American Numismatic Society

Introduction to Numismatic Terms and Methods


1. Introduction

Numismatics is the study of coins and money, of coins and coin-like objects. The value of coins as historical evidence was understood even in antiquity, but the systematic development of the study of coins as a proper discipline, with a methodology of its own, began only in the late eighteenth century with the work of Joseph Hilarius Eckhel, an Austrian priest whose Doctrina Numorum Veterum (Vienna, 1793-1799) was an attempt to comprehend all of ancient Greek and Roman coinage in the span of eight volumes. Eckhel's work spawned few immediate imitators, but it provided the impetus for the systematic cataloguing and study of the great numismatic collections of Europe. In Austria and gradually elsewhere, chairs in numismatics were established in the great universities, and the major cabinets were placed under the supervision of trained historians and archaeologists. In North America, where there was no academic tradition (but, above all, where there are no genuine finds of ancient coins), interest in coinage may be associated with the maturity of the country and interest in its origins. In the late 1850s "numismatic and antiquarian" societies sprang up in the major cities (Boston, New York, Philadelphia, Montreal, Chicago).1 Some of these attracted the involvement of prominent academics, but the discipline has never penetrated into the university structure. Numismatics is seldom taught in this country and then only as an adjunct to other pursuits; given the current attitude of colleges and universities to their numismatic holdings it is hard to see when the discipline will assume more than a minor role even in graduate curricula.

The objective of the American Numismatic Society's Graduate Seminar has always been to provide an introduction to the discipline, not for the purpose of training professional numismatists but in order to make future members of the scholarly community aware of the existence and proper use of one extremely important form of evidence. The beginning of any discipline is the proper use of vocabulary and methodology, which this text has been prepared to introduce.

2. Vocabulary

It is first necessary to have an understanding of the meaning of the term coin itself.2 Webster (second edition) gives:

A piece of metal (or, rarely, of some other material) certified by a mark or marks upon it to be of a definite exchange value, and issued by governmental authority to be used as money; also, such pieces collectively.

Metal: The most obvious physical attribute of a coin is the material from which it was produced--almost invariably, up until modern times, metal. The metals selected had to be abundant enough to provide the raw material for an exchange medium, but scarce enough to have value in their own right, and the selection has varied from culture to culture. In China, the initial metal of choice was copper; in India, silver; and in the west, silver or an alloy of gold and silver known as electrum.

Normally in describing coins in prose the English terms are used, but standard catalogues almost universally employ abbreviations taken directly from the Latin rather than from the periodic table: thus AV (aurum) = gold, AR (argentum) = silver, AE (aes) = copper or one of its alloys. This last abbreviation is used generically to describe any coin consisting principally of copper; when it appears in prose, aes is frequently translated as bronze.3 Occasionally the abbreviations El (= electrum) and Bi (= billon, an alloy of silver in which the silver comprises less than 50%) are encountered, and Cu is becoming more common to describe copper.

This literally unscientific terminology and abbreviation describes the principal element only; when standard chemical abbreviations are used, it is almost always in the context of a formal analysis of a coin's content. Only in recent times has it been possible to determine with any degree of precision the metals of which a coin was comprised, so the older abbreviations have a use in describing the major component of a coin while disclaiming the precision of a scientific analysis.

Weight: The Webster definition does not mention weight as an aspect of a coin, but in antiquity the only way of stabilizing a "definite exchange value" was to strike a coin to a specified weight and to regulate its alloy: the tariff or exchange value of a coin bore a very close--sometimes even direct--relationship to its intrinsic value, and thus it is possible to determine the relationship among denominations by comparing their weights. In some coinages the comparison of weights among series may determine the standard to which that series was struck; this in turn may be significant for chronology or attribution.

Today it is customary to express coin weights in grams, though in older catalogues one may encounter Troy grains; usually a conversion table is provided. Whatever system is employed, it is important to relate that system to the one used at the time the coin was produced. Many coin denominations derive their names from weights, e.g. Greek drachma = 1/6000 talent; in the Roman system as = pound, uncia = ounce; semuncia = half-ounce, semis = half pound, sextans = 1/6 pound or two ounces, and so on.

