get the Roman foot determine (§15 note 9).

De ponderibus, nummis et meosuris libri V auctore Jac. Capello. Francof. 1606.

An uncritical compilation of previous research; What deserves attention, however, is the fairly correct determination of the Roman pound, which he probably weighed from coins found (§21 note 8). Excellent works are those of

1. 1. Seal ige r, de re nummaria dissertatio: about postumasexBibliotbeca Academiae Lugduno - Batavae editus a V. Soellio. Lugd. Bat. 1616 (printed in Thesaur. Grooov. vol. IX p. 1493 ff.) and by

I. F. Grooov, de sestertiis seu subseeivorum pecuniae veteris Graecae et Romanae libri IV. Amstelod. 1656 ^). The earlier edits of the same subject in Gronov's hand, the first in Leyden 1619, the

. others published on Deveoter in 1643^), are less complete.

The former first drew attention to the Heronians Fragments from which he communicated extracts from manuscripts; the latter treated, at least for his time, exhaustively, what can be found in ancient writers regarding coins, and is still useful in this regard. Further developments Steps in metrology could only come from a more careful one Use of immediate sources, especially coins go out. This is where his career as a doctor and chemist broke out excellent

L. Savot, disconrs snr les medals antiques. Paris 1627.

He first carried out extensive research into the fineness of the coins (p. 650*.), found that the coins of the Al- In times of careful minting, they were beaten as finely as possible but that they were always present in the imperial period until Diocletian Goodness decreased. This is followed by in-depth investigations about the weight of the Roman coins and the resulting The determination of the weight cannot be taken from the weights Pound, also about the value relationship between gold and

6) This edition is quoted below. The work will often also after the paginal heading under the title de pecunta vetere listed.

7) Lipsius p. 161. Labbe p. 310.

1. 2. RECENT LITERATURE. 17

Silver, finally over that started by Paetus and Vilialpandi nen regulations of the pound and the foot, which a certain be subjected to so many criticisms and proven to be untenable. the. Made further progress

J. GreaveS; discourse of tbe Roman foot and denarius. London 1647 (repeated in Miscellaneous works, London 17^7, after which in the following- which is quoted).

He first showed the difference between the Attic drachma and the Roman denarius, and justified its provisions the same on careful balance. Much to be appreciated also contains, although poorly arranged and dry in the Form, the work of

E. B. Bernardy de mensuris et ponderibus antiqais libri tres. Edit altera, purior et duplo locnpletior. Oxon. 1688.

The small work by is excellent

J. C. Eisenschmidj de ponderibus et mensnris veterum Romanonun, Graecorum, Hebraeorum. Argentor. 17J)8.

The author had carefully examined many coins, drew the re- results with great sharpness and combined everything into one pre- detailed systematic presentation. It was the best so far- Handbook of Metrology® published thereafter). Much less busy Arbuthnot's Tables of the ancient coins weights are informative and measures (London 1727, Latin by Koenig, Utrecht 1 756), which were widely distributed as handbooks, but not new ones Residtat, but contains many inaccuracies and errors. 2. Towards the end of the eighteenth century, French scholars carried out the investigation with zeal and enthusiasm. follow up. Particularly noteworthy are Barthelemy and delaNauzein various treatises from the Academy of Inscriptions, the former also in the appendix to his journey of the boy Anacharsis. The collecting system is voluminous but of little use. work of

Paacton, Metrologie on traite des mesnres poids et monnaies des ancient people and modern people. Paris 1780.

Romedel'Isle, Metrologie ou tables ponr servir a Intelligence des poids and measurements of the ancients. Paris 1789 (German by Grofse, Brann- silent 1792),

is estimable because of the coin weights; but the author, who was not a scholar of the subject (pref. p. XIV), was not able to to utilize the material systematically.

8) Hussey p. 7. Hnltscb, metrology.

18 ^BUEflE LITERATURE. 6 3.

In the same Pci'iode appeared in Eagland Raper, Inquiry into the meaiure of theRomun foot, ia den Philosoplil- eal traoBBclions from J. IT60; and EDqairy inla tbe value of thu aBCJBDt Grecli ind Romaii moiiey, iii den Pbilos, trana. from J, 1771, both very valuable studies. His determination of the I Roman Purseg is the safest so far (§ 15, 2). I Eckhel's great numismatic work, Doctrina numo-

nim veterum, only in the proiegomenes contains some me- trology regarding. Very appreciated because of the richness Cebersicbten from Mfmzgewiditen and the prudent Kriük, with which uses the same to determine the weight and value of Roman coins wasted is the writing of

Letronne, coasid^rutionB geniiralcs sor l'eviilaBtion des monnalea GrBcqoos B[ Romaines. Paris lSt7 '). A service that was useful for its time, although rather superficial. written manual was I Worm, de poudvrum, DDmmoraia , ineDBur.'irain ac de anni ordinandi I raüunibus upud KnmaaDs et Graecos. Stutgard lS2t.

This is based on thorough studies and looks much higher written with great skill, only in the details of the coinage I always considered Dense to be a very reliable work HnEsey, oasay an the ancient weights and motiey, and thti Roman Greet liquid measures, with an appendix on the Roman and Greek fooC. Oxlord 1S36. In between, there are also things to mention because of the material worth full investigations of

Cagnazzi, sn i vnlori delle misure s dei pesi degü anlichi Rnmani, BDDti dagli originali isislenti nel real Muaeo Bnrbonico di Napoli. Naples 1S25. German see' poorly translated by k. v. Schfinburg. Copenbagen 1B2S; \ also the Abrifs from

B igey, traitc de nietrolegie nncienne et modern. Paris 1334, I ond the uncritical but useful as an overview. T collections of

Pancker, metrology of the ancient Greeks and Romans, lu the Dorpater

Yearb. Kr Literalar, Volume V. 1835.

The question about the Greek and Roman long and

I FISchenmars submitted to a careful revision

less, about the length and area dimensions of the ancients, in your hand-

2. RECENT LITERATURE. 1 9

luDgen the historical -pbii. Class of the Berlin Academy of the 1812-13. 1825. 1826. 1827,

in which he particularly criticized the arbitrariness of the French geo- graphene rejected and the main points of the so difficult and controversial subject matter with prudence and prudence stated. Unfortunately, no one has followed him on this path yet and yet this part of metrology needs more than any other others of a new exhaustive investigation. The little one Writing by Fenner von Fenneberg, studies on the Length, field and route measurements of the ancient peoples (Berlin 1859), which offers some worthwhile contributions, can just be found in the main point, the presentation of the Philetary system (Appendix § 11, 2) did not meet with approval.

Metrological science led to a new stage Böckh in his metrological investigations Weights, coin feet and measures of antiquity in their combination menhange (Berlin 1838). The work is too important and still sounds too much of the present to be a few here Words compressed together, and for that very reason easily misunderstood. existing judgment would be justified. Only that may be the case be shown that Böckh's investigations are one of them The aim of this manual is too different pursue as if they had served as a basis for the same can. The hypotheses put forward there about connection and derivation of the various measurement and weight systems, some of which necessarily still require proof, for example These have already been partly refuted by recent research in a manual intended for practical use be included. Apart from that, both this one has Work by Böckh as the sections of his that belong here State budget of the Athenians (2nd edition Berlin 1851) provided ample profit. This applies to a much higher degree this from Mommsen^'s epoch-making history of Roman coinage (Berlin 1860), which is in the manual not only, as is not otherwise possible, as a basis for the not only for the Roman coinage, but also for the Greek coin currencies are the guiding considerations has offered.

What foreigners are doing recently is much less important time in the field of metrology. Dureau de 1 a Malle gives in the first part of his Economic politique des Romains (Paris 1840) a brief overview of the Roman

20 THE NEW MEASURE, WEIGHT AND COIN SYSTEMS. § 4.

Metrology, especially weight and value determination Coins. Without deeper criticism, even in some cases with an astonishing The extensive work of the spa is composed of clumsiness. niers Don Vazquez Queipo, essays on les systems metrics et Monetaires des ancient peoples (3 vol., Paris 1859). Even those Coin tables, which take up the entire third volume, are due little due to the omitted description of the character usable.

§ 4. Overview of the most important new Majs-weight-

and coin systems,

Since when determining the old measurements, weights and coins zen the knowledge of the newer systems, especially the French If it has to be presupposed, it seems necessary To avoid repetitions later, the most important thing here is a brief overview i).

1. Length and area measurements. At the previous un- The old French partly carried out research into the old measure of length. Chinese, partly the English footmafs.

According to the most careful recent investigations the Parisian foot changed to the English one like 106575: 100000, it is therefore 1 English Fufs = 0.938306 Par. Fufs = 135.1160 Par. lines 2).

The Prussian or Rhineland foot is something smaller than the French one, according to legal regulations it contains mung 139.13 par. lines.

To the newer French system, the unity of which meters than the ten millionth part of the northern quadrant forms, the dimensions mentioned are in the following ratios:

1 Par. Fufs =0.3248394 Meters 1 Meter = 443.295936 Par.Lin. lengl. - =0.3048012 - 1 - = 3.280833 eng. Fuss l|preufs.F.=i0.3137946 - 1 - = 3.186798 preufs. F

1) Unless otherwise noted, the editorials are based on Gehler's Physical dictionaries, newly edited by W.Brandes etc. Vol. VI Dept. 2 p. 12540*. given.

2) Muncke a. a. 0. P. 1297. According to Bird's older provision from 1758 was the connection between the English and the French foot 10000:10657; then reduced Ideler, Abhandl. 1812-13 p. 146. Raper (see § 15, 2) has the ratio 10,000: 10,654. On the latter two Determinations combines Wurm (p. 6) the completely useless value of 135.1414 Par. Lin. for the English foot.

HIB NBÜEN »ASS- WEIGHT- II»D MÜMZSVBTEHE. 21

e geographical mile as the fifteenth part of a pittler Brelengrade contains 22803.3 par. feet 7407.4074 meters (= 7.4074074 kilometers) 23601.5 preufs. FusS). The Prussian acre contains 180 D of rods = 25920 DFufs and is = 2553.226 DMeter. In the newer one French system hüden 100 DMeter 1 Are, lOOOÜ OMeter 1 hectare.

2, The body dimensions, In the French system the Unit of hollow volume of liters = 1 cubic decimeter (= ^,1^^ cubic meters) = 50.4124 Par. CubibzoJl.

In the Prussian state the normal rate for liquid ities the quart = 64 preufs. cubic inches

= 57.7237 par. cubic inches = 1.14504 liters. When measuring the wine, 60 quarts give 1 bucket, 2 buckets 1 ohm.

The Prussian bushel, which is in lOMetz, each of 3 quarts is jeheiled, contains 3072 preufs. cubic inches '= 2770,742 par. cubic inches = 54.96149996 liters. The weights, the main advantage of the new French sian system is that according to the basic unit of the same, the meter, not just all lengths- FJäcben- and body measurements, but also the weight is determined. This Weight of one cubic decimeler of distilled water, at i"C. (the point of greatest tightness) and to which Reduced in a vacuum is called a kilogram, the same thing is 18827, 15 grains of the total Paris weight, the thousandth Part of this is the gram = 1S,S27 par. grains; this is the one Unit according to which the weights are used throughout the following of the coins').

The pound of the old French mark weight was cin- divided into 16 onces, the onces into 8 gros, the gros into 72 grains. l pound = 489.5058 grams

1 grain ■■

0.0531 grams.

3) Idcler p. 165.

4) Franznsea and Dentsche used to calculate in Paris grains, dii Englishman and Graias of their tray weight. But the Recbnong tiacl Grammen, which is common in modern Roman Catholic countries, according to Ein nihrang of the new club pound also JÜr DentaFbe beqDemer.

22 THE ^ECEX IfASS- WEIGHTED- D5D MC5ZSTSTEME. f4.

The English imperial code is the TroypfoDd, which in 12 ounces, the ounee divided into 20 pennyweights of 24 grains will. Its ratio to the French weight is different be determined. Chelius and Hanschild ^ ) put it = 373,243 grams; according to Weber, who is followed by Bockh^).

the troy pound = 373.2484 grams the grain = 0.064800 grams.

In Preafsen and several other German states is the former customs pound = 500 grams as a general weight introduced This new Yereinpound disintegrates into Prussia and Saxony in 30 Loth at 10 quents, 100 cents, 1000 grains. 100 Pounds make a centner. It is accordingly

1 centner = 50 kilograms 1 pound = i 1 Loth r= 1G|^ grams.

4. Coin currencies. In Germany there are, see from Bremen and Hamburg, according to the coinage agreement dated January 24, 1857 three coin systems. From the club pound fine silver is produced in Prussia and the northern states 30 thalers, in Austria 45 guilders, in the southern German states 52^ guilders (Rhine currency), everywhere with 10 percent increase set of copper struck. In addition, the southern all states including Austria Vereinsthaler.

The thaler breaks down into 30 silver groschen in Prussia 12 pfennigs. The remaining Thalerland (except Mecklenburg) also divide the Tbaler into 30 groschen; some, like Saxony and Hanover, the penny into 10 pfennigs. The Austrian one The guilder breaks down into 100, the Rhenish into 60 kreuzers.

The weight of the thaler is 18ff grams, the fine silver content 16f grams.

In France, according to the coin laws of 1803 one kilogram of coin silver, which has a fineness of -^, Beaten 200 francs. Accordingly, one franc weighs 5 grams and holds on fine silver 4^ grams; therefore behaves like einsthaler exactly like 27: 100 and is equal to 8.1 Sgr.

The newer gold stamping does not need to be taken into account as the pure silver currency exists in Germany, so that even the new club gold coin, the crown, only that fluctuating exchange rate according to the market price of gold.

5) Physics. Dictionary ßd. 6 p. 1303.

6) Metrol. Unders. p. 15.

5-5. THE FLEEVE MEASURE, WEIGHT AND COIN STEMES. 23

The Preafsian Friediichsdor with his legaleurs death 5f Thaler is too isolated to base the estimate on this could have been based on old gold coins. It is therefore Gold everywhere according to certain ratios to be discussed later- nits were reduced to the silver standard.

5. The dimensions and weights are in the tables, except to Prussian, also to French size and weight, which The latter is almost universal in scientific studies is common, has been reduced. With the coins, the re- duction on the Prussian Dreifsigthalerfufs.

The different dimensions, weights and currencies of the German states were allowed to be included in the tables neither the space nor the clarity. However, to everyone In order to meet needs, the supplement (A) is included the most necessary reductions to the dimensions, weights and values ments of the larger southern Prussian states together been set. There are also in a second supplement (B) some newer foreign length and area measurements Prussian and Roman forces were reduced. The occasion This is because there is a lot in new scientific works often kilometers, leagues, hectares, English miles and acres occur in relation to ancient conditions, and works, according to which the same reduces amounts that are understandable to us may not always be at hand.

FIRST PART.

The length, area and hollow dimensions.

First section*

The Greek dimensions of length and area.

§ 5. The system of Greek longitudes.

1. As with all peoples, so also with the Greeks and Romans originally derived the length measurements from the human derived from the human body. First you measure it directly with individual members of the body, the width of the hand, the foot or the poor and accordingly formed the names for them Dimensions corresponding dimensions. Heron remarks about this correct: xä jLisTQa i^rjvQrjvTat i^ dvd-QcoixLviov ixeXtJVy rjyovv daxTvXov, xovdvXov, Ttakaioxov, ouid'af.irJQy mqxBcog, ßTqf.ia- drew, OQyviag xat Xomojv^ and in agreement with this says Vi- truv: mensurarum rationes ex corporis raembris coUegerunt, uti digitum, palmum, pedem, cubitum i). Now by doing this natural measurements transferred to rulers, and gave them a fixed, If the amount no longer fluctuated, it was used others in simple round ratios. So the foot closed four, the forearm to six hand widths, the arm span or Fathoms counted as six feet 2). The transition to the larger ren dimensions that are no longer directly affected by the human body can be derived in bar, the step naturally takes the form because stepping out is the simplest way, like a human being

1) Heron Fragment 1.1, Vitruvius. 3, 1, 5. Compare also the Zasammen slellnng of body marses at PoII. 2, 157 f., Ukert, about the type of Greeks and Romans to determine the distances p. 6 f., Ideler, Ab- bandl. the Berliner Akad. 1812-13 p. 173.

2) An overview of the relationships of the most important parts of the human body gives Vitruvius. 3, 1,2.

28 r.RLECHISRUE LA^GE^HASSE.

can measure a larger distance. Have the most German This is printed out by the ftSmer in their pass and mileage system; but even among the Greeks it is Wegraafs, although it was originally Although it was standardized according to the FuXse, in practice it was usually the same the step has been determined.

2. The system of Greek longitude measurements gives... essential Herodotus (2, 149): al 6' knazov ö^yvtai öixatai elai arddiov B^anXei^qov, E^aneÖov fiev r^g S^yviijs fiET^BO- fihirje toi TEtgafTJxeog, twj- noöwv ftiv tet^anaXalatiDv I6vt(üv, Tov ÖE Tttjxsos e§a7takalazov. So he adds up the stadium 6 Plethren or 100 fathoms, on the fathoms 6 FuTs or 4 cubits, on the foot 4, on the cubit 6 handbreadths. Indefs Isn't the width of the hand the smallest measure he knows, because sometimes he gives instructions according to ödKrvloi, finger breadth- th, The daktylus is the fourth part of the hand width, i.e. the second part of the foot, as agreed by Pnllux, Hesy- chios «and others*) testify. He was the smallest Greek Length measure, hence later, as Heron states, also fiovdg called; but where stricter regulations were necessary, it was sometimes still healed in half, third, etc.*).

The next larger size, the hand width, naXaiair^ — for which only later naXaiartjs say ^) - giebl Heron agrees- agreeing with Heroüot | of the foot; it contained, as just now was noticed, 4 dactyls ").