The "mark or marks upon it," which certify a coin, are categorized in different ways, and in many cases using terms that are familiar in themselves but have different meanings for numismatists.

Type, for example, is one of the terms most misused by beginning students of coinage. It can easily be read as if one were asked, "What type of coin is it?" and answered with a classification ("Roman" or "Islamic" or "U.S.") or with a denomination ("stater", "denarius", "peso"), or simply "gold", "silver" or "copper". Any of these would be natural responses to the sense normally conveyed by the use of the word "type" in everyday English, but all would be wrong. For our purposes, "type" refers to the central device or motif (Doty uses the term "dominant design") of either face of the coin. On one face of the United States cent, for example, the type is the bust of Lincoln facing r.; on the other, the Lincoln Memorial.

The field is the area on the face of the coin around the type, or which provides its background. The field is often subdivided into left and right. When "to l." and "to r." (or "in field l.", "in field r.") are written, they refer to left and right as the viewer sees them, although when we are describing the left or right arms or hands, they are the left or right arms or hands of the figure portrayed. Some catalogues eliminate the verbiage by using a graphic device, e.g. A|*, where A appears in l. field, * in r. field, and nothing beneath.

One part of the field has its own name. This is the exergue, a term which originates in Greek ex and ergon, literally "outwork" or an accessory to the main work. This refers to the portion of the type beneath the ground line, which is often explicitly rendered and always implicit. In ancient coinage it is often left blank, though on the titulary-laden reverses of Roman coins the type is sometimes spelled out here; later it is used for mint or issue marks and, especially in modern times, for dates.

Subsidiary to the type itself are attributes and adjuncts. An attribute is usually something attached to or held by the figure portrayed: thus a bust might be laureate or diademed, hold a sceptre or palm branch; a standing figure might be naked or draped, wear headgear or not, or hold branch, cornucopiae, orb, spear, sceptre and the like. An adjunct is usually disconnected from the figure itself--seated on the ground line or in the field, perhaps flying in the field crowning the type, or even attached to the throne on which the main figure sits. In composing descriptions of types, it is well to subordinate these elements verbally: first the type, then its attributes, then adjuncts. Generally speaking the description of images will move from left to right after the central figure is described.

Legend is a term derived from the gerundive form of the Latin verb lego, and means "to be read". It describes the verbal content of a coin. The legend may indicate the issuing authority, describe the type, combine with the type to specify the occasion commemorated, or convey virtually anything desired by the mint official (whose own name might be part of the legend). Legends may encircle the type or flank it, and may continue in the exergue.

The ethnic may or may not be present. The term originates in Greek and is most commonly encountered with reference to Greek coins. It refers to the name of a tribe, nation, or city-state responsible for issuing a coin. ΑΘΕ ("Athens") and ΣΥΡΑΚΟΣΙΩΝ ("of the Syracusans") are ethnics; the only ethnics employed on Roman coins are ROMANO (on early AR and AE and ROMA (on Republican silver and aes). When the entire legend consists of an ethnic, the terms are synonymous. The term ethnic is used seldom if at all in other fields.

Photographic reproduction is, relatively speaking, less expensive and therefore more common than ever, and it might seem that such attention to verbalizing the elements of coin typology is unjustified if not downright pedantic. But a disciplined approach to the visual content of the coin forces attention to detail and minimizes the impact of value judgments about what is important and what is not; moreover no photograph, however good, can replace the firsthand examination of details that only a cataloguer can give.

The remainder of the basic numismatic vocabulary has to do with the manufacture of coins and the effects of the techniques employed on the coin's appearance. There are two methods for the production of coins: casting and striking. Casting is the simpler: molten metal is simply poured into a pair of joined molds which are then separated or broken, and the images incised in the molds appear in relief on the final product. The sprues which often join one hollow in the mold to another are trimmed off and thrown back into the melting pot for reuse. Without extensive labor casting does not allow for precision in weight, and with reuse molds tend to produce steadily blurrier images.