The third Mafs derived from the hand was the OTiid-aftij, Span, the distance between the extended thumb and

I

3) Poll. 2, 157: tfoj^^i) aiiyxkfia»fvTf; oi T(ri_a(iegJ!äiiTvloi ~ rö S' aiiTo xni noinf ffrij. Uesycb.; nnilfiioii naiti/irj rh Kirripojf tfn- xtiliovjiftgov, etymol. M. and L Soxfiri, EosUtb. in 11. 4, 109, Hernn Fr. 2,2,4, SnidBÄ ont. noiis, nm^vg and ajädiov. — Examples of measuring naeli finger widths give analogue. are anim. 5. lä, 4, Tbeopbr. are, plans. 9, 6, 3, Polyb. 27, », 2, Dia Cbrys. 61 p. 331. One and a half fingers are XQla ■^ffiaxtÜiit called Polyb. 6, 23, 1 1,

_ 4) Herno Fr. 1, 2: narcaiv läv fiitniav ilaxiaröieqov (1. iläyi- m

&) prefer the use of the forms traXaiaiti and nuXuiaiijg s. L beck lu Phrynicb. p. 2U5; ntilaioijjt I end up first with the LXX, then J with Seitas Emprriens and the Lexicographers. r

6) Hernn Fr. 1, 4 ; jiaXniatiiv rftnpiov xnlovai i*vt5 diet tb tia- • ffEcpac l/iii' iaxTvlovs rj Sia lö ttvai rfia^Tov tov noäös. About the 1 For the construction of the palaces into 4 dactyls, see the note in the 3 cited places. ' Measurements near PalHsten give x. B. Rerod. 1, äÜ, Xenoph. cyneg. 2.4. 9, 13, Polyb. T, 22, 4. 6, 23, 9. 27, 9, 2, Uiodor. 1, 55, Atlia. 5 p. 199 p.

1-3. GREEK LONGITUDINAL ICE MASS. 29

small fingers; it contained 3 palaces or 12 dactyls i.e. f of the foot or half the cubit^).

3. The two next larger dimensions are the foot, ftovg = 4 palaces or 16 dactyls^), and the EWe^Ttrjxvg = 1^ Fufs, 6 palaces, 24 dactyls 9). The latter is according to PoUux (2, 158) the distance and wXe^qdvov TtQog tov fxeaov daxTvlov axgov, i.e. the forearm including the hand up to the outermost Lace. The division into 6 palaces is peculiarly Greek, because the oriental cubit had 7 palm widths, 28 fingers and was correspondingly larger^^). Different circumstances may have worked together to make the Greeks the smaller Mafs of 6 hand widths. The most important was probably the reason that this ratio corresponded best to nature;

7) PoU. 2, 157: ei tovs daxtvXovg anoTiCvag ano tov fisyaXov Tinbg TOV fiixQOTttTov fieTQOig^ anid^ecurj to /li^tqov. That's right agree with Hesychios, Pbotios and Etymol. M. aoter TiaXaiari]. The editorial team for 3 palaces and 12 dactyls Heron gives Fr. 1, 6. 2, 2, 6. 3, 3 and that £tymol. M.a. a. 0. Pliny 7, 2 § 26 correctly compares the anid^afiri with the Roman dodrans =f Fuis (see § 12, 1 below). according to measurements S])ithames are very common, as in Hesiod. op. 424, Herod. 2, 106: kxati- Qü)&i (Ff dvrjQ iyy^yXvTiTai , /nfya&og n^/miTrjg ajit^a/Liijg (3f Fufs high), Xen. cyneg. 9, 13, Aristut. are. anim. 8, 29, 4, Polyb. 6, 22, 4, ibid. 23, 14. 34, 10, 9. The anid-afiri is used as corn together with the nr\^vg also by Plato Alcib. pr. p. 126 C mentioned.

8) Proof of the relationship of the foot to naXaiarri and SdxTvXog has already been given above note 3; see also Heron Fr. 1, 7. It should also be mentioned that for half the foot in Theophr. are. pl. 7, 2, 7 rifimoSLOv occurs, and correspondingly for 1^ FuiV TQirifjLi.716^ (hov at Xen. Oec. 19, 4f., for 2^ Fufs nivd-rifiinoSiov ibid. § 3 and 5 and nivd-^rifjiinodia in Polyb. 6, 23, 2. Compare the Latin French expressions semipes, sesquipes and pes sestertius (§ 12, 1).

9) Herodotus in the passage already mentioned (2, 149) gives the ntj^vg 6 palaces. Hesych determines him to be 1 j^ feet. under d. W. and Suidas below. otddiov. Likewise Heron Fr. 2, 2, 10: n^/vg e/ti naXaiardg g\ Sa- xTuXovg x6\ xaXslrai 6k xal ^vXonqiOTixbg Tiijxvgy and consistent thus Fragm. 1, 11: 6 n-fj/vg 6 Xi&txog ^«i anid-afiäg ß' ^ noöa eva TiQog rc^ rifilOH ^ naXatardg g' etc. These were the old descriptions. At the time of the compiler, moods that were only used when measuring the Stones and wood were considered, while otherwise, as he says in Fr. 1, 8, 3, 5, there, the cubit was calculated to be 2 feet or 8 handbreadths. So does Suidas below nijxvg. Compare about this later one in classical antiquity Foreign division of the cubit, which appears to be of Byzantine origin seems, Letronne recherches p. 264-267.

10) The Egyptian scales clearly show this division (Appendix § 11, 1), we also know it from the Jewish so-called holy gen Elle (Böckh p. 265 f., von Fenneberg p. 92 f.), and the same is from the Persian cubit had the same amount as the Egyptian one (Appendix § 10, 1).

30 nniRcuiacBE längenmasee. s b.

In addition there was the advantage of the duodecimal implantation and the Please note that the smaller size was more manageable than the larger one. There are already traces of a shorter period among the Egyptians. ren Eüe, and among the Jews the common cubit also had nui- 6 hand widths. The Greek cubit divided in this way refers to Herodotus as a distinction from the larger persi-i see Elle as ftsz^tog ^lijxvs " ), i.e. as Mafs ühlictae ori the common Greek one.

The same need for smaller, more manageable dimensions also introduced the Greeks to the use of the foot, while In Egypt and the Orient only haste reigned'^). So Herodotus, who referred so often to the Orient, still uses it refers, more often to the cubit than to the puf, but since then it has been used instead of the whole ell, the two tiers of 4 palaces are always more frequent figer "s).

Another very common weapon was the fathom, OQyviä, the space between the tips of the two sides outstretched arms. This information given by Pollux is correct The Etymologicum Magnum also contributes by also referring to the

11] Herodotus 1, 17B is the width and height of the walls of Babylon in particular, he noted in an explanatory manner; ü

12) Prev. Tbenius in Ullinann's and IJbreit's Theut. Studies and Reviews ]846, 1 p. 12^, v. Fenncberg, Examiner. over the Langen-Feid- and WBgeniBrseS.91. 12».

13) The Bustiniinang of the Studion already begins the oldest tradition ' dag Fursiunra xnrück; Likewise, the plelbron after the Ful'se is not new

the cubit baseliniifltj the measure of luU PuCs was the basic dimension Parthenon in Athens; in Egypt wnrdB by the Ptolemies la the Egyptian table Ella oin the corresponding FuTs, the Phiietäriache, introduced, and aocb Then the FdI:s can be found everywhere next to the Elle in business. Frequently "Shut up!" The choice between two measures strives for the numerical data To live as roundly as possible. So giebl Polyb. 6, 23 the length of the Roman plane Scbildea to 4 feet, the length of the scbailes and the top of the pilnm 3 cubits each, the height of the helmet crest ^a 1 cubit, the diameter of the

kchest image to 1 span, he takes the run everywhere, iu which The dimension in question can be aired out without using axes. Aehn- Of course, there is a change between hustle and bustle, elleu and orgies in the masses. information in Herodotus 3, GO.

I

I

Äm:e?

Derivation of the word from öfiiyeiv indicates'*). The Orgyia (according to Herodotus, 4 cubits or ß feet.

4. The Greeks used the measures mentioned so far the larger lengths that cannot be directly controlled by humans could be borrowed from the human body, thus turning it into a single The ratio is that they are a hundred times as large as the foot when the orgyia took place. The former is the TrAs'&pov, the latter this axdötov. The term nXeSqov was originally understood Length of the furrow that the pilgrim makes in one go, up to he turns around again, a route that is just like the allitalic one voTSKS was calculated as 100 feet^^). It was therefore fraudulent the plethron determines the sixth part of the stadium, and so BS apart from Herodotus also the lexicographers and others ' *),

The axädiov (in the plural oToöia and OTädioi) referred to wob] originally saw the racetrack as fixed, determined pre-drawn route ^ ' ), but the length of the racetrack was

14) Pol. 2, 158 sings clearly: tl J' 'äfiipio löf x^Tea; IxjflVftcts, (lif »ol ro m^QVov «tircaii (Jv/j/itTpitv, opyma xaXeiTai rö fifzgor. Same Bedentang: apparently has the word aucb for XeDDpbaa when he Mem no. 2, 3, 19 says: /«ip«? u^f yÜQ, et 6foi BÜiaf ja nHov ögyviüs äiixoria ufia naiijaai, oix uv äivaivro. The place in the Elj^mul. M. lau- tet: oqyvta ari/Aaim t^ji' ixiaaiv tiäv j^fipiüv a'vv rijj TiXarn lov orij- 3-ovg, ituQcc TÖ OQtytiv Kwi Ittitlviiv Iß yvia. Graduation from ÖQiyiti' is correct, but the endong does not contain the adverb yvia, sondero dai Suffix ~via as in «^uiä from ayui. — Just like Herodotus 2, 14^ is correct the öeyuiä Heran Fr. 3, 2, 13.

15) Aef the explanation given by nXi&Qov for Homeriscly Form ndiäQov, in which the verbam nfkta&ai is not misunderstood. It So the nX^^QOv is ideutiseb with the oskiscben and ambrischeo vortui »dar versui, which also originally had the horn-nosed furrow, Since only a Placbenmars is mentioned (§ 12, 4), the two are like that too Homeric passages where 7iat9QOV seven hands (II. 21, 4117, Od, 1 1, ä77| auffasaeo: Ares and Tityos covered, dragged to the ground a distance of 9 five-foot lengths.

16) The ßestiuiDinngen about the amount of the nlO^gov gave up Herodotus a. a. 0. Hesych. below jz(le9Qov: aindiov Hxcoy, after the Emen- datio from Feriinoiua to Ael. var. are. 3, 1 (p. 193 Grooov.}, Soidas and L aaaaioP! TU nX(^poy (?;f(i) nöäa; g', also aoler rtXOfiov, where he still adds; to roü axaälou txrov itigoi, ojtfp tajl jirjxtuv S=' StitotQou (also fatla after Ferizonius' Emendation), Slov yctg ro arttiiöv lari tngn- ;(0(iCiui', Euatath. lu IL 21, 407, Heran Fr. 2, 2, 16. [Always the flbweiehtnde Determination of Luliann's Aacalonita, which refers to Hebrew Atafs, cf. v. Fenneberg, Unters. p. 9ö.

17) Yisdor a. a, O. gives the abbey: (Hercules) [irninde stage nppellnvit, quod in line respirassatsimniqae stelisset; "sahuntruthrhine" borrowed because, according to Isidor's own statement, not both of them stood there the run was the main thing. Rather, aTa

32 ÜRTECHISCHC: LÄiNGKNHA^sE. §^4-J

just wonders about the distance that a sprightly man runs at high speed He can go back without having to wait for breath to create. An ancient tradition brought to us by Isidurus (Orig. 15, 1 6) asked to be kept, wrote the first such provision to the Hercules, who was considered the founder of the Olympic Games: 'huG (stage) priinum Herculem statuisse dicunt. euuique eo spatio determinasse, quod ipse sub auo spiritu confeclsset'. One Pythagoras already knew a similar legend when he was calculating the stature of the ilercuJes was based on the assumption that the same one measured the Olympic stadium with his feet and made it 600 feet long. Gellius (N.A. 1, 1) reports us about it Plularcb : 'cum fere constaret curriculum stadii, i]Uod est Pisis apud lovem Olympium, llerculem pedibus suis metatum idijue fecisse kmgum pedes sexcentos, cetera quoque stadia in terra Gr.iecia ab alüs postea institut;*, pedum quidem esse numero sexcentum, sed tamen esse aliquaiitulum breriura, facile intellexit (Pytbagoras) modum spatiumqiie plantae Herculis ratiune propoitioiiis habita tanto fuisse quam aliorum procerius, qaanto Olympicum atadiiim longius easet quam cetera'. It be- So, as can be seen from this passage, all of them contributed Olympic stadiums in Greece as well as the Olympic 600 Fufs, and if they are a little behind you in their length - in Pythagoras' view this was simply because up, that their dimensions have a smaller foot than that of the Hercules, that of ordinary people, is taken as a basis had been. This provision of 600 feet therefore also applied without exception for the length measurement, which is taken from the racing Bahn derived and also called Azadiov. Herodotus calculates. As has already been stated, expressly like 100 orgies 6 feet on the stadium, and reduced in this proportion two places (4, 41, 86) orgies in stadiums; the same will also be the case Later the stadium was 600 feet wide. ben 1 *).

After what has been said, the following overview results Greek longitude'");

(Ttof the Bennbuha as the festa living, door the SeliDellUuf through the Barriers marked route. Compare Passow, HandwIlrterb.uDt.d.VV.

IS) Heran Fr. 2, 2, 19; Suidas nat. araSiov and fiiUov: to aiäätor fxeiaöäag x- i"'- "i-^^e"*-- ölov tb atäSiav iati THQaxoatiav (ti^- Xtaiv). Aacb the redactioD of the stadium at 625 roman Bclie Ful'a is an indi- real proof that the same 600 Greek va\i enlhüit, that the Vötnischbe Pufs to the Greek in the Verliöltnils 24: Ib dies.

l'i) The numbers in the table that correspond to each other indicate the ver-

§6,1.2. GRIEGB1SGH£ LONGITUDINAL MASS. 33

azdotop

1

TtXe&QOv

6

1

oQyvid

n^Xvg

Tiovg

100 400 600

16f 1

66f 4

100 6

1 H

1

TtalaiGTv

800 2400

133^8 400 24

2

6

1*1 4 3

1

däxzvlog 9600 1600 96 24 16 12 4.

§ 6. Overview of the less common length meters,

In addition to the dimensions discussed so far, there are some already with older writers, and sometimes with several later ones less common measurements are presented for the sake of completeness must not be ignored. In the following overview At the same time, the foreign measures are included, which are at Greek writers appear.

1. KovdvXog^ after Rufus Ephesius^) the middle one Articulated bones of the fingers, is formed by Heron (Fr. 1, 3) into 2 finger- widths specified.

2. JcjQov have Homer and Hesiod^) as length measurements. PoUux, Eustathios and the lexicographers declare it to be the same- significant with TtalaiOTT]^). Vitruvius^), who has the same determination gives, adds the correct derivation: 'doron Graeci appellant palmum, quod munerum datio graece dcÜQOv appeal: id autem semper geritur per manus palmam\ Until later times, kept this meaning of dwqov to describe the Bricks, one type of which, as Vitruvius notes, is pentadoron, the other tetradoron biefs, depending on whether they have five or four hand- broadly kept in the square.

ratios of the dimensions next to it, e.g. ß. 1 ardSiov ^=^ 6 nXid-Qa = 100 oqyvial etc. The first column gives the reduction of the stadium, the second that of the Plethron, etc., e.g. B. 1 anid^afiri = 3 naXaiajaC = 12 SdxrvXoi.

1) De corporis humani partinm appeliat. p. 30 ed. London. : rä nqiata ttQd-Qa TiQoxov^vXoi, ra ^e i(pt^s xovSvXoi, t« ^k reXsvjala fietaxov- SvXoi.

2) Hom. II. 4, 109: xiqa kxxaiSExaStoqa, Hesiod. op. 424: (Tfxof- ScjQog autt^a.

3) Poll. 2, 157, Hesych. and Suidas below. ^(oqov. Eastath. to IL 4, 109: tqItov ani^af^rjgTo ^üHqov, o Xiyeraixal naXaiOxri d-rjXvxtSs xal [6] TiaXaiarrjg agaevixcjg' tan dh ^läarrjua retQa^dxTvXov,

4) 2, 3, 3.

Hultsch, metrology. 3

d4 nniEciirscRE la^ige.miaese.

GlwcUbuileutüDd with “iß^offfii; warea according to Polliu.^) also ' doxtt^'l and daxTvlod6xfi*j, the former comes in the same sense Äristophanes'^) gate. The different explanation of Photius, wonacli äoxfi^ as much as ajti&aftij should be, muls on one based on error').

3. The öixäg refers to Heron as öifioiQov onid-ofi^g and accordingly besfiranit them to two handbreadths^). Better He would call it, by derivation, the half of the foot have what the older writers, as above (§ 5 note 8) has been noticed, ^fiifcödiov use. Uit the Öi^äg is allowed Do not confuse the kix

4. 'Oq&6(J(oqov is the length from the wrist to to the finger fungi, like Pollux '") supposedly. After the question

5) 2, 157: rfo^/i^ J* ouyxXiiaa-iVTCi al rftrupte ääxivXoi, xal SaxTvloSöxi!''!' TD 3' aiiio xitl TrnlnKFi^. Gbenso Explains

6) Equo. 318.

7) At Anslopbanes a. n. 0. you bite it from a white sheep, he ate before he was hit one day, ufi£oy ^y i!iioiv Sojf-- fA,uiy. Snidas, who cites the passage, explains äoxfi'} Inr aTiiSafi^; alleia the scholiist correctly observes; itvo nalaicnä;. (xicivöfifya yap tA lojrvA TÜv Sip/iäj(ov llg nXÖTog av^iTui. The scraper will emerge there not two spans long, but two hands' width, Ancb the etymol. explains the passage in this sense. It therefore undermines the statement of Phatioa nnt. oaiiJaui;: Ttiv ani&a/j-^v xivis xal äoxt^'iyalavaiv oviioK^aTZ- vo; probably because of a mix-up. Hesychius and Snidaa uncritically bind both explanations. i

8) Heron Fr. 1, 5: ^ Si^ä; lj(ei JiidaiaiBs Jilo ijyovy äaiavXovf öxTiö, xovSvXovs i^aaagas xel xaXuiat äl/ioiQov amS^afiijg. In the following- i this is for äij(ä( nndoubtful i-'X^S "> read; Xij(Bg Si Xiyetui zo xmv äio iaKiiXav ävoty/ia, loS ävii^ft^os Xfyai xal zov lij^avoS. Compare, the following note

S| Poll. 2, 158: (I IOC ufyay SäxTvloV J^ Xixav^ ävuretyitS , (firzQoig), TD fi^tgoy Xi%äs, similarly also Phol. unt. aniaafi^ and He- ran in the place mentioned in the previous note. That's fine, . ^ dnfs in the fragment at Greaves discourae of tbe Roman foDt p. IS. _ the Xt);at is set at 10 dactyls. .1

lU) 3, 157: 10 änö xaQnoü tei; äxp9oSmQov. This agrees with llesychioa overeio, which, however, has littleW'^ dantliob says: ÖQihöiStiigov ftirQov, ih öpffoc r^f ^ffiyöf «Jio uKpov io3 T xR(ini)ü /i^XQ' '"" 3axiiiXov (where vitleicbt äxpou before Tofi iTrxiiJ^u ca j lastist). Waserhinzolugl: oirfia " ' ' based on precise fieslimmuDg.

ii9afi^v, can m

■ anf ainer ob- '

3-5. GREEK MEASURES OF LENGTH. 35

According to Greaves, it contained 11 dactyls, meaning it was the arctic •d^afMi] very close.