In the West, this method has been employed almost exclusively for base-metal coins and those of such large size that it was impossible to strike them with manual force, such as the Etrurian and Roman aes grave and, in later times, large medals and plaquettes. In China and in regions influenced by the Chinese numismatic tradition, casting was the standard method of coin production until modern times.

Striking involves the physical alteration of a quantity of metal by impressing an image upon it. It involves the use of dies. The term "die" comes into English from Latin via Middle English. In the sense used here, it compares to machinists' dies, which are used for cutting or stamping an image, generally in metal but also in wood or any other malleable material. In machinists' language, the matrix is the lower and usually larger of a pair of tools; it is fixed, while a similar but somewhat smaller one, designed to fit into the larger, is held in the hand or attached to a cam that is brought down against the matrix. This the die.

In numismatics, both these tools are referred to as dies, irrespective of size, since until the advent of machine-produced coinage the two dies were seldom made to mesh with each other and in fact looked much alike. One, however, was rendered immobile by being fixed in a block that is referred to as an anvil. The upper die, sometimes enclosed in a casing, was usually hand-held but in modern times is attached to its machinery. This is known as the punch or the trussel. By extension, anvil and punch are often used to describe the dies held in the anvil and the punch. The term punch is also used for a smaller tool used to impress letters or parts of letters, and occasionally parts of the type, into mediaeval and modern dies.

Flan, the piece of metal placed between the dies for striking, comes from Latin flare, "to blow." The term is conventional for hand-struck coins; planchet is often used for modern ones, but blank is an acceptable substitute for either. In antiquity, flans were most often made by casting; the coin production process was therefore two-stage: the blank was cast (and, for precious-metal coins, probably corrected for weight by filing), and then struck. In mediaeval and later times, metal was sometimes hammered or rolled into sheets and cut to weight before being struck.

With few exceptions, dies bear images which are incised into their surfaces (intaglio) prior to use; thus the effect produced is in relief, and the image is a mirror of that which appears on the die. In modern times dies have usually been made of steel. Such ancient dies as we possess (and their authenticity is seldom beyond dispute) are made of iron or work-hardened copper. (A die does not have to be a great deal harder than the surface it is intended to strike in order to produce an image.)

Often, especially in hand-struck coinage, it is clear which face of the coin has been struck by which die; the distinction is important. Unfortunately the terms which have been devised to make it -- obverse and reverse -- have different sets of meanings, both of which are in common use and both of which have some validity.

Properly, obversus means that which faces you, and reversus what is turned away from you. Obviously in the simplest sense this distinction is dependent on the eye of the beholder. Von Schrötter's Wörterbuch der Münzkunde is followed almost verbatim by Fengler, Garrow and Unger and in translation by Doty: the obverse is "the side of the coin bearing the more important legends or types" [Ger. Hauptseite or Vorderseite]; since coinage is a prerogative of state, and most states have been monarchies, the more important face is most frequently that which we would today call "heads", after the head of the ruler that gave the coin its validity.

In many branches of numismatics, however, including the classical, the term obverse denotes the lower die and reverse the upper or hand-held die. The fact that the obverse usually bears the more important image, or "head", is the result of technical considerations. Dies absorbed stress at differential rates: reverses tended to break more frequently than obverses because they absorbed the impact of the hammer directly and were not shielded by the flan. Since the execution of a portrait, be it of a god, hero, or human, usually required more care and more talented artisans to produce--in short, was more expensive to produce--minters favored this face of the coin by making it the protected die; this face was usually the obverse.

This is not invariably the case. There are many coins which bear no head at all, and others--the fifth century coins of Syracuse and the staters of Corinth are but two examples--on which the "heads" side is clearly the reverse. The Romans struck some two-headed coins on which it is practically impossible to tell which die was fixed and which movable, and there are some issues--for instance Byzantine solidi struck after A.D. 692--on which there are two heads, one secular and one religious, and where we arbitrarily define the obverse for descriptive purposes as the face bearing the religious image.

Not everyone concedes the necessity of using the terms obverse and reverse in preference to "front" and "back" or "heads" and "tails". Neither of these pairs of alternatives, however, bears any relation to the technique of coin production, and for statistical purposes it is important to know which face of the coin was produced by the obverse die and which by the reverse die.