5. Jlvytiv and Ttvy^iij are two close to the nfjxvg turned Mafse as she also from the tip of the elbow be counted on. The Ttrjxvg reached from there to the top of the middle finger, but the jtvytiv only up to the joints curved fingers, the lowest part of which extends to the first link remains in the same line with the hand, so still counts; the Ttvyfxi^ up to the clenched fist. This one There are regulations in connection with Pollux^^), with which the Values given in the fragment by Greaves are correct match well: ij öe Tcvyfxrj iazc dccxTvXwv i7j\ 6 de Ttvywv x', 6 de nrjxvg xd'^^). At most it could be as something seem too much to talk about the first member of the Mit- Four dactyls can be counted from the fourth finger to the tip of the same; but it is sufficiently explained by the fact that in this way the Ttvywv just like the palmtpes of the Romans just five hands wide received As Mafs, the nvytiv already comes with Homer before, later also occasionally in Herodotus, Xenophon and others ^^)\ We only find the Ttvy/iiij as length mafs in the name of fabulous people of the Tlvyfxaioi. Originally it was thought In any case, there are dwarves the size of a Ttvyfi'q^ So not much higher than a foot; only later was it implemented to give the fable a little more probability, to its height added some things and made them TQtOTtl&afxoc ^ *).

11) 2, 158; djTo (oXexquvov ttqos tov fiiaov SdxtvXov dxqov j6 ^tdarrifia nrjxvs' ei ^k (fvyxdfJLxpeias rovg ^axrvXovg, an* dyxdSvos in* ttVTovg nvydjv t6 fi^TQoVf ei ^h axjyxXeCaeiag nvyfJLri» about nv- yoiv compare also Eastath. za II. 3, 6: nvyovaiov lOTt didaxrifitt r6 dno dyxiovos eong tov (jlixqov öaxrvXov rj xal twv SaxjvXtav auvearaX-

fJLiV(OV.

12) The nvyav is determined in the same way by Heron Qr. 2, 2, 9.

13) Homer only has the adjective nvyovaiog: ßo^Qov oQv^at o

14) The first mention of the Pygmies and their dangerous enemies, the cranes, as is well known, can be found in Homer H. 3, 6, including Eustathios noted: XfysTai ^k otl ol Ilvyualoi ovdh nfj/vatoi xo fx^yei^-og eiai, nagcjvofxaOf^ivoi ydq eiai nvyovi. Ctesias at Phot. Bibl. p. 46 a, the moving them to India makes them a little bigger: /niXQol 6i üai XCaVy ol

3*

»

36 CBIECHISCUG LANGEHASSE. 9^; n-IS.

6. B^/(0!, step, fraudnacliHeroni'') 2^ Fufs. The- The same distinguishes, in addition to the simple step, ß^fia anloiiv, still the double step, ß^fia äiTrlovv ^= 5 FuTs, a mafa, that Olfenbar is modeled on the Roman passage by the Greeks The step is nowhere seen as an actual measure of length. thinks, although it is certain that there are a lot of developments among them Distances were determined only by stepping out (§ 8, 3).

7. Svlov, an Egyptian MaXs, is only used by Heroa led and to 3 cubits (r= 4J feet = IS handbreadths) determined.

8. The stilb is used to drive the animals, served after the Etymologicum Magnum and the Schoiast to AjioUonios also as a measuring rod, the latter heslimms them xa 10 feet, as did Heron, who had the same amount under the Na- men xälafiog knows ^ ''). Compare the Roman per- Hca (§ 12, 4).

9. 'i^fifia, an Egyptian mafs, as it only comes from Heron and Didymos is mentioned, was probably the name for the measuring cord. It contained 40 cubits or 60 feet.

10. JlavXog is twice the stadium as avkög had according to Ätbenaeus 1') also the meaning of OTßJiov. DeriJto^^o- d^6fiO£ had the whole stadium up to the column and back again to go through, like the scholiast to Arislophanes and after give him Suidas; the öiavloQ therefore contained 1200 feet or 800EUen'8).

fiexiiÖTicioi aiiiäv jinxfiav 3vo, ol (ff TrlftOioi iviis ^uKT^o; Ti^/tof, and in 90 they were savb oach Megastbenes at Strab. 2 p. 70 and 15 p. 711 TQianlO-iifioi, whereby Plio. 7, 2 § 2 <> and Gellios 9, 4, 10 agree. In general, vei^l. Grenzer camineDt, Ferod. p. Iä4f, note 128.

Ib) Fr. 1, 9. 2, 2, 11. The opposing determination of the iulinnna voa Aikalon, according to which 2 cubits or 3 feet are counted on the scrims, refers to Bebraean Mafs, like Fenneberg Unters. p. 9ä proves.

16) Schol. in Apollo. Rhod. 3, 1323: Sxan-a XfyfTcu xai u fiiToov yiii dexdTrovy, QiaaaXüv filpiu'«, *o' noi/imixii Si Tis ^äßäo; ovtu xalehat. Also Heron Fr. 2, 2, 17 and Enipbanios in the fragment Le Mojne Varia aaera p. 500 gives Akana 10 feet.

17) 5 p. 189C; näv ro äiaiernftfvov (lg lö&vnjra ff/^^« ailov xakavuiv, äanfQ jü OTaäioy,

18) Schol. to Av. 292 (and after him Snidas): Jlavlo; Mynai 6 Jii Tov lyBiv Tor S^öfiov iv T>i noQclif, i6 JliriQiSaal lo otä^iav xal üjto- OTpi'fiai. — ■ '4i.Xiog. diaviag u itiaiääiog ronot 3 /ifipov jiiyffwv ff', According to Heron Fr. 2, 2, 20, who gives the correct determination, do so is reading. AN Dnppelstndion also explains the etaiAos Vitmv, 5, 11, 1. Compare Kraose Gymnaatili and Aganiilik I p. 345.

I

§ 7. GREEK HATE OF AREA. 37

11. ^l7t7tL%6v is the route that is in the Xtctcloq ÖQOfiog was returned. The word only comes in as LäDgenmafs a Solonian law, for which Plutarch i^) provides the explanation gibt: to iTCTtindv dtdaTiqfxa xaaadqtDv ijv OTadlcov. With that the information from Pausanias and others agree ^^).

12. ^olixog, the endurance run, whereby the stadium was originally initially seven times, later even more often up to twenty-four has to be passed through at some point, according to a gloss by Hesy- chios^i) have also been used as length measurements. Yes We have no other information about the amount of the same than those in the second fragment of Epiphanios^a)^ according to which 12 Stages can be counted on it.

13. MlXiov, the Roman mile, is used by the Greeks According to the authors who first mention it, there are 8 stages calculated. For more details see § 10, 1.

14. naQaadyyrjg, the Persian Waymafs, contained According to Herodotus and Xenophon, 30 stadia. Compare Appendix § 10, 1.

15. 2xolvog, an Egyptian mafs, is mentioned by Herodotus 60 stages, from Eratosthenes to 40, from others to 30 or 32 Stadiums counted. For more details see appendix § 11, 3.

An overview of the Greek longitudes is given Table II A. B.

§ 7. The area majse.

The only area measure that was found among the Greeks that can be proven with certainty is TtXe&Qov, it is the same like the Italic versus and actus (§ 14, 2) the square of of the same name, contains, as does Hesychios expressly states, 10,000 square feet ^). The Roman ones

19) Sol. 23.

20) PaasaD. 6, 16, 4: ^QOfiov ^tal tov InnCov /nrjxos dCavXoi Juo. Hesychios: tnneios dgofiog tsTQuaraSiog Tis, which means the corrected reading kind under Inntxov: TeTQuarä^iov za compare is. Phot. p. 111.4 (Person): Innilg (1st tnnaiog) 6 ix TsaaaQcav araöCtov Sgouog.

21) ^oli/og, uirgov yijg, About the SoXixog as cross-country skiing cf. Krause Gymn. I p. 347 ff.

22) Le Moyne Varia sacra p. 502.

1) Hesych.: 7i4lsO-Qov fxixQov yrjg, o (pacft fivqCovg noSag ^€«v, what to compare Frontin with. de limit. p. 30 (Gromat. ed. Lachmann): pri- mum agri modum fecerunt quattuor limitibus clausum, plerumque cente- Dum pedom in utraque parte, quod Graeci plethron appellant, Osci et Umbri vorsum. A description of the surface plethron is given by uripides ion 1 137 ff.

38 GREEK AREA MEASURES S7.

Writers who use Greek sources translate nli'd-QOv regularly by tugerunty although this over 2^ times greater than that (§13 note 3), and vice versa Plntarch and Appian the qmngenta iugera of the Licinian law

The a^ot;^a may also be a Greek surface mafs been. The word usually means the farmland without reference to a particular measure, but Herodotus^) it takes for an Egyptian area measure, which is 150 cubits kept in the square. The Greek government must also make a similar contribution sche Arura, if there ever was one have; the different determination of Suidas^) is certainly based on a mistake.

Like aqovqa, the ^t;iy, a Homeric measure, also depends with the plowing of the land, because yvtjg is that Krummholz at the plow. The texQayvov in Homer s) means obviously a piece of land that a lively worker could use in one can plow for days, i.e. something similar to the Italian Jugerum Mafs. Whether there were four Plethren the same, like Hesychios and the Etymologicum Magnum ^) must remain open.

When reducing the Greek area Prussian and French Mafs, which Table V gives, is the Attic foot (§ 10, 2) is taken as a basis. After that is a Plethron almost exactly the same f one Prussian morning.

Polybius 6, 27, 2 names a square whose sides are each 100 Fafs from that Center points are distant, TSTQcinXe&Qov.

2) Plut. Camill. 39. Appian b. civ. 1, 9.

3) 2, 168: ii ^k aqovQa ixarbv nri/^ojv lotl AiyvnrCtov Ttuvri^,

4) nt. d. W.; ^ aqovqa nodag fj^et v\ If Suidas here, like Ideler p. 179 rightly assumes that he meant an area measure, so he did expressed inaccurately by using the wording as 50 feet Square feet understands. So you have to add a navTTj or navTa/o&ev add so that the length of one side of the area is designated. The Zablan information alone is also corrupt. A word that originally Lich means the arable field, cannot denote a mass of ^ Plethron- don't have. Anyway, it is. with Jomard, exposition du Systeme etc. ia Description de 1' £gypte edit. Panckoucke vol. VII p. 527, noöag qv' = 100 cubits to read.

5) Od. 18, 374 and the explanation of Enstathios: TSTQccyvov SidüTTifia Tif oaov rjv agorgiäv, tog eixog, cf*' rifiiqag rovg äya&ovg iQydrag xal ^Qca/biivovg ßovalv ofioCoig. Same to Od. 7, 113: Tetqd- yvog, ov ixdajrj rmv TsaadQbrv nXsvgeav yvrjv f^f v, which shows, that yvrj may have originally meant the length of the furrow. UsvTti* xovToyvov räfievog has Homer II. 9, 579.

6) Both equate the yvti to the nXä^Qov.

§ 8| 1. DETERMINATION OF THE GREEK LENGTH DIMENSIONS. 39

§ S. Determination of the Greek length mejse.

1. While with the Romans we have a solid unity of... Length measure, find the foot to which all other measures are in an unchangeable relationship is set, and this foot can be determined with all the certainty that is desirable, So, as far as the Greeks are concerned, we are not even presented at first. about in certainty whether they agree or differ of different length dimensions. The presumptive answer on this question it must be the case that there is probably just as little here There was greater agreement than in the hollow dimensions, weight, coins and even in the calendar. But against that That speaks so well with the Greek writers themselves as there is no mention of different length measurements anywhere and Even among the Romans there are only uncertain hints about this. the. Hajiptly based on this negative evidence the modern German metrologists and geographers almost overall stick to the view that there is only one common one Fufsmafs all over Greece ^). Completely in tune There are French scholars, particularly Freret and Gosselin are to be mentioned, among which, of course, are not to be approved Conditions have come about for the main country genmafs, the stadium, assumes very different values^).

1) Mannert, Geo^r. the Greeks and Romans I p. 2006:, Ukert first inv. Zach's Monthly Correspondence Vol. 23 v. J. 1811 p. 488 ff., then more detailed in the monograph: on the manner of the Greeks and Romans to determine the distances and about the stadium, 1813 (see especially p. 37). Ukert addresses the question again in the same spirit his Geography of the Greeks and Romans I Dept. 2 p. 51 ff. Likewise, decided on the unity of the length measure Ideler in the first part his investigations into the length and area measurements of the ancients, handl. the Berliner Akad. 1812-13, historical - philosophical class p. 181: 'in The peoples of Greece must agree on one point. come, in the use of the footmafse. This view closed definitely refer to Wurm p. 95 ff., Böckh M. U. S. 281, Forbiger Handb. der old Geogr. I p. 552 f.; although Ideler himself in the continuation of his Investigations in the papers of the Berlin Academy from 1826 and In 1827 a different result was reached.

2) Freret, sur les mesures longues des anciens, in Mem. de TAcad. of the Inscr. XXIV p. 492 ff., Gosselin, recherches sur la geograpbie syst^ma- tique et positive des anciens IV p. 290 ff. Compare about this as well as several other Ukert about the nature of the Greeks, etc. p. 49 ff. On secure foundations for d'Anville in his Traite des mesures itine- raires (Paris 1769), which was built on top of the Olympic stadium in ^ Roman mile

40 DETERMINATION OF THE GREEK LONGITUDE MASS. § 8.

Starting from the remark that the information from the old Greeks across terrestrial distances neither from each other agreed, much less with the more recent measurements could be reconciled, they couldn't find the reason for it in the inadequate determinations of the ancients themselves, but They searched for the differing information in accordance with with our measurements, that they are completely different. which types of stadiums were set up. I believe the right to do so in the various information given by the ancients about the surroundings to find the bottom of the earth. All of this information, they assumed, are based on correct measurements. So if Aristotle The circumference of the earth is 400,000, Eratosthenes says it is 252,000 stadia, So both mean the same dimension, only the former uses it a much shorter stadium than the latter. The unsustainability this whole hypothesis and the contradictions to which this- the same leads, are thorough and convincing by Ukert and Ideler. have been presented sufficiently so that they are now reflected as once and for all sets can apply 3). Nevertheless, careful management has equation of the information contained in the ancient Greek writings give information about local distances, with the more recent measurements led to the fact that the unconditional unity of the length dimensions, as the German geographers assume, are not can be held.

2. When discussing this difficult question, it is necessary It should be pointed out again that first of all in The system of length measurements was in agreement. As we saw, a stadium closed under any circumstances 600 feet, and the ratio was just as little other more important length measurements are fluctuating. Take Let us now make sure that the basis of all measures is consistent certain dimensions of the body formed and that of it derived sizes do not exceed a certain limit can fluctuate, it follows that with some restrictions the sentence is correct, that the Greeks are equal of different length dimensions. So it can e.g. B. a stadium, whose foot is only 6.3 inches (Prussian), as in French

nnr the shorter one from ^ Meile and the so-called Aristotelian one from Y^YT degrees = 0.0675 or ^ Roman mile. That's the latter has no permission, will become clear later.

3) Ukert Geogr. I, 2 p. 51 ff. and about the nature of the Greeks, etc. P. 46ff., Ideler Abhandi. the Berliner Akad. 1825 p. 169 ff.

S. DETERMINATION OF THE GREEK LENGTH DIMENSIONS. 4t

see scholars have put up ^), never been in use be. However, the slight differences that could be found were individually so infinitesimally small that they could not were taken into account, especially since it was rarely the case that to compare different foot dimensions precisely with each other^). This is how Pythagoras came to the conclusion that the Olympian Stadium was built with a larger footprint than all other existing ones in Greece at the time, but he had this not directly from an equation of base rods found, but only from the different lengths of the city then closed^); and what's more, we can't find it anywhere Greeks themselves provide information about various footwear, let alone because sharp determinations about the difference between them.

As far as the EUenmafs is concerned, at least one suits us Equation of the Greek cubit with a foreign cubit from the mouth of a Greek. Herodotus^) says that the royal The common Persian cubit is 3 dactyls larger than the common one Greek {fxsTQiog Ttrjxvg). Noticed elsewhere^). He said that the Egyptian cubit was the same as the Sami one. He does not say how large the latter was; but it is evident that she deviated from the common Greek cubit because he otherwise the Egyptian cubit would simply be equated with the Greek one would have. Herodotus and his contemporaries knew that the common Greek EUenmafs from the foreign ones Ellen was different, and even knew the exact difference of the former from the Persian cubit. Now that we are know the Persian cubit from monumental measurements, like this we based it on Herodof's Greek cubit; it results is approximately 465 millimeters^), is correct thus coincides with the cubit of the Attic foot as well as the so-called

4) This is the alleged stadium of Aristotle, derived from its information about the circumference of the earth (1111^ anf the degree), first from Freret a. a. 0. p. 507 ff. put up. In such stages Herodotus is said to have dimensions of the Black Sea (see § 9 note 5 below).

5) V. Fenneberg Subs. p. 4 ff. For example, B. Polybius no un- Difference between Greek and Roman forms.

6) See the passage from Gellius cited in § 5, 4.

7) 1, 178. Compare above § 5 note 11.

8) 2, 168: 6 Aiyvnriog nij/vs rvy/dvst Xöog idjv t^ ZafiC(p,

9) The Persian cubit holds according to Oppert's measurements (Appendix § 10, t) 525 to 530 millimeters; we calculate from the smaller number 3 dactyls of Attic foot, about 465 millimeters remain. The Attic cubit is 462 millimeters according to Table II B.