There are three terms which describe the physical attributes of a coin after it has been struck. One of these is die axis, and it is the easiest to render concretely. This term describes the relationship of the types to one another when one is viewed in the vertical position and the coin is rotated on its polar axis. The die axis of virtually all United States coins, for example, is inverted--that is, when either face is viewed upright and the coin is rotated, the other emerges upside down. These relationships are most often expressed in print by an arrow or arrows: ↑ = 12:00, ↓ = 6:00. When two are present, one is always at 12:00 (e.g. ↑↓ = ↓ = 6:00); in modern literature only one arrow is used, since the other is implicitly at 12. Just as the die axis may be rendered in hours, it may be rendered in degrees in the arc of a circle, so that occasionally you will see 175 o or 345 o, etc. Numeric notation is preferable to other systems when recording coins, since numbers are less liable to scribal error than arrows.

In hand-struck coinages, when dies are simply mated as they come to hand, a fairly random distribution can be expected. Sometimes the shape of the dies themselves leads to a preference for striking at specific die axes (with a square die, e.g., 3:00, 6:00, 9:00, 12:00). If dies are fixed, however, they can be important clues to attribution, since preferences change within mints and sometimes extend over space in a single time frame. A good example is provided by the coins of Hadrian, where for reasons unknown to us there is a shift from 12 to 6 over time. Likewise the early coinage of Massachusetts changes from 6 to 12.

Two other terms are module and fabric; the first of these is a component of the other and has a perfectly good synonym. Module means simply diameter. This measurement is carefully recorded in older catalogues, since in many coinages the compilers did not know the proper names for the denominations and size was a clue; moreover there was no easy way to reproduce a coin to scale. Since the advent of cheaper commercial photography it has become more common simply to illustrate the coin, though this puts the reader to the inconvenience of measuring for himself. Diameters are usually given in the metric system, though older British catalogues sometimes use inches and tenths. What to do with a coin that is not round? There seem to be two alternatives: give the minimum and maximum diameters (e.g. 17-19 mm.), or measure uniformly on one axis for all coins. For square coins, use 17x19.

Fabric, like "type", is not to be taken in its everyday sense: it has nothing to do with the material from which the coin is made. It refers to the general appearance of a coin as a piece of metal, and incorporates shape, weight, diameter, and thickness, all of which reflect the mint's method of fabrication. Weight and diameter are of course measurable with some precision; in hand-struck coinage it is less easy to make meaningful distinctions in thickness since this varies not only from coin to coin but on the same coin, and an average or maximum value is not readily calculable. Words like "thick", "dumpy", "flat", and "broad" are often used to characterize the fabric of a coin or of a series, and the best way to establish their relative meanings is to have contact with large numbers of coins of different mints or periods. An extreme illustration is offered by the solidi of Constans II, which are of identical description except for their fabric, which reflects their place of minting.

Finally it is worth mentioning some terms which describe the alteration of a coin's appearance after striking, or simply mint errors. A brockage is an early form of mint error which results from the use of a previously-struck coin as a die. We suppose that this normally resulted from a freshly-struck piece adhering to the punch die as a result of surface tension, or simply the adhesiveness of heated metal; a virgin flan was then inserted on the anvil die and struck with the punch, so that the obverse previously produced by that anvil die appears in incuse as the reverse of the new coin. Eventually the first coin drops from the die and coining proceeds as usual; the flawed pieces escape detection and find their way into circulation.

A double-strike is just what it sounds like. The same die is brought down twice or more on the same coin, whether intentionally (to raise the relief) or accidentally from the recoil of the hammer. The traces left on the coin will often be visible as a "ghost" or shadow of the type as it was supposed to appear.

This sort of mistake is to be distinguished from overstriking, which represents the re-use of an earlier coin as a flan. Overstriking is seldom employed in modern times, but has often been used to validate or revalidate coins for currency, to freshen their appearance and thus render them more acceptable, or to redefine an area of approved circulation. It was also a quick and dirty way to remonetize earlier coins.