. 42

: THE UHIECHISIT LONG HATE.

geoaiinteu olympicben StedioDS of 462 MJIüineter. According to dea Bcuern information about the actual dimensions is now the The question of the origins of Greek haste is easy to answer. words. The Egyptian and also the Persian cubit, that one was equal, were in 7 palaces, 2S dactyls getfaeiit"'). The small- Asian Greeks and partly aiicli the islanders, like the Satnians, maintained this lUafs unchanged^*), in which Hellas proper became the seventh palace of the Oriental lectal cubit was thrown off and the shorter, duo- decimal divisible cubits of 6 palaces, 24 dactyls. That's her According to Herodotus, something larger was larger than the Persian Elle, because the latter is only 3, not 4, dactyls longer determined to be the sternest one should not cause any concern. The Greek The Chinese cubit was borrowed from the oriental one, but the measure therefore not yet transferred exactly to the line. That's why Nor should we conclude that by establishing the ^li- tqtoq nrjxvs Uerodot's the unit of Greek longitude egg meadows. This Elle, who likes to see herself as a Greek, is just the measure Tone 6 palaces, one palace shorter than the oriental cubit; but that the same without any fluctuation throughout Greece had been the same, it would have been too much to believe. Also standard hero dot his stadium according to this cubit any more than Xenophon did . his own according to the Attic foot.

I 3. This leads us to the question about the stadium. See

' a slight difference in the size of the foot or ulna mafsea had to be taken out several hundred times, and that this really did not escape the attention of the Greeks we have the already cited testimony of Pythagoras that the in Olympia, Sladion was built longer than any other in Greece. chenland. This is exactly what the indication of a late Roman one leads to Scriptwriter, the censor, according to which the Olympic and the Pythian stadiums of various lengths were ' *). Still

I I I

10} Compare Appendix § 12, 1 and 10, 1.

11) The Llcinasialisclie Fofs (App. § T, 1) is, among other things, the persUcheu Ella formedj the Sami cubit, vahrai^hviiilLcli the maJ's oncb other island- greekbop, is, according to Flerudo, the same as ügyptiscljeii.

12) De die nalali 13: naui ut liraltistheaea f^eometrica ratione colleglt Daximum terrae ciruaituni esse stadioniui ducentuia quinquaginta dnum nilium, ita Pytbagoras, quot aladia inter terrain et siogulas Stellas esscnt, indieiTiC Sladiam autem ia bac mundi lueasni'a id nutissimum iDtelligen-

lunt praet

:Dm VDRaot, pedun a longitudini

iraioviginti quinque: oam it Olynipicuni, qood est 9 likes this passage as a reference

3. DETERMINATION OF THE GREEK LAFFGBN MASS. 43

All Greeks speak where they use Greek language Mafoe determine, only from stadiums par excellence, without the slightest to give an indication of a difference between them; and if you wanted to conclude that it was just a city dion as a length measure was common throughout Greece, So the difficulty still remains that it hasn't been said anywhere which of the different racetracks forms the basis for the assumed general length mafs. Of course, most metrologists took little offense to this. taken by believing that no other stadium could do this as the most distinguished in Greece, the Olympic one be. This is how the length measure, the size, got its name The same arose from the information provided by Polybius and Strabo and others, that 8 stadia go to the Roman mile. It It can only be shown below (§ 10, 3) to what extent it is It is likely that the eighth-mile stadium is really that was Olympic; but even if the identity of both is granted, the unit of Greek longitude is mafse still not saved because the older writers,

confirmation of Pythagoras' statement about the different lengths of the Greek Reonbaboen apply; but it is absolutely no further to use; because you can explain it and use it however you want you come across contradictions. First of all, the relationship can be between the Italian and Olympic stadium cannot be properly determined, because The censor assumes that the fafs of the Italian stadium, d. h. the Roman Fafs (§ 13 note 6) was the same as the Olympic one be. But since the Olympic foot couldn't have been smaller in any case can be considered as the Attic, which is larger than the Roman (§ 10, 2), so It is obvious that the censor was wrong. His statement about So the Olympic stadium contains nothing more than what we know. from the passages of Gellios and Isidor wisseui cited in § 5, 4 that the Olympic stadium contained 600 of its own feet, which censor without further ado equates the Roman one. Yes, if it's correct, that's it Olympic foot was the same as the Attic foot (§ 10, 3), then the error is writer even more striking, since then the Olympic and Italian sta- dion are the same, so the numbers 600 and 625 do not have different lengths of the same, but rather the relationship of the underlying foot dimensions. press (600 Olympic feet s=s 625 Roman). It is just as uncertain Information about the Pythian stadium. According to the usual assumption should pedum. D can be read for od, so the Pythian stadium is 500 feet namely Roman :s= ^^ Roman mile. Indefs is missing any justification for this. The most likely thing is Krause Gymnastics IS. 136 assumes that the reading pedum oo is correct, and it So in Censor's time there really was a stadium of 1000 feet in Delphi. have to give.

I

44 DETERMINATIVE CRIG DEtl

especially Herodotus and Xenophon, proved to be one i shorter stadium than y.ues to 8 to the Roman mile; have. So we will always come across a difference • of the length measurement and have to ask again how it is The fact is that the Greeks themselves don't mention a word about it. The puzzle is solved quite easily if we consider, aitf which way the Greeks determined greater distances were. An accurate measurement with the measurement only and The basis for a fixed duty ratio is only in the last cases Filling to think^^), people were usually content with that to determine longer distances by walking. So know we of Alexander the Great that he did this in this way It was easy to measure the stations that he covered with his army ^ *), and the information must also be based on such provisions Xenopbon's about the March of the Ten Thousand is based, to that extent They didn't take to the streets, but those from the heelers did were measured 1 6). This vei-haltuifsmärsign still always works A different way of determining the route was reliable was even more convenient, but also far less accurate, I mean the determination according to which the journey is made required time. A day's journey, the march of an Oeerea, the Daytime travel and nighttime travel of a ship became one certain round number of stages, and then the distances traveled were calculated ^ "). It is necessary

13) Exactly the same features are found in buildings, as in the case of delB Hekalonipedns for albums (§ 10, 2) stntlgi-found; it is therefore advisable, that the ftaeabe of Tbubydides (2, J3) about the length of the manners, the from Atliea to the port, is based on a sukheo Messna^. Compare Direct your v. Athens p. 32 of the translation, Ideter Abbandl. 1821) 8. 17 F. nnd Dnt. § 10, 2. This also applies to the cultivated soil at least lam Tiietl would be measured exactly with the measurements only, see wirous Herodatus 1, B6, where a^olfip Sla/J^Tfl•^aaa!^€lt for both the Vei« measuring the acquired land as liir the measuring of that from the Sclsvea KD ordering country is branded.

14) Pliny mentions Saetoa as HinerWR menior in 7, 2 § II Alexander the Great mentions tjebenetenseibeo calls Athenaeus 10 p. 442 B 'AXf^iv^Qov ß^/ianaiiig and keeps a writing from him; ^ta&fiol lijs'MeSavdQov nopiias. Compare Ideal treatise. 1812-13 p. 172.

lä) Compare Jdeler treatise. 1S27 p. 123.

16} Ukert Bber provides further proof of the type d. 3. w. p. 8^14 and Geogr. I, 2 pp. 55 - 65. Herodnt 4, 101 protects a day's journey za 200 stadia, Paosanias 10, 33, 3 to 180 stadia. The march of an army giebl Herodotus 5.53 on 150 stadia (verBl, Idcler Abhandl. 1S27 p. 120f.), the same 4, SO the togtahrl of a ship to 7U0, the night voyage to 600 stadiums; This was usually taken for the 24-hour journey of a ship

I

3.4. DETERMINATION OF THE GREEK MEASURES OF LENGTH. 45

There is no detailed explanation of how big mistakes can be made. fen, especially if an error occurred due to special circumstances yeranlafst was, as we see, most clearly in the information Herodof's view of the dimensions of the Black Sea (§ 9 note 5). Nor do the ancients themselves make any effort to do so all such determinations are only approximate, and that one it must be used with caution ^'^). For smaller distances conditions that could not be addressed, e.g. B. the width of rivers, the estimation by eye was sufficient; we can So don't assume that we have precise measurements in front of us, if Xenophon, among other things, the width of the meander to 2 Pletbren and that of the Euphrates to 4 stages ^ ^). Finally It should also be taken into account that there are many distance determinations. ments in stages from the reduction of foreign measures, such as the Egyptian Schoinos or the Persian Parasange are standing. Here, too, no absolute accuracy was sought - ity, but withdrew it for the sake of more convenient calculation to set as round a ratio as possible. Now let's take it In addition, the information is usually in those foreign dimensions were only approximate, then we are all the less allowed to go into the figures presented. want to find precise measurements from reduced stages. Still The error becomes more obvious if you actually receive an incorrect message. nifs is taken as a basis, as Herodotus did in the Reduction the Egyptian scboins does (§ 9, 5).

4. All these more or less imprecise determinations However, the stadium needed a specific stadium, i.e. h. which exactly measured length of any racetrack is not at all important to lie. Herodotus knows no other standard for his stadium as the human body mass; Xenophon as an Athenian had to but we know the Attic foot exactly, and yet we find with him a stadium that is six hundred times larger than this Fufses lags far behind. In any case, the length was content of 600 feet, which was the basis for the standard size, in a comfortable to reduce men's conditions to the step size; and everything leads

There are generally around 1000 stadiums, but there are also lower numbers higher regulations. Compare aufser Ukert p. 11 f. also Ideier Abfaandl.

1826 p. 9, Forbiger Handb. I p. 550f. 17) Ukert Geogr. I, 2 p. 65 f.

IS) Anab. 1, 2, 5. 4, 11 and elsewhere very common. Ideal treatise.

1827 p. 124 takes the Olympic stadium without JNoth for these measurements claims, although he admits; that the numbers are only approximate estimate based.

» ^

point out, äali man io round numbers 2 step to the orgyi^l

So 200 was calculated on the stadium'^). It is namely dtf-l average human step 0.S meters =2.549 preufe. Fufs "')j I This gives the stadium 509.8 feet, and with a solcbi» ] Stadium can be used the information of the older writers scboaj combine far better than with the Olympic one, which 588,fra Fuss contains. Because the Stadioa J has to be approximately this length Herodotus had, and the stadium of Xenophon and Bratosthenes is still, as will be shown below a little shorter; which is easily explained when you consider a varying scale is the step. We have to So avoid it completely, in the stage information of this Writers to find accurate measurements. Only later, when you became known as the Roman mile, the stadium became one fixed size by fixing it at |- the mile. But there the information from the older ones, who were still there a short time ago, was retained. had served at the stadium, without attending a meeting to think. Strabo, for example, has the eighth mile as a normal mafd. diion, but in addition he gives some location information to Bra- Tosthenes and other older geographers, who certainly do shorter stadium is the basis^^). So that's what they believed Greeks really only have a stadium as long as it measures They had a length of 600 feet; alone with a certain degree of accuracy and under what conditions Settings in general determine this length in each individual case was, they didn't care about that. Let's be more precise measure, find a difference in the stages is only based on the inaccuracy in measurement*"). Bs is but Even after what has been mentioned, it is completely useless for a name to look for the shorter stride stadium; it has since it never fi^ a special stadium in contrast to the so-called Olympic pische never had a special name, and so- with no mention of the Pythian stadium, which ■

19) Idelor Treatise. 1927 p. IJ2f. 1

20) Henschel, the most comfortable measurement and weight stone, Cassel ^ 1855. p. 6ff. '

21) This is a convincing example of the IdHer treatise. 1S2T p. 127.

22) In this sense, oocb Rennel, tbe geographica! sfstem flf Herodotus Tis p. j-i aas: Che diRerent rtsuICs orising rrnni tbe comparisnn of the DDinbers of Stades, witb tlie groond on wbicb Ihey were compnted, are lo be aseribed to Iho dilFcrence of hunting amoDgst Ihe iodividuals w niade the compiilBliona (we say eoviptilaUom, because it maj supposed Ih Her diatanies were, in many cases, lueasured).

§9.1. THE ITINERARY STADIUM. 47

firaDzosis that geographers have raised, every legitimate 2«). The best way to describe it is as a step or itinerary stadium.

§ ^. Continuation, The Itinerary Stadium,

1. The stadium in which Herodotus had his itinerary The provisions are based on the four hundredth times his fievQiog Ttfjxv^y as the stadium of Xenophon's six hundred times the Attic foot. In any case, it's shorter been. To determine a desired indication of the same would Herodof's statement about the base of the pyramid of Cheops give, according to which a stadium of 170.44 meters = 543.1 preufs. Fufs calculated, if not the completely different value from the determination of the pyramid of Menkaure, pointed out that these are not exact measurements, but only unreliable information, probably from Egyptian countries genetically reduced, present ^). So we have to try that HerodoV's stadium to be determined elsewhere. Aristagoras, the Tyrant of Miletus, describes (5, 52 ff.) the route from the coast Asia Minor to the residence of the Persian king and finally gives the distance from Sardis to Susa is 13,500 stadia or 450 parasangs. Herodotus expressly mentions him

23) The name Pythian stadium is based solely on the nn* safe place GeDsorio's (see note 12 above), from which in this regard hung does not allow us to conclude anything. Because first of all, the censor decides that Pythian stadium not at 500, but at 1000 feet and secondly there are There is no indication that the same thing was ever used as a measure of length. Nevertheless, Ideler retains this name after Barbi^ du Boccage and d'Anville tion. Compare Treatise 1826 p. 12 ff.

1) According to Herodotus, the base of the pyramid of Cheops is 2, 124 8 plethrums on each side, according to new measurements 227.25 meters (by Zach, Monthly Correspondence.TVS.TO). This gives the stadium 170.44 meters = 543.1 Prussian Fufs, i.e. a noticeably shorter amount than the later one Greek stadium has (§ 10, 2). But the information about the pyramid of Mykerinos (2, 134) leads to a much larger stadium. The base is According to Herodotus, it carries 3 plethrene less 20 feet, according to new measurements 103, 10 meters (Letronne recherches p. 184); the underlying state dion is therefore = 220.93 meters :=3 703.9 preufs. Fuss, taking into account that the pyramid has currently lost its clothing, i.e. the newer one The measurement still delivered a value that was too low. Herodotus' information therefore cannot be exact; That's why Ljctronne's experiment has it (recherches p. 183 - 193), they with the real information through displays “To reconcile different hypotheses is a lot of concern.” Perhaps the most advisable thing is to write 2,134 TEOaiQtov for tqkHv.

48 UAS ITlNKHAUSTAlllU.-'. 9D

keti, dal> the Persian Parasang actually contained 30 stailieo and that the measurement of the path according to Parasaagcn for must be kept reliable. Rennel^) calculates the sum of the di- right distances between the stations mentioned by Herodotus to 2S0 geographical miles and thus comes to a city Dion from 510 Prussia. Fufs (46.3 to the mile), i.e. the same Length as above (§ 8, 4) for the stadium of 20ü step has been accepted. Indefs mufa perhaps by taking the The curvatures of the path hit a little higher than the tunnel has done, one more little thing needs to be added; but man would still be far from the Olympic stadium reach ^). The state comes to an even smaller amount Dion Lierodot's from his statement about the length of the Path from the Altar of the Twelve Gods in Athens to Pisa and to the temple of Olympian Zeus leads D'AnvilJe ^ ) calculated net from it a stadium of 471 Ful's.

There is a very peculiar connection with it Stadium, according to which Herodotus calculated the dimensions of Egypt determined. His information about this is based on measurements the Egyptian Wegmafs, dei' Schoinos, was based. Through a misunderstanding now, the cause of which can only be guessed at But that doesn't make it any less certain, Herodotus calculates almost twice as much, namely 60 furlongs on the school nos^). Therefore all its location determinations are based on Egypt.

gt Hnruilatus [>. Itif. Established for them lan is strongly bent in Usus and Mnssnl Fn EPoKranliiiiched miles that he called the dem69S

is, still gi^ to the 1120 English {.

has found a direct distance and gets a Sladi from it

anfdcu earth degree, 46.3 on the geogr. walk a mile.

3) Idelcr Abbandl. 1S27 p. 117.

4) Near Karle d'Anville's, Renuel ]>. IG and Idder p. 114f. follow, give the direct details of the chosen path, preceded by

I assume that the same went through Arcadia via Orhrnmcnog, 130 rom. Mei-

^^len. Herodotus 2, T has US5 stadia. Cm these two numbers together

^^^ compare zn kiinnen, must have something for them from the letter

^^H Curves of the path deducted north. D'.Aaville (trnite dos

^^^1 mesnresp. 175 ff.) follows the principle of geographical distinctions

^^H cip, because it shortens the itinerary distances by ^, nm the direct ZD

^^H received. Ideler p. 1 14 supports him by pointing out that

^^H grülWrea distances, where one station compensates for the other, di«Ma

^^^1 eighth is to be regarded as the maximum of the loss. Hieraacb be-

^^^1 calculates the stadium on which Herodutus' statement is based exactly

^^H on ^ rliniische or ^ gengr. Mile = 471 prcurs. Fuss.

^^^B 3) Since the Srhoineu originally used the Statinnew for the ship's goats

l

J

1.2. THE ITINEBAR STADIUM. 49

tens, which he gives in stages, in the ratio of 60: 1 To reduce schoinen and then the one below (Appendix § 11, 3) stated amount of the schoino should be taken as a basis.

2. The safest option is the older, shorter stadium Detect Xenophou. The length of the path that the Greek Chinese army from Ephesus to the battlefield near Kunaxa The distance covered amounted to 535 parasangs or 16,050 stadia ^). Now the direct distance between the individual cities is tions that Xenophon gives, after the careful investigations searches for races), which uses all possible auxiliary means medium used, a total of 1321 Roman miles, resulting in after deducting ^ for the curvatures of the path, a stadium of 443 feet (53.2 to the geographical mile) results in®). One would To go too far, one wanted to claim that the stadium was xeno- to have found phon's safely; but this much is obvious that the same applies to the stadium of 200 paces assumed above or about 500 feet much closer than the so-called called Olympic of 588^ Fufs.

The geographer also needs such a shorter stadium

were, then it is probably understandable that Herodotus, through MiFsyerstadt- nifs took the Itioerar-Shoidos to 60 stadia. But you're not allowed to about believe that he really has a special short stadium (of just 314 feet) for Egypt; there was for him, as for all Greeks, only a stadium, so the error is only in its erroneous re- duction of the Schoinos. Nor is there any belief in such a half- stadium to think about when considering his information about the extent of the Pontus (4, 85 f.) compares with the real distances. He determines Here everything depends on the day and night journeys of a ship and puts them on hold a certain number of stages. But since the ships are on the stormy Black Seas mix much shorter distances on average every day than anywhere else, Herodotus stretches the length and breadth of the Pontos far too far. However, this error should not be explained by want to attribute a special shorter stadium to it. The whole difficult question about this semi-stadium has been dealt with exhaustively. delt from Ideler Abhandl. 1826 p. 6 ff.

6) It doesn't matter that the authenticity of the matter in question The passage (Anab. 2, 2, 6) has been doubted, because the same is obtained Total, if you take into account the individual information that Xenophon has about the March of the army from Sardis to the battlefield Linden, added (=: 517 parasangs), and according to Herodotus (5, 54) 540 stadia or 18 paras sang for the way from Ephesus to Sardis. The information is So as accurate as few that we have from antiquity. Approach it Evidence is provided by Idea Treatise. 1827 pp. 122f.

7) Illustrations of the history of the Expedition of Cyrus (London 1816).

8) For further details see Ideler p. 114. 122 f. Rennel himself (Iliustr. p. 11) calculates the itinerary stadium to ^irw ^^^ degrees = 493 preufs. Fuss.

Hultsch, Melrology. 4

50 IIAS ITI.NEIIARSTADION. S 0, S

£ra(ost!icnes were used for some measurements. The Egyptian Schoinoa amount, as shown below (Appendix § 11, 3). whoever will, about 4 Roman miles; But Eratostobenes Redinet according to Pliny^) 40 StaiiiicD on the same, it worked So from his stadium JO to the Roman mile (1 stadium = 471 feet). The same stadium or just a little bigger res also lay, like d'Änviliei"), with great probability proves, based on his determination of the earth's beginning, as well as well as the Conection, which Hipparcb in this regard- carried out.

3. The other traces would also lead too far a shorter stadium, which d'Anville and Hennel demonstrated Bcn have to follow up. I believe that this is already the case guided will suffice to justify the result that we briefly summarized in the following: It can correspond to the information about Location distances that we see in the older Greek writings until the middle of the second century BC. BC and theilwetse find something beyond that, not the so-called Olympic Stadium of | the Roman mile (588^- preufs. Fufs), nor an exactly normirtcs Mafs at all have lain. Rather, in general, Dio Zald is the one Steps have been determined that step out home on a. Stadium came. They probably counted 200 paces, what a stadium against 500 preufs. Foot follows This fluctuating scale also became partly Larger distances can be achieved directly by riding out true, in some cases foreign linear dimensions were then reduced, In some cases, distances were roughly estimated time or with the eye. The more inaccurately measured became, the more the error must multiply, and Although one can assume as a rule that with increasing The inaccuracy also means the plus of the estimated distance

I I

10) DiscusaioD de la meaaTe de la lerre nsr Eratosthene in deu Hcm. ^1 defAcad. t. 26 p. 92 I.T. ■

I J

9) 12, 13 § 53: schoenua pat«t Ernstosthenia ratione stadju XL, hoe eit pHBtmni V milia, allqui XXXll stadia sini^ulis schoenia dedere. Since the Schainos, as we know for sure, is 4 Roman miles eDthiel^ 90 we recognize in the 32 stadiums Olympic or Aehtet mile sladien, and then calculate the stadium of Eratasthenes ZD -^ the Roman mile. On the other hand, the five miles that Plinin gives are VDp him iri'tb lim lent to the 40 sentences of Eratasthenes redncirt, ioden also for the Olympics

§10.1. THE OLYMPIC STADIUM. 51

Dung About the real grew. To therefore from the information the writer approximates the real distances To be able to determine, you have to look at the itinerary stadium a little more set shorter, about 470 feet or -^^ the geographical Mile 11).

§ 10. The Olympic Stadium,

1. The first Greek from whom we have a comparison between the Greek stadium and the Roman path- mafse has been handed down with certainty is Polybius i). The next- convenient and simplest way to make such a comparison was for him the Greek and Roman feet as equal and then the ratio of the stadium to the mile determine. So he got %y\^ = 8^ stadia on the Roman mile, and according to Strabo's testimony^), who probably a passage from the geographical investigations in the fourth century Polybius had the thirtieth book of his history in front of him really calculated that way. Only in one place in the third book ^)

11) According to this approach, the stadiums in Table I are reduced to miles. cirt (1 mile := 23601 Prussian Ful's). From the eastern stadium there is The table with a view of Xeoopbon's Anabasis also shows the reduction tion of the parasangs (1 parasang = 30 stadia == f mile).

1) Eratosthenes is also said to be based on the metrological fragment of... lulianus Ascalonita (in Gonslant. Harmenopuli manuale legum 2 tit. 4 in the edition of Heimbach or in Suppl. novi thes. iuris civil, et canoo. Hagae 1780) determined the Roman mile according to stages: t6 fjiCXioy xara ^EQaroad-^vrjv xal SvQdßojva rovg y€(t}yQä(fovs ^/st öxaSiovg r{ xät y'\ Now it is certainly possible that Eratosthenes, who (according to § 9, 2) is a Far shorter stadium than used on the Roman mile, nevertheless He mistakenly reduced it by eliminating the foot dimensions sat. But it is noticeable that Strabo is in the following note citirteu Just appoint Polybius as an informant for the reduction of %\ leads, and not also Eratosthenes, from whom he did it just as well should know; Furthermore, Lulianus also wrongly attributed this reduction to Strabo. tion, while he himself always attributes the mile to 8 furlongs reduced. So this note seems quite suspicious.

2) 7 p. 322: (^ 'EyvcerCa oSos) fitXCoyv iorl jisvraxoaCüJV rgia- xovta nivTB' loyiCo/n^vip Siy (og fihv ol noXkoC, t6 fiCkiov oxTaarddiov, TfrqaxiaxChoi, av sJev atd^ioi xal in^ avrolg ^la^ xoffiot oy^orjxovTcc, atgdhllolvßioQ nQoarid-elg tm 6xTa

3) 3, 39, 8 he gives the distances from the Strait of Gibraltar to the Rhone and adds: ravia yaq vvv ßsßrjjbtdTtarai xal aearj^

4»

52 THE OLYMPIC STADIUM. § 10.

He expressly only counts 8 furlongs per mile, and the same Strabo expects to notice that this is the general invoiced. This is how we find the 8 miles at Sui- that, which of course also presents two even larger stages^), and, what is far more important, in all Roman writers, which reduced the Greek to the Roman measure (§ 13 A. 6). Probably they had at first, just to get the fragment away- create 8 instead of 8^ furlongs per mile; but it was In this case, the round number is really the more precise one, because we can have a Greek Fufsmafs in two different places prove that the six hundred times it increases with the eighth mile sta- Dion matches exactly.

2. The magnificent Minerve Temple built by Pericles Athens, the Parthenon, was, according to Plutarch '') by the Athenians also called the hundred-footed, kxazofZTieöog, called. Old writers themselves used this word, like Har- pokration ^) reported, variously explained; according to some it should merely poetically denote the large dimensions of the building. others pointed it to the harmonious conditions of the same. On the idea that the expression is entirely in its own right to be taken in a simple sense came among the more recent travelers first Le Roy^), who has the hundred-cell dimension in length of the architrave. Later Stuart^) measured the pages of the elevated arena on which the columns of the peristyle stand. He

{iBCbitai xara ataö iovg 6xt(o Sia *P(ouaC(ov iniueldyg. Compare Ide- cp treatise. 1812-13 pp. 183f.

4) MCXiov fi^TQov yrjg' rä Sixa fiCXia e/ovat ardöia n , Ueber the longer stages that he also mentions, see below § 11 note 4 n. 6.

5) Periclus. 13. Gato 5.

6) ^JExaTOfinidov Avxovqyog h r^ iniygaipofiivfp IdnoXo- yiöfibg (ov mnoXCTivrai' 6 7iccQ&€V(bv vno tivüjv 'ExmofATiiöog ixa- XeiTO cf/a xdXXog xal evQv&fitav ov ^la uiys&og, (og MsvexX^g ^ KaXU- (fTQarog iv i^ negl Lid^rjVCüV. Similar Suidas unt. ixarofinedog, cf. Leake Topogr. Athens p. 414 A. 1 of the translation.

7) Les rnines des plus beaux monuments de la Grece p. 49. 51. His Measurement of the architrave showed 94 par. feet 10 inches; but that is the result not entirely sure because he measured it with an imprecise scale and was only able to correct the error later. Focherot scores 95 par. Fuss. Since the latter measurement makes the feet slightly larger, the former slightly larger smaller than according to Stuart, it is advisable to take the average between to take both, which results in 136.68 par lines for the Attic foot

8) The antiquities of Athens measured and delineated by J. Stuart and N. Revett, London 1787 vol. II p. 8f.

2. THE OLYMPIC STADIUM. 53

found the width to be 101 feet 1.7 inches and the length 227 feet 7.05 inches English. Both numbers relate so exactly to one other like 100:225 or 4:9^) that this ratio is necessary- It must have been nimble in the plans of the builders. We have i.e. really and precisely in the dimensions of width and length 100 and 225 Attic feet. Then arise for the foot

from the measurement of the width 12.137 eng. inches - - - - Length 12.138 ■

So on average 12.1375 English. inches = 136.66 par. lines.

Surprisingly, many more people have had this result. More measurements both on the Parthenon and on other buildings confirmed at Athens, because the average of the same gives just just the same amount '^). So we can use the Attic foot with great certainty

136.66 par. lines = 0.30828 meters = 11.787 preufs. inches

put on. The stadium in Athens is also, as is the case with many Probability can be proven, according to this very fuTs-

9) Only 0.225 ZoU was asked to be deducted from the 227 F. 7.05 Z. of length. draw, or add nar 0.1 ZoU to the 101 F. 1.7 Z. of the width, so that the relationship becomes completely accurate. So if the longer one Page only ^ ZoU less or the shorter side^ur about ^ ZoU more cheat when she asked Stuart to find it, the ratio would be 225:100 come out less accurate than Stuart's measurements results. It follows that the calculated one for the Attic foot The value is so precise that the error can only be one inch; advance- assumed that the ancient builders built with an equally precise scale measured when Stuart used it.

10) Worm p follows these measurements in detail. 108 IT., but be- may the values that he p. 109 in par lines, another small one Correction, because English feet are 135.1414 instead of 135.1160 par. This means that the average value of 1 is 36,687 lines, which he obtains from the monnmeotal measurements is 0.026 lines too large failed. But he now takes the value of 136.61 Lin. added, which gives him from the equation 8 stadia =: 1 Roman mile, and According to the average, the Attic foot is definitely 136.65 Lin. So his result happens to be very close to the one I found. steUten. In my opinion the comparison with the Roman one can be made mile will not be taken into account as the ratio is only a round that should be ; But the average of the measurements is, I believe, best drawn so that one can first take Stuart's measurement of the upper arena as the presumptive most accurate one, and with it the others Measurements now compare according to Wurm (by making the necessary gen Gorrectioneo) for the foot:

54 THE OLYMPIC ETADIOC. ORGANIC.

marshals have been cut '>); ebeoEO the OmfassuDgsmauera AtheDs and the long walls that lead to the ports of Phaleroa and others Pciraeus led'^). So there can be “no doubt that the The feet found through the more recent measurements are really the ones goseAffluent Attic was.

It must be pointed out right here that the... Attic FuTs are very close to the Roman ones from 25:24 stands, and that the stadium of the Attic foot, which exactly 569.42 par. Fufs = 589.35 preufs. feet is, is only slightly larger than ^ the Roman mile >■ *).

3. A second Greek Fufsmafs, about the amount of which we are precisely informed is the Ptolemaic Fuss, the the gromatist Hyginus mentions '*). After this feet were

the average of LaBay'a ondFocherof's measurement 136.68 par. L. the 12 additional MeBaangcn at the Parthenon .... 136.89 -■ - the Dorcbscbnitl of the remaining a stBlIten 35 MeBSuDgea . . the fellowship aas sums 4 ( 136.68 X 2 -f 136.58 x i

49

136.66 par. L.

it Stnart's Mesaong of the Arena. Zq same re- mWegeBÜDtli Metrol, Unters. S. lOSf. Ideler S. WJ sets the attisetieD FnTs solely according to the relationship to the Romans Feet to 13S,458 pure. lines. Paucker Metrology of the Büm. nnd Greeks in the Dnrpatcr Yearb. Vol. 5 p. 10! receives as average value ■12,137 eng. Znli = 136.66 par. Lin.

11) V, Fenneberg tintersnch. P. 122 ff. makes it true, that's it the true length of the Greek stadium from the walls to xnr Heta has to be calculated, and that the latter is about 25 feet from the rear removed healthy. He calculates based on this assumption the mesangs of Chandieruod Le Roy, which the Athenian stadium 591^ Par. Fal'a long found the stadium's fafs to 136.3 par lines, which sebr closely agrees with the above reanltate.

12) Ideler Treatise. 1836 5. 17 f., Leake Topogr, p. 312f., the Demen V. Albums p. 32 find with Zn^irnndelegnng the Olympic stadium, dafa Thucydides' information (2.13) about the lengths of Athens is correct • correspond well to the previous measurements; thisa Olympic stadium but is none other than the ancient one.

13) The Attic foot of 13(1,fi6 par. L. is similar to the Roman see, the (according to g 15.2) 131.1 Par. L. cheats, like 25.018: 24, so very close to 25: 24. The Roman mile is 4711, 4 preal'a. Foot, so it stands only 3.37 FdI's behind the acblfacben of the Attic stadium.

14) Gromnt ed. Lacbm. p. 122 f.: in provineia Cyrenensiam agri sunt regii, id est illt, quns Ptolemy rex populo Romano reliquit; — pes eorum,

'^tolemeicns appcllatur, habet mnnetalem pedem et semnnciam. ;ica mnnctalis is the riimiscbe, as shown in § 15, 1. — Dafs the Anabc Uygin's have a reliable and accurate Macbricbl.

I I

J

surveyed the royal lands of ProviDz Cyreitäkü, which Ptoiemaeus Apian had left to the I-üiniscian people. Hvginus Li^ agrees with the same l^V ^^^ Roman furses, where- out, since the Roman Fuls (according to § 15, 2) 131.1 Par. Li- Nien contains, 136.5ti Par. Lin, issued. But this is true agrees with the Wci-the found for the Attic Kufs, that There can be no doubt about the identity of both feet.

Si) we find this at a border post in Greek Cullur same foot dimensions as in the middle points of the same. The inside To prove the connection between the two, the special research to fill a sensitive gap here has to be left up to. The remains would become more and more Greek buildings, as far as precise measurements of them are available, based on a methodical study in Uetrell' dos to be subjected to the following fufamafses. After what has happened so far The material lying on the ground can at least be found, presumably agree that the oldest Greek foot, that of the Hereon has been proven at Samos, 315 millimeters d. i. plenty f was the oriental cubit shortened by one eland width, and that the same as the Tcmpclbants of Päslum and Selinus can be traced, gradually up to 308 million meters The amount of the Attic foot sank at the time of Pericles"'). This MaTs probably traveled via Sicily to Kyreae. reaches; But that doesn't happen in Greece proper either Athens was limited, the remains of the Temple of Zeus appear to have been to Olymp|jia to prove«! '^). The Olympic stadium is moving unfortunately no longer measured.

So we see that dum on | the Roman mile put stadium a widespread! it is based on Fufsmafs, which is based on the analogy of the fih^Log

The only thing that guarantees this is the name of this stepkeeper. üidus the important [BBdstBD under iea römLHGhCD t'etdmesaBrQ (Lacbmann 11 p. 130) , sandera also the ^ni^e kind and manner, he never saw the IteductiuD of Ptotemai FlacbeuinBlaes looks at the romanized item in detail (see appendix below). S 13, 11-

1 5) See the details in Aohang § 5, 8.

16) According to Blouet Expediliou Buieutifique de lu Uoree I pl. 62 mifit the DDtersC« stage of the Temple of Zeus 3I>, 6 meters wide and 67 meters in length. Uas believes under the foreknowledge that the Brazilian Officer cbnebe Pufa amounts, 3Uä MUlim. for the foot. If Fansaniai 5, 10, 3 The width of the temple is 95 Ful's ~ 29.26 meters, he says wobracbe the distance between the corner columns; decided in high but he counts on the LüngB 230 Fol« = 70.84 meters.

fi^ ih^iit i.i>ccMgi hiAMu» m BiHrfcFFn, gu.

iMfft teifn»!/ 1>M» (M i}\jm\f\4 tm'h%tmmim would be, because no Gnecfae has i^ f^Ut \Mt^mtmh mtUtr Antn Came to know the oknipic Mmf Aik Aiti n\\%m%ntm tradition the foundation of the stadium mi'Si Olyffipia vifrb$gt4t and nomii the management of the tmUmmmi if^vm'SmvSxm lJingi;nmafi$e connected to this place, »M Umn\ A\i^%Pfk ^«tml;iH^^ie<;biMche Mafs, its exact amount we have taken from Mim Am '\'m\\uA\m\iUan Athens, right probably from urm am called the olympisdie, and is therefore the finriiiil nhia^nUirt«) Hesse drawing is best retained.