Countermarks have much the same effect, although they consist only of small punches applied to the face of the coin. They can be round or rectilinear and have their own legends and types, just as do coins. They are different in appearance and function from bankers' marks or test marks, normally thin incision-like marks on the surface of the coin intended to determine whether it was of pure metal throughout.

Both overstrikes and countermarks have obvious applications as methodological tools. The coin created by overstriking must obviously have been manufactured later than the coin on which it is struck, and a relative chronology for two coins can thus be established by a single piece. Often when a mint employed the technique it was indifferent to the nature of the undertype, and several different coinages might be employed for flan material: this can help refine chronologies or provide a clue to mint attribution.

Countermarks establish a chronological relationship between the coin and the countermark itself, and may sometimes be used to date each other, when they overlap on the same coin. In addition the use of identical countermarks on different series helps to establish the contemporary circulation of those series.

This summary shows how much of numismatic vocabulary has to do with to coin manufacture and the resulting product, and it reaches back to the beginnings of numismatic study. In the beginning that study was purely descriptive, and consisted of little more than catalogues of private collections, intended as much to celebrate the acumen of their owners as to broaden the base of numismatic knowledge. The turn of the nineteenth century, however, represents a watershed, and the beginning of the development of modern numismatic method.

3. Methodology

One of the most important elements of the work of Eckhel was his realization that serious study could not be based on a single collection.4 His Doctrina was far less parochial than earlier works, being based on examination of some hundreds of collections; from this time forward, although massive catalogues of single collections continued to be produced, it was impossible to ignore pieces housed elsewhere. One of Eckhel's contributions was his creation of a geographical system moving from west to east, based on Strabo's geography, that is still in use today for the arrangement of Greek coins. Eckhel's synthetic approach invited more detailed studies, and by the 1850s and 60s specialized monographs were being written on individual coin series. Some of the major periodicals that are still with us today had begun to flourish, aided by the advent of photography. Numismatics could now advance beyond simple cataloguing and develop as a proper discipline with its own methodology for determining who struck coins, where, and when; today we can even ask "why?" with a reasonable prospect of getting an answer.

Each numismatic problem has a set of tools that are appropriate to its solution, and the following attempt to categorize them is not intended to be prescriptive but rather to indicate the range of methodologies available, their potential, and their pitfalls.

3.1. Style

This element is placed first because, despite its elusiveness, it belongs first in the development of numismatic methodology, and because it gives the first means of classifying or dating a coin.5 Just as the term "fabric" refers to the general appearance of a coin, style refers to the general appearance of the types. Thus every coin has a style, which consists of the sum of its images and epigraphy and their usage as translated by the engraver to the surface of the dies and thence to the coin itself. Fabric itself can be a part of style.

"Style" as a tool has acquired a bad name mainly because of its association with aesthetic judgment, and the use of aesthetic preconceptions as a ground for attribution. One distinguishes good or bad style, fine or gross style, crude or skillful style, and on that basis attributes an issue to the place or period that one expects would produce such a style: early or late, Greek or barbarian, metropolitan or provincial. The difficulty of the approach is its apparent subjectivity, both in labelling the style and identifying its producer. For one author, fine-style coins might be the earliest, then degenerating into crude copies; another would see the crude coins as early efforts that gradually evolved toward sophistication. To be useful, style must avoid both aesthetic judgments and prconceptions.

Used rigorously and objectively, style is a useful tool for the numismatist, but the approach must be descriptive rather than judgmental. Rather than label a figure's hair as well or poorly rendered, one should describe precisely how it is rendered: as straight or wavy lines, ringlets or locks, small or large tufts. How are the eyes drawn? the mouth formed? How is the neck or bust truncated? When we speak of the style of a coin, it is not enough to look at the images only. Do the coins have borders? If so are they of dots or lines, or foliate or bead-and-reel? Here we may be speaking of the style of a mint as well as the style and skill of an engraver. Distinctions between open and closed P and R, barred or unbarred A, and the atriculation of curved letters such as C and S (as well as the distinction, if any, between C and G) are examples of features that my provide clues to attribution, and analogous differences exist for every language and script. The presence or absence of interpuncts should also be noted, though the standardization (even abbreviation) of coin legends in reference works sometimes makes this difficult.

A novice may not notice such distinctions, or make much of them; but once they have been pointed out, valid stylistic distinctions should be clear to any viewer regardless of aesthetic taste. But style by itself does not provide an attribution, except in comparison. Style can be characterized as "early" or "late" only when independent criteria apply: dates on the coins, hoard evidence, die study, or parallels from other mints. It is in fact possible, with care, to distinguish style that gradually evolves toward sophistication.6

It is more difficult to quantify than almost any other aspect of a coin. It may be good or bad, fine or gross, the work of a third-rate hack, a skilled or unskilled copyist, or the inspired creation of a Kimon. Even if the skill of the artist were known and measurable, it could fall short of contemporary standards, epitomize them, or surpass them. To be useful, analysis of style must avoid aesthetic judgments, or at least not employ them as chronological attributives.

Part of the difficulty lies in the artists themselves, and here it is instructive to read what Henry Adams has to say of Augustus St. Gaudens, arguably the greatest of modern sculptors and medallists, the designer of the twenty-dollar gold piece which is often called the best coin design of the last two centuries:

St. Gaudens himself was in Paris, putting on the work his usual interminable last touches, and listening to the usual contradictory suggestions of brother sculptors. Of all the American artists who gave to American art whatever life it breathed in the seventies, St. Gaudens was perhaps the most sympathetic, but certainly the most inarticulate. General Grant or Don Cameron had scarcely less instinct of rhetoric than he. All the others, -- the Hunts, the Richardsons, John LaFarge, Stanford White, -- were exuberant; only St. Gaudens could never discuss or dilate on an emotion, or suggest artistic arguments for giving to his work the forms that he felt.

(Education of Henry Adams, p. 1072, Library of America edition)

If the artist himself could not say what he was trying to do, how can we?

What does seem granted is the following, as put by Harold Mattingly: "Differences on which a numbers of observers agree must clearly exist. They are there, even if some scholars fail to see them. They can be seen, when the eye is sufficiently trained." And this epitomizes the difficulty of style as a criterion: questions of likeness or unlikeness, and uncertainty of application, very often arise in situations where other evidence is equivocal or nonexistent. As a general rule, where there is some more concrete criterion that can be used to resolve a question, it should be exploited; where there is not, stylistic analysis must rest on as full as possible a gathering of numismatic evidence, a solid foundation in contemporary monuments and artefacts, and be tempered by the awareness that the criterion is an easy target for skeptics.

Some further cautions are in order. When we speak of the style of a coin, it is not enough to look at the images only. The term also embraces elements extraneous to the portrait or the principal type, and their treatment. For example, do the coins have borders? If so, are they of dots or lines, or decorative (e.g. wreath or bead-and-reel)? Here we are speaking of the style of a mint. Even such seemingly technical aspects as the die axis may be considered aspects of style.

Again, although transcription of the legend is a standard feature of coin descriptions, they are often noted more for their content than their form. Nonetheless, distinctions between open and closed P and R, barred and unbarred A, and the articulation of curved letters such as C and S (as well as the distinction, if any, between C and G) may provide clues to attribution. The presence or absence of interpuncts should always be noted as a possible clue, though the standardization (even abbreviation) of coin legends in reference works sometimes makes this difficult.

3.2. Dies

Each surviving coin preserves an impression of the dies used to produce it, however that impression has been modified by wear or damage over time. Thus it is, theoretically, possible to reconstruct all the matrices from which a given coinage was produced, to observe their deterioration, and to organize the whole body of a coinage in the relative order of its striking based on die replacement.7

Formulated in the abstract, die study sounds amazingly simple; but there is no disguising the fact that comparison of dies can be difficult and tedious. The raw material--the coins, reproduced photographically or in casts, must be gathered not only from collections worldwide, but from auction and sale catalogues, exhibition catalogues and the like; and often it is impossible to identify dies even after lengthy examination. The main obstacle in many coinages is the fact that most issues is that they are too large for die study; in others the surviving sample is so small that the number of dies approaches the number of specimens known. Still other coinages are not suitable candidates, for the technique would not resolve the questions being asked. But the rewards are great: two coins sharing one or both dies must share a common origin in time, or place, or both.