4. mm Uiihitr^icbt over the Greek length measure and illn ItriHuciion (hmHnlburi after the Attic (Olympic) foot ^Am\ T(tu. 11 - " IV. In Tuh. II all are shown in $ 5 and 6- ntlirtmi Mt'l*^<^ltli*(ilHUi MhI'hu xiicompiled. Table 111 contains (liti vl(iint()|i(i|l from FiifM, Kilo, Or^viu and Plothron, Table IV the vh^lftM^ht^n (hm HitulloiiH. lu dor icUsterün is based on the reduction HUl' Mt^()KVuphU<^ho Mollon nurdmii round containers of 1:40. \\m\ uuKt^fAhrou llotragt^ also is 1 ddfMivXog =» | inches (|M*mtni.)i l HO(V' Hi<^lti K<^)tx na I Fufa, 1 nfjxo^ not quite = \\ Vwh. \ ^i^irf— 5ft Fuft». 1 nU^ijov = 98 Fufs, 1 oira- ii^w «t M)0 FulV WH /„ gt^ogr. Mmlo. #

I « hto t^rHlt> Shur f iuoa even longer stadium than that olympl«i«'hi^ w^r» lliulon »ir \m IMuturch, who in the biography d«^ tu tirtitH'hU!^ Kh^ \\u or tllnar dessMi punishment buildings and SliH^iV^t\>^mi«^)^Ui\y[t^4t »pHchl. then Agt. that's the Simian mile ^^h><^« kMu^r m ^» S St^dit^n M« £r hMt^ at least that

^SWK' v^y,**^*« »v*" ^r ««t*«n(«*rv lM<^r Akk ISll — 13 p. IST v^flK «tii«^^ Itv'ViN^MMiNft

k^'k^l M^^'Mii^MiK'k lh*Mk IM l W >k H l l| l H> ll<>r VMMCk $ tt^ A. 13 MHT 3m3T |4Y«rSw

^«V^^^ ^t«' IMM' 4wtvk

V^ ^'r \\ t A\ 'WIMNk IMMk WMtM* tWltel^Wwmi 5sSlaw*Hi (pMPMR^ €MWV JHOM»

1. S. THE lXnGBRBPI STAGES OF THE KAMBMBt« ß7

Stadium Gate Eyes, which is named after a passage from Dio (3aMiiut was included 74 times in the Roman mile. This font The author says that the jurisdiction of the city inspector is fects extend up to 750 stadiums around the city solke ^), and thus unmistakably denotes the same distance, which in the Digests s) is determined to be 100 Roman miles. We find the same reduction in the mile at luNanus from Asca- lon ; Photios also knows no other stadium, and let's continue The traces of this can be traced back to the tenth century BC). We have the origin of this length measure in the East, partly in Asia Minor, partly in Palestine^); We can therefore use it as the Asia Minor or the Oriental call talic. Since around the second century AD. must be the same, whereas before it only had provincial validity, spread more widely and displace the eighth-mile stadium have; at least we find it among Greek writers Since then there has been no trace of this, but as before been shown, multiple evidence for that longer, which l^times included in the Roman mile.

2. The other reduction, according to which 7 furlongs to the mile are calculated, appears first in the second metrolo- Gian fragments, which were written by the bishop in 392 Epiphanios wrote writing negl fihQiov aal ata9'fi(3v

There is no need to offer a plotarcb in the longer stadium from H to the romisebe mile commeiot babe, defieo Fari, the perfiiehen Elle zagebö'rig (App. § 7, 1), sebon in Asia Minor long before Plotareb- was mixed in, and which we later find §0 generally widespread, - (Linguistic and factual obedig is the explanation, which v, Fenneberg Unders. p. 34 from the passage in Plotarcb.)

2) 52, 21: noXCaQxog — anoSuTtvvoOoif — tva day SUag — toU T€ iv T J noUt — xäl Toig t^(o avTtjg fiixQ'' Tiivr^xaVTa xal inraxotfüoy araSiwv olxovai xgCyn.

3) 1 UL 12, 4.

4) laliao. AseaL (see § 10 kmm. 1): to fiCXwv xara to vhf xqU' Tovr f9^g araSta fity %)rti C'S. Pbotios ont, d. W,: aruäufV o t6nog Tov aytorog xtd fifQog ri rov Xeyofi^vov fiiXlov kntu yaq tifinfv ötU' 9 tu noiovffi^ iiCltov, Likewise Soidas, Hesyebios uni, fiO^ßy bat Mäti BestiaaniBgea the girl who za 7| «od 7 stadiums, next to em9»dür, dear the later cf. Beraard de mentmrU f. 235, v, Fenoeberg Doters, p. 114 f roBisebe, but the Fbifetirisebe« Hy§Um z«born ügyptisebe mile (Appendix § 11, 2). From Pbiletarisdbm Stadiea give something iibef 7 atff the roaisebe mile.

b) L'eber die Sfvrea, welebe saeb Klei«asiea rabreii, 0, Aab« f 7, 1, iber Palistiaa Aab. f9, 1.

58 THE LÄNGBaBI« STADIUMS DBB RAISERZEIT. $11.2

is removed; also in Hesychios and Suidas^). Here is the exact amount of the foot tax that was paid by the Egyptian is derived from the Turkish and Persian EUe. That- the same was 350 millimeters (Appendix § 7, 1), the stadium was 210 meters ter, seven times 1470 meters or almost exactly 1 Roman mile of 1478.7 meters.

6) Epiphaoios in Le Moyne Varia sacra p. 501 (see § 2, 2): r^ fiCliov tx^i aradia C' riyovv nli&Qa fxß' — , h^toi 6h to fjLlXiov knra xai fj fiiav atddta liyovoiv IjjfCtv. Hesychios: (aUiov fiixQov odov orra- i£(ov inrä' ol 6k CS, noddiv ,6(f' (according to Ideler's Emeodation p. 192). Saidas: (aIIiov fiirgov yfig* ra 6ixa fAClia iyovai aradia n\ aXXtog' ro arddiov ?/€t n66as x* ^^ 6h fiCliov nooag ^6a', cf. v. Fenne mountain p. 114.

Second AbscbDitU

The Roman length and FMchenniafise.

§ 12. Overview of the system.

1. As with the Greeks, so also with the Romans the length measurements were derived from the human body: 'mensm'arum rationes ex corporis membris collegerunt, uti digi- tum, palmum, pedem, cubitum\ as Vitruvius (3, 1, 5) notes The smallest measure, like the Greeks, was the width of the finger, digitus {ddxTvXog)'^ anything that was measured below the digitus, was named after parts of it ^). Four finger widths give the width of the hand, palmus {ftaXaianj), and again four hand widths correspond to the length of the foot, pes, the therefore contains 16 digits^). This division of the foot was According to Fronfinus, it is common in most areas of Italy to be described as the technical one, because they are used the surveyors, the architects and probably artists in general

1) Balbns in Gromat. ed. Lachm. p. 94: mioiina pars hanim mensara- rum est digitos: si quid enim infra digitam metiamar, partibos respondemas, ot dimidiam aot tertiam. Compare Isidor Orig. 15, 15: digitos est miniina pars agrestioma meosnrarum. Examples of measurements according to parts of the digital We find tus in Frontinns, who in his writing de aquae ductihus ttrbis Romas begins the Daodecimal division down to the scripulum (= ^^). uses the digitus; see § 26: digitus quadratus in rotundum redactas have diametri digitum unum et digiti sescunciaoi, scripulum. Compare ibid. § 32. 39 ff. Gromat. p. 407, 10.

2) Vitruvius. 3, 1, 8: e cubito cum dempti sunt palmi duo, relinquitur pes qnatuor palmornm, palmus autem habet quatuor digitos: ita efficitur, ut pes habeat XVI digitos. Colum. the. r. 5. 1: mode omnis areae pedali mensura comprehenditur, quae digitorum est sedecim.Frontin. aquaed. 24: est digitus, ut convenit, sextadecima pars pedis.

60 RÜHiacUE LÄHMIASSE. S

and craftsmen^). In addition, however, they were also used DuodecimaltheiluDg, according to which the whole five is considered as as iD 12 unciae disintegrated. We then find for the parts of the foot the same names as according to § 20.1, where there is more detail about this Roman Duodeciuialaystem is spoken, the parts of the body weight and muuzasses led. For example, a dodrans = ^FuTs, bes =^ -|, Iriens = ^, quadrans = ^, sicilicus = ^-g Fufs; and According to the coin system, there is also an issue for 2 fufs. pressure dupondius, for 2^ Fufs pes seslerlius in front*). This duo

noduli ant ad digitarnia aut od n Campania et in pleriaqne ttaliae locis, unciae iopopularibas ratioaibag adbuc observantnr. For the use of the EiDtfaeilang of the barrel in d/giti in Peldmesaern and Arcbitects show Anni. 2 guided sides of the Calumella andVitra- vIdb; The same blessing followed after Frontin. 25 also the plumbarii. The Old pufsmarsstaben either have the SedecimaltheiluagatleiD, or these with the Dnodecimnltheilnng EDsaiamen ^presents, nieniats but the latter alldia. Vec^L ideal treatise. 1812 — 13 pp. 128f. — Nash digifi mafs acbon Cato the R. r. 45: (taleae) supra terram ne pIns IV digilos traosversos eminent; eb. 18 a. ö. Compare Caes. b. civ. 2, 10, 4, Vitrav. 5, 6, 3. 10.2, S, Plin. 31, 6 § 57 u. S., Cnlnm. ä« arbor. 26, luff. 12, 6S. Mariangabea uaeh paimi are not rare; in Pllnius x. B. 12, 13 § 48 (7, 2 § 28 he asked ' the feminine infarin palma). No other treatment than that of the hand width bat pabnas ht'i Varvo da r. r. 3.7: colnoibaria singula esse opportet — intos ternonim palmorum e\ oinnibos portibas, where you can buy fanz way to a legendary palmite) vua'or, who like the Greek ani- äo^ij ^ of the Fursea should be, thought. For the aniSitfirj baben The RSmers don't have their own expression, they always only use it dodraoa d.i.f FoTs. Plinias 7, 2 § 26 says expressly: Trispithaml Pyi^aeique narrantnr ternaa spilbamas longilndine, boc est ternos do- “drantia, non exceedenle”. In the meaning of (rn(*((//ij mentions Dal- iriiMzfirst the church father Jerome in Gzecb. c. 40 (t. V p. 522 B ed. Basil.): (palmas) rectios graece didtur nakairliiii et est sexta pars cnbiti. alioqain palinus antUn/iti snnat, quam nonnulli per distinctione palmam, porro naltnaiiir palmnni appellare consuernnL Later, of course, the- This language usage was general and thus also passed into Italian (jMl>Ra= range] above. Compare Idcler p. 129. — Anfser digiius and p

4) Compare Table VI A, as well as the complete overview of this unit lung, and see the following note.

I I

1. 2. ROMAN LINGEISMASS. . 61

decimal division, which according to Frontinus is in popular use (mjpo- pularihus rationibtis) was common, can also be found in the written steep, particularly common in Pliny, since they are so probably because of their clarity rather than because of their convenience and shortness of linguistic expression recommended^).

2. Among the dimensions that are larger than the foot is in ascending order first to mention the palmipes = 1 Fufs and 1 Palmus, i.e. 1^^ Fuls or 20 Digiti 6). The EUen

5) The following examples may be used as evidence for this:

■J^ Fofs: Plin. 13, 15 § 94: mensam qaattaor pedes sextante et sici- lico exceedentem. Marini atti de' fratelü arvali I n. XXIII line 32.

3^ Fufs: Hygin. de eondic. agr. (Gromat. p. 123): pes eorom, qoi Ptolemeicus appellatnr, habet monetalem pedem et semunciam. Marini a. a. 0.

^ Fufs: Plin. 6, 34 § 214: gnomonis C unciae; 18, 16 § 146: alternative tadine unciali.

•I^Fafs: Plin. 13, 15 § 94: crassitudine sescunciali. Hygin. de eondic. agr. p. 123.

^ Fufs: Plin. a. a. 0.: sextante et sicilico.

1^ Fufs: Cato de r. r. 18: foramina longa p. III S I^ (pedes tres se- missem quadrantem); Yell. 3, 10, 11: pedes duodecim et quadrantem, yergl. 9, 4, 10. Crassitndine quadrantali Plin. 13, 15 § 93.

i Fuss: Vitruvius. 10, 2, 11: de materia trientali; Plin. 27, 5 § 34: foliis trientalibus.

-^ Fofs: Plin. 9, 48: qaincunciali magnitudine, 27, 11 § 98: herba quincuncralis.

^ Fufs: Cato de r. r. 18: foramina longa p. III Sl^-u. ö.; Colom. 3, 13 a. 15: daos pedes et semissem; Plin. 17, 21 § 160: sesquipedes in lati- tndinem, in longitudinal semisses. (Even more common is semipes, e.g. B. Cato de r. r. 123, Varro de r. r. 3, 5, Plin. 9, 5 § 11 n. ö.)

f Fuss: Vitruvius. 5, 10, 2 and 7, 4, 2: laterculis bessalibus.

f Fuss: Vitruvius. 3,4, 4: tcnuiores dodrante; Colum. the. r. 3, 13: dupondio et dodrante, cf. 3, 15 and above, Plin. 15, 30 § 131: ramos do- drantalis, 18, 19 § 178: sulco dodrantali.

I^Fufs: Vitruvius. 3,4, 4: crassitudines eorum graduum ita finiendas censeo, ut neque crassiores dextante, neqne tenpiores dodrante sint eoUocatae.

H Fufs: Inscription at Marini atti I n. XXHI Z. 32: PED VS zz = —) d. h. pedes V because cem semunciam.

2 feet: Colum. the. r. 3, 13: dupondio et dodrante altum sulcum, cf. 3, 15. 4, 1.

2^ Fufs: Leges XII tabul. at Volus. Maec. § 46: lex etiam XII ta* bularum argumeoto, in qua duo pedes et semis sestertios pes vocatur; co- lum. de arb. 1.5: agrum sat erit bipalio vertere, quod rustici vocant sestertium.

The inscriptions provide more examples of the fractured separation of the foot Gruter p. 67.2. 207 (printed with the correct fraction signs in Zell, Handbook of Roman Epigr. I n. 1751) 592.4. 810.8.

6) Vitruvius. 5, 6, 3: gradus spectaculorum ne minus alti sint palmi-

62

KNEE MASS.

I

I

arch, cKhitus, with inclusion of the hand up to the tip of the miter. teltingers, like the Greek jr^pfi'S (§ 5, 3), became 1^ Fu& or 6 palm trees (= 18 unciae == 24 digiti)). AJ's Longitudinal Mars serves the cubitus instead of the usual pes ia the language of ordinary life in cases where a Comparison with the era length was closer than with that Fusse; Furthermore, it can also be found in those writings steep, which Greek sources use, as a superstructure setting of sr^x^s; but in the system of geodetic measurements he wasn't included*). The synonymous expression for cubitus, tilna, comes in two completely different meanings measurements as length measurements. The poets of the Augustan period

pede. The word has Plio as an ailjective. 17, 20$ 143: patmipedi inler- vnllo; roast stands for palmipodalit, never in Varrn d. r. r. 2, 4: lime inreriusultumpalmipedale, Vitrnv. lU, 20, 3, eb, 21, 5, Coluin. the. r, 3, 19.

7) Exct^rpla de mensar. (Grnmat. ed. Lachm. p. 373); cabitns ea^ qni Daturaliter a cubjto ad digitorum smnniiuteia pertendit, ver{;l. § 5, 3 touched site of polio:! over the nij;^!';. Vitrav. 3, 1.7: CD bittain animadverteront ex sex patmis constare digitisqne viginti quatuor; eb. § 6: e cubitn com dempti sunt palmi dan, relinqaitnr pra igaatDor palmu- rnni. Balbaa (Groreat. p, 95, 4): cabitns habet sesqnipedem, aextantes duos (i.e. dodrantea dqos according to p. 91, 19), pnimos VT, uaciaij XVITI (see p. 96, 3. 245, 10. 33a, 7). — Gellios has a different reductioD of the eubitut 3, 10, II: Herodotus — in primo historiaruin ioTeotnni esse sub terra scripait res ti corpus cabita longitudinishabens Septem, quae faeiant pedes dnndecim et quadrantem. So he ninint the cubitus oiet ^'iX"^ '0 '3^ Pfh instead of zq 1} Fors. This is explained by the fact that he although in agreement with the Greeks 4 cubita {ni^-fi«) anf the body laagE, but different from those 7 Fafs {§ 10) anf the same recboet; like that So he has 4 ü^^fir =. 7 Fnfa and 7 n^x^if ■= 12^ Fnl's.

S) Compare Ideler Abhundl. 1812^13 pp. 130f. Bet among the Greeks the different Marses separated from the body next to each other, ancestral one could say that one thing is ultimately the situation of yours system of the Langeamafese form; Among the RSmers, the pei is unmistakable as a unit of the Laogenmafse, hence the use of the iru~ bifui, who, as the aaderlhalbfaehe of Ful'ses, does not fit in system, much more limited than that of the Greeks rzijyiis. Andertlialb Fufs is usually given through aesgia'pes, x. b. Plut. Trin. 4, 2. 58, Varro de r. r. 1, 43, Colura. the. r. 3, 13, S, Plin. 35, 14 g 1 70. fieispiele far niAifilj give Plaut. Poen. 4, 2, 15: cnbitum Inngll litteris, compare flud. 5, 2, 7, Cic. leg. 2, 26, 66: eolBmellam (ribas cabttis nl- tinrem (according to Greek source), ad Att. 13, 13, 3: btenninra prneterii^ cnui illc£o^:tinn~l'(fi];assidaocnrBDrDbitnin nullnni proccsscrit (cf. Suet. Tib. SS), Snet. Au|c. 43: angnem quinqaaginla cnbitnrura, Plin. 7, 2 § 2S: rerpora hominnm eubitnrnin qninum et binarnm palraarnm, cf. eb.§ 22 and "■ "-- ■ -v. 24, 34, 9: (Archiinedes) rnnrnm ah inio ad santmuni crehr'"

I

\ Plin. 7, 2 §24: ii

8-4. ROMAN MEASURES OF LENGTH. 63

Ages refer to either the cubitus itself or at least a closely related measure, probably the length of the whole arm, as the third part of the height of the human normal body. On the other hand, Piinius uses several times, where he gives the circumference of trees, the word as a superscript Setting the Greek dqyvid^ to designate the arm- span or fathom of 6 feet ^).

3. A measure of length that was found exclusively in the writings of the Surveyor occurs is the gradus, step. £r is half the foot span or the passit, i.e. = 2^ feet i®). More That's why this convenient measure didn't spread. because people had gotten used to the passage (§ 13.1) as that Unit of distance measurements should be considered.

4. The length of the measuring rod, pertica, whose arm is architects and surveyors served was 10 feet, hence them also commonly appears under the name decempeda ^i).

plantas esse caliitalis, 8, 48 § 198, eb. 52 § 212, 12, 12 § 45 o. ö. — Im Edict Diocletiaa's depretiis rerum venalium is used by Banbolz Dacb Cu- biti and digiti, counted according to the foot for the parchment and the reins Mommsen, Ber. the Sachs. Ges. d. Know. 1851 p. 58.