What makes die study workable is that dies are not mated with one another forever, nor do they have identical lifespans. When one die breaks or otherwise falls out of use, it is replaced by another. The history of dies and their combination may be represented graphically. For any single coin, the relationship might be described as A-a where capital letters represent the obverse and lower-case the reverse. If the reverse wore out and was replaced, then we would have a relationship among the three dies (one obverse and two reverses) that might be rendered A-a, A-b. Now let us say A breaks, and a new obverse (B) is substituted: the sequence becomes A-a, A-b, B-b. If this last pair of dies is discarded simultaneously or almost simultaneously, C and c will come into use, and we may arbitrarily extend the series C-c, D-d, D-e, D-f, E-f, E-g, and so on: [IMAGE TO COME]

By itself, this gives us no more than a diagrammatic representation of the combinations headed by A-B and D-E, and it does nothing to place C-c anywhere in relation to them. Moreover, the entire sequence can be "flipped"--B could precede A, and E could precede D. Fortunately there is a useful means of establishing the sequence. This results from the fact that even when dies develop stress marks or breaks, they are not immediately discarded; only when a die begins to produce intolerably defective coins is it withdrawn or recut. By observing advancing deterioration of the same die, and noting its linkage with others, one can establish the order of introduction of the latter. A can be placed before B and D before E if either shows advancing wear or breakage in combination with a/b and d/e/f respectively. Still, in the illustration above, to place C in the middle and A-B before D-E, some criterion independent of the dies must be applied; this can come from style, from sequence markings of the dies, or from appearance in hoards.

Rarely are all of these lacking, but equally rarely are things quite as simple as this. It is seldom the case that a mint employed a single anvil with one-for-one substitution of obverses and reverses, at least for very long; at many mints, the "die box" was in use. A single die was fixed in an anvil with reverses cut for use in combination with it. When the unfixed die was removed at the end of a work period, it was put back into the "die box", and at the next work period it was a matter of indifference which of the reverses in the box was put into use. Thus a die might be in continuous use or not, and the state of the obverse(s) with which it was paired might show uneven progression or virtually none at all. It might in fact be paired with many obverses: a good illustration of the random double die box at work is the coinage of C. Piso Frugi.8 Considerations such as these complicate efforts to calculate the lifetime of a reverse in relation to the obverse.

This is, in brief, the method of establishing secure relative chronologies through dies; then begins the search for absolute clues outside the die sequence itself. Sometimes it is possible to establish a firm beginning or end of a series on historical grounds: ideally a die bearing a date in some form might begin or end a series, or both; or a reverse die used in an undated series might also occur paired with a dated one.

In modern times more basic information -- though more difficult to calculate -- has come to be appreciated: that is the size of an issue of coinage. We know that the absolute number of coins produced in a given series is a number probably irrecoverable when mint records have been lost; and since coins began to be lost, discarded or destroyed almost from the moment they left the mint, the surviving record is woefully imperfect. Simple counting of coins is no solution, for factors beyond our knowledge govern their survival rate. But of dies we have, in theory, a better record, for only one coin of the thousands that a die might produce needs to survive to document that die. We might, then simply count the dies to establish a relative size of an issue, to which others like it could then be compared.

The number of coins that could be produced by a die or dies is a subject of continuing speculation,9 and in the history of coinage there are doubtless thousands or even tens of thousands of dies which have vanished from the record because they broke on the first strike; similarly there are many which produced far more than the average number of coins. But it is still fair to suppose that where other elements -- machinery, alloy, weight, fabric, working conditions -- remain unchanged, the number of dies represented in the surviving sample provides an index to the original number actually used. The utility of this information depends upon having a reasonably complete record of dies, and formulae which will be mentioned later can be used to test exactly how complete our record is. But it is safe to say that a coinage produced from ten dies is likely to have been about five times as large as one produced from two, provided that a) there are no artificial interruptions in normal minting activity (changes of type or legend, or end of a magistracy); b) nothing (shortage of engravers, for example) arbitrarily extended die life; c) our modern sample has not been compromised by recall, recoinage, or the like in antiquity and d) the samples are sufficiently large to be compared. In fact the list of coinages not affected by one of these caveats is depressingly short.10