9) Suetonius declared after Serv. to Virg. Ecl. 3, 105 idna for the same interpreting with cubitus f nnd' Solinus, the epitomator of the Piinius; cf. Ideler p. 131. Servius himself approves of this interpretation of ulna to Virg. Greg. 3, 355; but to Ecl. 3, 105 he gives another explanation Clarification: ulna proprie est spatium, in quantum utraque extenditur maus; dicta äno tcjv (okevüv, id est, a bracchiis. In this meaning of Kiaf > ter obviously has the word Plin. 16, 40 § 202: arboris one crassitudo quattuor hominum nlnas complectentium implebat, and eb. 32 § 133: (platanus) crassitudine quattuor ulnarum, which leads to similar §203: crassitudinis ad trium hominum complexum. — The use of the Didites of the Augustan age is clear from Ovid. Met. 8, 748 ff.: Saepe sub hac Dryades festas duxere choreas, Saepe etiam manibns nexis ex ordine trunci Circuiere modnm, mensuraque roboris ulnasQuin- que ter implebat, d. h. five fathoms, the fathoms or arm span three «2nae calculated. Virgil agrees with that. Ecl. 3, 104f.: The, quibus in terris — Tris pateat caeli spatium non amplius ulnas. The poet in this riddle means the grave monument of the Mantuan Caelius, With tris non amplius ulnas, the length of the human body is drawn. pers, which, as is well known, like the fathoms, usually have six feet is calculated. With Horat. Epod. 4, 8 and Virgil. George. 3, 355 is the same interpretation of ulna is at least not inadmissible.

10) Balbns, expositio et ratio mensnr. (Gromat. p. 95): gradus habet pedes duo semis., cf. p. 96, 4. 245. 339. 372, 2.

11) Baibus a. a. 0.: decempeda, quae eadem pertica appellatur, habet pedes X. The meaning of the pertica is explained by Isidore. Original 15, 15: pertica autem a portando dicta, quasi portica. omnes autem praeeeden- tes mensurae in corpore sunt, ut palmus, pes, passus et reliqua: sola pertica

64

ii&HiscuE L]i^Ge^)lASSE.

I

She was the legal guide for all land surveys, What is clearest from this is that their square is the The basis for the area dimensions is provided (§ 14, 1). So heirsen also the surveyors themselves decempedatores. The twelve day of Decempeda was the actus, actually the length of the furrow, which the plow bulls pull in one run, UDd those after the old Italian decimal system like the Greeks to tOO FuTs, but according to the Roman duodecimal calculation it is 12(J Fufs was chosen i*). So the Actus appears several more times as Length maXs^^), otherwise it is always used as an area mafs (S 14, 2).

An overview of the measures discussed so far is given Table VI A—C. 4

partator. The decempeda mention Cic as Mersstaüge. Mil. 27, 74, Hear. cum. 2, 15, l-\, the perliea Prop. 5, 1, I3U. Ver^l. RadorlT Gramat. Inäüt. p. 2m, Ideler p. 13p. — Decenipedatares has Cic. Phil. 13, 18, 37.

12) The arspÜBglichB meaning ton actus explains PUn. 18, 3 § 9; ■ ctoa (vocabatur), in qna boves agereotDr com aratro ano imnetu iuato ; here erat CXX pedum; wumil to sluicbfln Cfrfum. the. r. 2, 2, 27: sul- cum autem docere longioreiD quam pedain ceatnm viginti cootrarinm pecori eil, quoniani plus aequo fatigatur, nbi hunc madum excessit. Daa- seibe was referred to in the Oskiscbea oud Unibrischea by venui or i'orfui^, only that there uach the originally Italian Deeiuialay stem the furrow IQO Pufs was dug long. Compare FraoL de liinit. in large mat. p. 30, Rodarlf Grninat. load. P. 261, Mumnisen, Itiim. business 1 P. 202 of the 3rd amendment. The Greek n}.iSQOv is also derived from and The meaning is therefore identical (§ 5, 4 A. 11).

13) The actus Bnibns p is taken as the length measure. 94: mensnra est complurium et inter se acqualium inlervallorum lungltujo fiuitu, ut pos per unciam, per pcdem decempeda, per decempedani actus; and jsd will the same also declared as Langenmars in the addition p. !)<>, 3 : actua habet pedes CXX (also p. 245, 13, 330). la in this sense says Vitrnv. 6, 7, 3: putei ibj alat facti, Qt iater duoa ait actus, and eb. § 7: iteiu inter actus dncentoB nan est iuulüe caatella coUncari; also PlJn. 31, 6 § et: in binos actus Inmina esse debehunt, Hygin. de limiL [Gromat. p. 192): actuarioB palos — iuter centenos vicenos pedes deSgemus. — That too the Jugerum (§ 14, 2), namely the width of it as Langenmars

it had, you could aas Pliu. 4, 8 § 31 conclude: in eo cursu Tempe

ongitudine el

jsquiinBe

i latitudini

Pliny alone translates this from a Greek (juelle, perhaps ans the same as Aelian. var. are. 3, 1 follows: tö fiiv |iqxa( Inl tm~ aaguxovja äirixii OtadCou;, lö yt fti)V tiXÖto; tg fiiv tan nXiS-QOV, ig 3i xai nieTov oi.Cy^. So it's the setquüagefum simply on 150 Greek Fufs (not ISO riim.Furs) to be redocided [cf. about the confusion between jiKit^gov and iugerum § 13 A. 3 a. K.). Otherwise He doesn't use the Jugerum as a length measure, but wants to just say that the Tempethal is wider than Ij Jogera Landes in the width extend.

6 13, 1. ROMAN MEASURES OF LENGTH. 65

§ 13. The way^nc^se,

1. While for the Roman field measurements the ten-footer portable measuring rod formed the basis, the path- measure exclusively on the steps. But in order to do the step- mafs to the basic unit of all length measures, the foot In order to set a comfortable ratio, one did not choose the simple one step, which is on average around 2|^ Fufs, but the Double step, jjassws, to the unity of the distance measures and standardized him once and for all to 5 Roman feet i). This word, which in ordinary language simply refers to the step is as a technical expression, its derivation (from pandere) according to, the foot span. It is the space when walking the individual foot from the point where it is picked up to to the one where it appears again, i.e. twice as much simple step 2). From the introduction of the five-footed The passage also explains why the Romans used the arm span or fathoms of six feet, which are so common among the Greeks Mafs was (§ 5, 3), not used 3).

1) Coluni. the. r. 5, 1: passns pedes habet V; also Balbos p. 95, Isidore. Orig. 15, 15. Vitr. 10, 14, 4: pedam milia qainque, id est passus niille. Plin. 2, 23 § 85: Stadium centum viginti quinqae nostros efficit passis, boc est pedes sexcentos viginti quinqae.

2) Dafs passus as a length measure after its derivation from pandere actually means the foot span, can't be doubtful if no older writer expressly states it; because Gellius the passage cited by Ideler p. 132 (15, 15: ab eo quod est pando passuvi veteres dixerunt) does not mean the noun passus, but that Supinum passum. The only question is how to calculate the foot span. Ken asked. The simplest thing might seem to be that passus the space from the Heel of one to the tip of the other of the spread feet draw so that there is 3 feet as a space between the two feet have to accept. Just because we never have such a foot span when walking do it again, but the passage obviously refers to a measure that is based on continued aggression, this is the explanation given above at least more acceptable. Think of the left foot in normal terms Stepping position placed in front of the right one, then between both feet 1^ Fufs space is. Now pull your right foot and sit put him back in a walking position in front of the left one, so the heel of the right one has it Measure 5 feet across from the first to the second position, this is a passage. So if you continue to step out, that's all you get count repeated appearances of the same foot. That's what it's called too in the excerpt. de mensnris (Gromat. p. 373): passus dicitnr, quod duobus gressibus gradiendo conficitur.

3) The Excerpt. de mens. (Gromat. p. 373) give the word passus

Hultscb, Metrology. 5

2. Larger distances were expressed by the Bümers Thousands of passages {milia passuum or bloa mÜia). Yes They also set these intervals on their military punishments Stones that indicated the distances'') and that's why miliaria called. So the thousand passages became one of their own Wegniüfse, the Roman Helle, albeit a special one Name for it was not formed. One of these appears first in Strabo in the Greek replica fiiXiov, much later only in the Latin müiarium^).

anoh the meaning of {dufter: pnasna etiam dicitur, qaaDtnm ambobus brachüs exteDsii inter langiasimos digitos est; but you can't find it anywhere so with klaasiactaen Schrinstellera. Although Plinias translates 5, ä § SU the fifty orgies, at which Herodotus 2, 149 visited the depths of Lake Müris Btimt (Xlftvii fovaa ßa&os miinjxoviöpyuios) du^l^h L pasius; doeb Is this just an inaccuracy of this Sebriftstellera, the sieve apdBre PDcb let the larger ones be placed on the ropes. So he gives how Ideler Fig. 1812-13 p. 130 note and p. 169 I'. proven, soon through pal- tnut, soon through semipes, soon through Bubilvs, waa Dioskorides dnrcb ajii- 9aff^luapresses; although it appears, as aas T, 2 g 26 (see above § U A. 3), who knew the correct fiedeotniig of ani^a/i^ well. 12, 25 § 111 he translates from Theopbr. bin, pt. ä, ti, 1 itxoai nliS-Quv dorch iugrrum XX, without noting that the Jogeram is over 2^ times larger than that Pletbran, because erateres holds 0.966 (Table IX), the latter 0.372 preuFs. Mor- gea (Table V). Compare § 7, 1, § 12 A. 13, Iduler Treatise. 1812-13 pp. 178f. 4) PlnUrch reports on C. Gracchua in his ViU c. 7 : tiq'os Si TovTois Sia/iiTgtiaa^ xaiä filktov öSov jtäaav xfovtig iiS-Cvov; aimtifi Tou fid^ou xaTiatijaey. But one shouldn't believe that Grace is cboi made the first such measurement of Stral'ben, Polybius says 3, 39, 8 about the strait of the Strait of Gibraltar led to the Rhone: Tttüia fäp vvv ßßti/jäiiaiai xitl aeaTj- fellmai xaiä aTaiiovi nxriü iTia 'PtOfialan/ tnifiti-ia; (see § 10, 1). So in his time there were already previncial punishments naob Pasaii aasgemeaaen nnd provided with milestones; around ao earlier diea murste in Italy must have been pushed. The Zäblong of milestones began from Rome in such a way that at the door where the punishment began first stone was erected. Compare Caninu ricerche sulla precis« esten- sione dell' anlico miglio Romano, in whose Via Appia I p. 233ir. Later lier« Angustus on the Fopam the so-called aureummtiiflj'iumBnfstellen, Welehea should be considered the starting point of all Italy's punishments, without However, the previous Zäblong of the milestones from the Tbaren onwards was changed. The Cass. 54, 8, plat. Galba 24, Suetnn. Otho 6, Tac. are. 1, 27, Plin. 3, 5 § 66. Compare the IVanze remarqnes snr quelques points de l'ancient geogr. in M^m, de t'.Acad. of the Inicr. t. 28 p. S'JOff'., Becker Handbook of Roman Antiquity. I p. 343f., Caoina a. a. 0. p. 23af.

5) Isidore. Orig. 15, 10: mensaras viarum noa miliaria dicimns, Graeei stadia — , millarium mille pasaibna termiiiatur. Balbos p. 95: miliarium have passu.i mille. M(hov Undet see first in Strabo 7 p. 322, then more often with later ones. The older Roman writers used rare

I

I 14.1, ROMAN FLACBI^nilASi^E. 67

In addition to the mile, the Roman scripts use parts r sometimes also the path as the Greek, the stage (§5,4), which they consistently represent as the eighth part of salvation, i.e Calculate 625 Roman feet ^). In particular, it seems that distances at sea, since the passage by its nature is only step-by-step mafs was, mostly determined according to stages ^).

The overview of the Roman routes is given in Table VI D.

which sii

625 Roman

^H^ distances

^^H mafs was, i

^^mMn area

^^^ gKlmäriigm:

§14. The FläckenmafsB.

As for the length measurements, the foot also forms for ^e FISchenmarae the unity: 'modus omnis areae pedali

B

6) ColDin. the. r. 5, 1: Stage habet passni CXXV, id esl pedea DCXXV, qaao (summa) octies multiplicaU efSuit uille passus. Plin. 2, 23 §85; stadiam centum viginti ([niaqne odatroa etfieit paasns, hoc est pedes BBXoentns viginti qaiaqae. Baibus p. 95. IsJJor. Orig. 1 5, 16. — CeusoriD. since the naL 13 calls this stadium of 625 romisclieii Ful's the itali see, However, it is different from the Olympic one with which it is rather, it was identical |§ 10). The relationship given by ColBmelk is the basis of all reductions of Sladion to miles xn, which are at rS- Find a variety of scafir plates, 7.. B. at Vilruv. 1, 6, 3, Plin. 2, 108 § 247, Liv. 22, 24, 5 compare with Polyb. 3, IUI, 4 (Be silent about Pol. 3, 311 t.V p. 576). But sometimes the staging information becomes Greek Sources retained without redncirt ta are j like this with Cic. de Sat. 5, 1 ; sex illa a Dipyla stadia eonfecimua, Plin. 19, 3 § 41 ; vim illam per qnattanr mi- lia Stadium Africae valuisse; cf. eb. 4, S § 3Ü, Unter den WegmaTsen The stage is also listed by Baibus p. 94, 12, under the field msTse n from Colam. the. r. 5, 1. In this sense Isidore mentions. Orig. 15, 15 BDcb a siadiaUs ager, whom he met in the midst of the curses" mafsen, but clearly explained as longitude Mars: bähet passus CXXV, id est pedea DCXXV, cnius oiensura octies compulata miliarium faciL

7) At Sidon. Apollo, ep. 2, 2 p. 40 ed. Sirniuud. Heirsl it from one See: ipse secundum mensnras, quas feruot nau ticas, in decem et September stadia procedure. Sn are also in the Ilinernrinm of Emperor Antonin the release to sea is determined consistently according to stages, while Senate still counts miles (Itinecaria ed. Wesleling p. 5]2ff.). The information is also available from Cic. ad Att. Iti, 7, ad fam. 16.2. Compare IdclerAbbandl. 1H12 — 13 p. 135. It should also be noted that dals Vitruvius. 10, 9, 7, where he gives an explanation for leveling the ships distances traveled hescbreihl, from miliaria tpatia navigaÜimit speaks.

bn ROMAN FLAClJEN MASS. (U.

mensura comprehenditur', like Cüiumella (der. r. 5, l)beiiierkL This applies twice as much, because part of it becomes an area the LäDgenfurs, pes porrectm, determined by their dimensions sions in length and width are given, partly serves the quadrutfufs, pes quadratus or coiislratus, daza to express the area'). 0 Mafssiab when measuring sen of the lands was, as noted above ($1 2, 4), the ten-pointed measuring rod, ilecenipeda, the square of the same ben was considered the smallest part of the Keldniarse; was underneath at most half still bereclinel, there are still smaller pieces escaped the estimate').

2. The larger area dimensions of the Romans are all- lich field mats and as such are closely related to each other worried about farming. This is how acttis referred to, as before above (§ 12, 4) g<*shows, actually the length of the Furrow which the plow bulls go into without being excessive can pull in one attempt, a route that was originally zii 100 feet, later after the duodecimal system to 120 feet or 12 Detemppedae was set. From the length actus formsti Then an area measure is created by itself by changing the field

1) About the surface area in the context of lengths and body dimensions says Bflibua Gramat. p. 97; plannin est, quod Graeci epippdoD appellant, DOS coostraluB pedcs; in naa langiludidem et latiladinem babemoa; per quDe mstiuiur Bgrna, aediGcioram sola, ex quibus altlludo aut craasitudo non prnponitar, ut apera teetoria, inauratnras, tabulas et bis similia. Compare the excerpts from Baelh. Geom. p. 415. The Langenfufs beifst pei forreclui at Baibus p. 95, the Qaadratfal'a pes quadralui at Colum. there t.r. 5, 1 D. 2, Plie. 93, 4 § 75, Isidar. Orig. 15, 13, eadlkb aacb io der ScbriFt de iageribas mctmndis Gromat. p. 354. 366; Balbol, on the other hand, have it p. 9Sn. 97 and the Excerple from Boeth. Geam. p. 415 dalnr the Ausümck pet eoTutralui, and pei quadralui is at Balbu] as well as at Pestus aot. quiub'an- tal p. 256 mueil. the cubic fnrs. About the calculation of the square calls thank you Calaui. the. r. 5, 2, if he z. B. about measuring the ager qiia- dratu! iUgl: cum sit ondique peduui totidein, mulliplifanlur io se you latera, et ifuBB summa ei multipliealione effecta est, eanidiceinus esse quadratorum pcdnin. — The measurement according to Püfsea beil'al pedare, each uoeh the foot niesgenB curses pedatura or podiimus. AudariT Gromat. 11 p.m. 231.

2) Varro de r. r. 1, BO: ingeri pars mioima dii^llur acrlpulum.id est decem pedes in longitudinem et latjludlnem qoadratnm. Oassame Mafa neant nusdriivklieh decempuda guadrata Pallad. the. r. 2, 12 Column. the. r. 5, 1 begins with the calculation of the Thelle of Jugerum with the half- ben Scripulum as the smallest theite: ut a minima parte, id est ab dimidio scripulo inripiam, pars quingentesima septuagesiuia sexta pedes elB- cit quinqaaginta. Immediately beforehand he remarks; iugeri partes non omnei posnimos, sed eas, quae cadunt ia aestimationem facti opei'is, nam minores peracqBJ (upervacanenm fuit, per qnibus nnlla merces dependitur.

I

2. 3. ROMAN AREAS. 69

according to the corresponding squares abtheiite^ This is how it came about the actus qtuidratus, usually simply called actus^). To plow such an actus was about half Day work required; That's how it happened that you got twice as much Actus or the entire day's work to a special area mafse, which is an elongated rectangle of 240 feet length and 120 feet width (= 28800 D feet). This is the iugerum, the main field mafs of the Romans ^).

3. By raising the Jugerum or Doppelactus In the main, the advantage was achieved at the same time, that now the division of the same according to the fraction calculation alone

3) prefer the Läogenactas see § 12 notes 12 and 13. About the origin of the Qaadratactus says Frontin. de imit. in Gromat. p. 30: priinum agri mo- damfecerunt qaattaor limitibns clausuni, plerumque centenum pedum inutra- que parte (quodGraeci pletbron appellant,Osci etUmbri vorsum), nostri cen- tenum et vicenum in utraque parte, cuius [ex IUI] unum latus, sicutdiei XII boras, XII menses anni, XII decempedas esse voluerunt. Compare Varro de r. r.l, 10: actus quadratus, qui latus est pedesCXX et longus totidem; co- lum. 5, 1: actus qnadratus undique finitur pedibus CXX; Baibus in Gromat. p. 95, Isidore. Orig. 15, 15. — Varro de 1. Lat. 5, 34 mentions next to that actus quadratus another actus minimus: one (actus) finis minimus con- stitutus in latitudinem pedes quattuor — in longitudinem pedes centnm et vlginti ; in which Colum. 5, 1, Isidore. Orig. 15, 15, 4 follow (in Isidor In the manuscripts CLX or CXL stands for CXX). It This act seems to have been the piece written by a Jugemm was cut off widthwise to create a narrow drift path. hold; as a path for wagons, like the Actus in the Dig. 8 tit. 3, 1 n. 12 is explained, it must of course have been wider. This means Explains Ideler's view, Abhandi. 1812-13 p. 142.

4) Plin. 18, 3 §9: iugerum vocabatur, quod uno iugo boum in the exarari posset, actus in quo boves agerentur cum aratro uno impetu iusto. here erat CXX pedum, dupiicatusque in longitudinem iugerum facie- asked. Compare 18, 19 § 178, Mommsen Rome. business I p. 195 note. The from The derivation of the iugerum suggested by Pliny is in any case the one before which Varro and Columella give; the former says the r. r. 1, 10: iugerum (vbcant), quod quadratos duos actus babeat (compare de 1. L. 5, 35), clear Colum. 5, 1: hoc (actus quadratus) duplicatum facit iugerum, et ab eo quod erat iunctumy nomen iugeri usurpavit. Etymologically is iugerum just a subsidiary form of iugum, which according to Varro a. a. O. one practiced in Spain agricultural area, which he, like Pliny, explains the iugerum: iugum vocant, quod iuncti boves uno the exarare possint. — The dimen- sions and the surface area of the Jugerum is given by Columella a. a. 0. : dno actus iugerum efiTiciunt longitudine pedum CCXL, latitudine pedum CXX, quae utraeque summae inter se mnltiplicatae quadratornm faciunt pedum viginti octo milia et octingentos. Similar Varro de r. r. 1, 10, quintile. 1, 10, 42, Isidore. Orig. 15, 15. — About the Jugerum as the state mafs of the Romans mer compare Rudorff Gromat. Institute p. 280.

I

70 RÖmSCBE PLATE5IHS3E.

Usual Duodeciraaisyslem*) Ms on the scrtpidum, i.e. Feel your way through the first part of the whole thing. This script lum is nothing other than the square of the decompeda = lOOD FQfs. Then the remaining parts of the ju- geriim can easily be traced back to square feet, the uncia z. B. as the twelfth TheJl holds 24 scripula = 2400 a foot. A voila- constant calculation of this DuodccimaltheiluD^ of the iugeruat There is Columella (de r. r. 5, 1), the same is in Tab. IX B at the same time compiled with the Bcductioo on newer Mäfs

Such a determination of the area of the fields However, scripula and square feet only appeared in formal and accurate calculations ¥or; People were content in common life deal with Detemppeda, Actus and Jugerum, including Cülumella the climate is still coming, which had ßO Fufs in the square, so the fourth part of the Actus was ■*).

4. The larger arable land of the Romans will be listed together and explained by Varro (de r. r. 1, 10): 'bina iugera , quae a Bomulo primum divisa dicebantur viritim, quod heredein sequerentur, heredium appellarunL Haecpostea a centum centuria dicia. Centuria est quadrata in omnes qua- tuor partes, ut habeat latera longa pedum oo co CD. Hae porro quatuor centuriae coniunclae, nt sint in ulramque partem binae, appeilanlur in agris divisis Tiritini publice saltus''). This here-

3) For the Diadecininlbrncii calculation of the Hinians see below § 20, j to 3, Harquardt Hörn. Alterb. 111, 2 p. 42H'. The saipalum oiler ^ of Jugernin would have been from Aetna j-^, for which it is in ' "' see Brachreehnun; linen beaundereo expression. D Great mnhr, why daa Jagerum and not the A.etu9 lam HauptmaTse became sublime. Dia EioEhfiiiung dea Jugernm in ScripnJa erwShnl except Colamellnnueh Varro the. r.l,lU:jd(iugeruin)babet scripula CCLXXXVIJI; There he gives an example of this; nnciam agri aut sextnntem. Hygio. de cDDdic, agr. p. 123 calculates the CyroDaic medimnnn on äigeram imum, uneiam, äimidium siTiptiliim (according to Lachmann's Emendaliaa). Meh- More examples are given by Colum. 5, 2, cf. also Liv. 5, 24.4, S, 11, U.

6) Colum. 5, 1; clima (]DOqao versus pednm est LX; also Isidur. Orig. 15, 15 and the Eic^ de mmsaris in Groniat. p. 372.

7) The steepness is given according to Schneider. Eiren, as Varro explains the Renfurio Fronlin. de limit. (Oniinat. p. 30), but he lue heredean the name quadratiu ager or sors: haec dno ingera iuncta in unum quadratum agrum ellicinnt, qnod sint in onues partes acins bini — , qaidsm priinnui appelintnin theunt snrtcm, et centies duclnm reutu- riam. In another place (de 1. L. 5, 35) Varro notes: cenlnria prirnnm a centuui iugeribns dicta, post daplieala retinuit nonien, nt Iribuä muUiplicatae idem tenent minien; what from Colnni, 5, 1 and ]aidor.>15, tä will be repeated.

I I

I

I

S15.1. DETERMINATION OF THE ROMAN FOOT. 71

So dium had 240 feet square = 57600 D If or 4 Actus, the centuria 2400 feet in square == 5760000 D F. or 400 Actus, the saltus 4800 feet iD's square =» 1600 Actus odbr 4 Ceixturias.

These are therefore the surface dimensions of the Romans Jugerum are all squares, the sides of which, if you look at them the Detemppeda, d. h. the page of the Scripulum, as a unit sets, behave like

1:6:12:24:240:480

(Page of scripalam, clima, actas, herediam, centuria, saltus),

od^ the surface dimensions behave like squares of these numbers. This is illustrated by the following table, in which The Jugerum is also included:

saltus

1

centuria

4 1

heredium

400 100

1

iugerum

800 200

2

1

actus

1600 400

4

2 1

climate

6400 1600

16

8 4 1

scripulum

230400 57600

576

288 144 36.

The reduction

the Roman area dimensions to newer dimensions

goes Tah. IX.

§ 15. Determination of the Roman foot.

1. The expression pes monetalts, with which the gromatist Hyginus ^) the Roman foot as opposed to foreign ones Fufsmafsen names clearly indicates that in the Temple of luno Moneta on the Capitol as well as others Normal measurements also included a foot scale 2).

1) Gromat. ed. Lacbm. p. 123: pes eorum, qui Ptolemeicus appellatnr, habet mooetalem pedem et semunciam — item dicitur in Germania in Tnngris pes Drnsianus, qui habet monetalem pedem et sescunciam.

2) It is included in the inscription of the Farnese Gongln (§ 18, 1;). ^mensurae exactae in Gapitolio', which shows that the normal Mars on which Capitol was placed. Priscian expressly testifies to this in the didactic poem de ponderibus etmensuris (Wernsdorf poet. Lat. V, 1 p. 494ff.) V. 62: quam (amphuram) ne violare liceret, Sacraverelovi Tar- peio in monte Quirites. The location of the storage becomes even more precise Normal dimensions are referred to by the term pes monetalis in Hygin; it was the temple of luno Moneta on the Gapitol, which, as is well known, was at the same time

r

72 DESTIHUNG DF.S IIÜHISCHBN FOOT. 9 IS.

This assures us that the Roman pufa was a solid and has been a constant size, and only really found themselves in the imperial period, from the second century onwards, traces of one slight reduction of the same-'').

To accurately determine the amount of the Roman foot Various paths have been taken, which in general nen led to a consistent result, but none- Because they are all equally safe and reliable ^). The closest one was it allows the FuXs to determine directly according to the standards that are still preserved to us. These are ihell's real furstyling sticks, they were never used for measuring, some were models from Mafs- rods placed on monuments. The latter, four in number^), are executed in ftelief and therefore have the ends suffered from weathering. Since there are three of these If the trees were divided into palm trees, the whole area was asked for sought to determine the middle divisions. Yes the whole process has been unstable and uncertain, that one cannot expect the exact value of the to have found a Roman foot''), quite apart from that,

Hünzstätle was. Liv. 6, 20, 13. Werusdorf m the Excnrae to Priscitn p. ÖOSff, Idelfir Abbandi. 1812-13 p. 15S, Hase Pfllaeologus p. 5f.

3) Raper in his later work about taking the writing into account an inquiry üita ihe memufe oj ihe Roman fant (Philosophiuil trausaclioiw neo) p. ibid proves that the Roman foot under the government did that Septimius 8everas and Diccletiao on about (1.005 of the Eoglian foot (^=3 0.7 Par. Liuiea) appears smaller than before. Compare etc. Note 12.

4) A detailed overview of the different species which the Roman foot was asked to look for as beasts, is given by Ideler Abhandl, 1812— 13 pp. 146ff., Wurm p. 691F. , Paucker p. 178 ff., Hussey p. 216 7.

6) Esslad 1. the foot on the tomb of Cn. Cossutios (Gruter loser, p. G44, 1), according to the owner of the property in which the property is Noment aaffaudeD was also called the Colotiauiscbe, first he< thinks of Partius (§ 3, 1) - 2. the foot on the Marmar of T. S ta tilina (Philaader called Pactus in Tbes. Graev. XI p. 1017 and Hcvillas in Saggt di disierlazioui academiche dl Cortuna III p. 116) — 3rd of the Futs on the Honnmcut of Aebutius (Fabretti de aquis et aquaeductibiis veteris Ro- maep. 73) — 4. the Cappanisclie Fufs (Revillas g. a. 0. p. 118).

0) An overview of the older measurement CDs from the lu previous note. aaffürteuFufsniafsstabebebegletRevillassnpra l'antico piedc Romano load Say di dissert. acad, di Cort. IIT p. lllff. The most reliable measurements

in the Mem. de l'Acad. of the InBcr. t. 28 p, 607 IT. The cap then behaves ponicbe feet xam engliacheu like 116: 120, what for the same 130,"' "

I

I

J

BESTlMML'.Nfi IIES HÖMrsCue> FUSSES.

73

that from the outset when the monuments were erected, an absolute lute precision in the follow-up of the Fufäniaraa batons is not intended. They hardly produce a more favorable result quite a number of still preserved base poles'). Because Echoes from the not insignificant differences in length This shows that it is more or less imprecise. are prayed; and since one cannot assume that the deviation chations after the plus as well as after the minus each other borrowed, then even an average calculation does not give a whole secure Werlh. But it is a completely arbitrary procedure to pick out any one of the measuring sticks and use it to be described as the only correct one.

Since the Romans meticulously enforced their land punishments and the Distances denoted by milestones would be through measurements the size of the Roman mile and in- dli-ect of the foot results when such re-measurements are carried out I could be employed with sufficient security. The ones so far

Lines (p. f>05), the atbutic surface is almost the same as capponide (p. 6U9), the Cossatiscbe uses sieve to par. Fnl's like 12S8^“ys.: 1440 ^. 6IU), d. h. the CassDlische Pufs contains l'iS.SSS par. lines; the Five of Statilius is equal to this. Revillas p. 12 hours brings a little more relief Values beyond Russia, in particular he gives the static FaP« 131.03, the Cossaliscben 130.75 par. lines, i.e. 2 lines more. Do Greaves discoarse of the Roman faat p. 233 is the Sulilian FoTs = 0.9T2 eagL Fufs, the Coasulian = 0.9e7 = 130.38 par lines. The latter value He considers it to be the only true vocal style of the Rumian cask (p. 222?',). 7) Locas Paetns de mensuris p. IGOTIT. (Thes. Graev. XI). [and there were three mafa sticks, three of which were the same length, ala reliable models of the rijiuischea foot explained (p. 1617). This» Hafs he ran a deepened entry on a fine marble slab and attached to the) Capi- exhibit great; this is the Capitoline Fnrs. Compare Revilns p. 11», Ideler p. 14^, which proves the latter at the same time as the buried one Model has become longer due to frequent remeasurements. IHncb Psetas' According to our own information, the Capitoline foot nm ^ is shorter than the Cossa foot tiache; Barthelemy mafs 13ll.5 par. Lin., later measurements rise to perm30,'Lines.~BBrUiälem;p.61U describes a brouzen Mars staff from the Vatican Bibliotüek, the same length with the Capponian Fivese = I30,ei Par. Lia. asked Rome de llsle Mitroi. pr^f. p. XVIII fin- det his calculation of the Roman Ful'ses confirmed by an anf dem The scale found in the mountains of Chatelet is 1 30.6 lin. holds. Six Maf^Uibe from your former Borboniscben Maseuin tn Naples are measured from Cagnazzi (su i valori D. s. w. p. 12 of the translation); they fluctuate between 129.19S to 131.34S par lines. A benchmark in the church's IHnsoom Ut equals U,29(it4ä Meter= 131,2ä Par. Lin., another in the Vatica- niseben library equals U,293UTU meters ^ 130,803 lines (Canina in the g 13 note 4 written p. 242).

I I

74 CONSTITUTION OF THE RÜMI5CIIE> FOOT. ICE.

New results obtained in this way should be treated with great caution *).

The method used by Läogenmafs should be completely rejected to determine the fiörpermafs. The Roman body dimensions However, according to the system, they were based on the length mafac, because the quadrant should contain the contents of a Roman cow's foot have. In practice alone, as shown below (§ 17, 1). will be determined according to the weight of the water or the wine they drank; so it is wrong from such hollow dimensions an exact value for the Roman Wanting to find footing, quite apart from the fact that the Romans did not take the temperature into account in their weighings, still used distilled water, so that's why one there is no sure match between body and length measurements were able to achieve^),

2. After all, it remains the safest foot stick to visit again, the old builders themselves at Temjjeln and other common things bound; because if ii^endno, this is how precise measurements were taken in such buildings.

8) They used verses of the kind that Cassioi, Astrach, MaSei and Revillas have employed (see the latter n. 121 IT.) are abne Werth. The HeeatCat from d'Anville eats more reliably on the mille Itoniain in the Mßm. de l'Arad. of the Inscr. t.28 p. 3460", the one for mile 576 Toiseo, for the vehicle 130,637 Lin. finds. A iSacfamessan^ a distance of approach piachen Strafse asked for 1471.233 meters for the mile and 0.29424 meters for the Fafs. :=< 130,436 Lin. (Letronne recherches snr Hernn p. 10). Canina finally also calculated from measuring a distance on the Vit Appia 0.295600 meters - 131.038 lin. (op. cit. p. 2498'.). This latter ' Werth came with the determination of the fluff taken from the buildings the worst.

9) Ads dem Farnesesicbeu Cungius (g IB, 1) directs Villaljiandi de pon- the, p. 499f. a foot that is more than 133 lin. amounts to whatever ZD is high. The path is even safer. the first Eisenschmid p. 101 f. hit. He starts from the Roman pound and calculates it then the ropes of the Quadrantal as a cube, the BO Pt and Qaellwasser holds. Sat he receives a Fufa of 132.45 lines. Cagnazzi p. 122 recbnet according to his PFnade J3I,3 Lin., which von Bückh p. 107 with R^cbt as not is designated as long-term secured. Dureau de la Malle Ecnn. pol. I p. 29 follows the determination of the pound by de la Nanze and BnrtMlemf and then received 0.29642 meters = 131.402 lines, for which he later (p. 30) according to Gosselin U.29li20ü M. = 131.35 lin. seUt. Dd but the Roman one Pound was actually larger than de la Nauze and IJarthclemy Accept it (see § 21, 3|, then the foot would be set higher be, so the value derived from it is all the more of the true length. of the rbmijcben foot differ.

I

I I

i.

[

and all that is required is a reliable re-measurement. There Now you can see the cross of the Roman foot from the ones mentioned above. ten monuments and corn sticks already to a certain extent If it were just certain, it would be easy to see how much Roman the basis of each individual dimension of a building lie, and from this in turn the amount of the foot comes be determined precisely. Raper has taken this path in his development quirt/ into the measure of tke Roman fool '"), and based on Desgodelz's work i^) as the Amount that the Roman foot had until the reign of Titus, 0.970 English Fufs = 131.10 par. Lines found la). This one on A value based on a large number of measurements is only given exceeded by a little of the result which Canina in his studies of the Roman mile from the length the columns of Trajan and Marc Aurel. It revealed This gives him a fee of 0.296350 Meier = 131.371 Li- nien ' ^). Raper was joined by Ideler, who was in the round Number of 131 lines remains standing'*). Worm, the Böckh (p. 198) follows, his calculation is also based mainly on lich on raper, but increases the result obtained from it a little bit more by making the foot 131.15 Lin. on- sets ^^). In any case, it seems advisable, according to Raper

ft 10) PMlosophical transBctiona 17G0 p. 774 ff.

11) Leb ediGces antlqaes de Roine, Pariah 16S2.

12) After he a. n. 0. p. 7!15— '8)9 the means to the Messan^en has drawn at verified temples, he comes p. 921) la the castle: 'It appears from tbe measures of Ihese buildings, tbnt tbe Ftoman facil befare tbe reign of Titus exceeded 970 parts in 11)011 of tbe Londna fnnt and in the reigns of Severus upd Dioctetian feil short of 965'. The exceeded be- records the relevant number as a mipininl amount, i.e. b. the Roman one Fufs was on keioea FaU smaller than 0.970 engl. FoTs, suadern after am a little something grürser, which, however, is out of the calculation, as it is after not 0.0Q1 English, Fufs is cheating. Since Raper, moreover, as he p. T7B noted, the Paris Ful's to the eDgliachen in the ratioDifs 10654 : lUOOU, SD is 0.970 English. Fufs ^ 131.10 Pav. Lines.

13) See § 13 Anui. 4 cited document p. 244-248. Both San- len are 100 Roman with connections of the base and the upper attachment Fives up.