3.3. Hoards

The evidence of hoards, like that of dies, was almost unexploited until this century, even though they have been coming out of the ground since antiquity. The British term "treasure trove" effectively conveys the sense of what a hoard is: a store of wealth concealed with intent of recovery but which, for reasons not usually known to us, was not recovered until modern times.11

Through most of the history of money there has been no institutional provision for the thrifty saver. Simply carrying one's wealth on one's person has usually been regarded as imprudent, yet all but the wealthy and the merchant classes have, until very recent times, been excluded from the credit system and depository banks. The general response has been hoarding, usually through deposit in the ground.

The hoarding instinct (which is, after all, documented for some animals) will have been reinforced by the perception of impending danger. Often the perception was justified by the event, with the consequence that there is a slight tendency for deposits (or rather, unrecovered deposits) to cluster in times of political, social, or economic unrest. Historically, the clearing of land for agriculture -- plowing -- accounts for most modern recoveries; in the nineteenth and twentieth centuries (the only ones for which there is even a semblance of systematic documentation), urban excavation (for electrical and telephone lines and subways), as well as illicit digging, have also played a role. The advent of the metal detector, depending on one's point of view, has been either a godsend or a disaster.

The utility of hoards as a dating tool is manifest, for obviously they must have been put down later than the latest coin they include. They do have limitations, however, since they are almost invariably private stores of wealth whose manner of accumulation can barely be guessed at. The terms "savings hoard" and "currency hoard" are nonetheless bandied about as if hoards could be so classified, but they are useful only insofar as they illustrate possible means by which hoards might have been assembled.

The savings hoard, in theory, represents an accumulation of money over time. In a modern savings account, you take a negotiable instrument--a bill, a check, a coin--and deposit it in a bank. When you go to reclaim your money, it is certain that you will never see the original check, and most unlikely that you will be given back the identical bill or coin. If, however, you were accumulating your hoard at home, upon recovery you (or a finder hundreds of years later) would have to deal with the same physical objects you put away. The savings hoard would not reflect the currency of any specific moment, nor would the wear of the objects in it correspond to their age, since as soon as they were put away they would stop wearing.

The currency hoard represents a sum of money that reflects consolidation and burial of assets at a given moment--that is to say, it represents a cross-section, however small or unrepresentative, of one kind of money in circulation at the moment of its closure. It would not, of course, consist of coin today, but it would almost certainly favor more recent issues, as in fact our modern currency does.

What is controlled in neither of these situations is what Miss Thompson called "subtle falsification"--that is, withdrawal from the hoard either as it was accumulated or in one swoop, before its deposit.12 In the case of the savings hoard, one would expect gaps of unpredictable character, as money was withdrawn to meet contingencies; and there would be occasional infusions, as, for example in the later Roman empire when soldiers were paid celebratory distributions on imperial anniversaries. In the attack on the currency hoard, what would probably suffer would be the most recent issues. The ideal currency and savings hoards would also show characteristic patterns of wear: the savings hoard would have no clear internal pattern, but would reflect the condition of the coins at the moment of their removal from circulation. The currency hoard would reflect the coinage was in circulation at the moment of assemblage, so that the most recent should be the finest. But the number of exceptions is great, and the application in particular cases is dangerous. To put it as pessimistically as Michael Crawford does, "the attempt to reconstruct a hoard's history prior to its deposit and loss is almost invariably futile."

There is only one sort of hoard whose classification might be regarded as certain, and that is the mint hoard or "bank" hoard. This sort of hoard includes large numbers of coins, usually of identical types, which can be supposed to have been buried soon after issue from the mint with little no admixture of circulating coin.

Sometimes--Asyut, Dorchester, Lohe--a single hoard is of surpassing interest or importance.13 But their real utility rests in the assembly and comparison of hoards containing common bodies of material. For example, when a large number of hoards from a relatively constricted period is available, they can be invaluable for establishing chronologies. A sequence of hoards will reveal a relative order of appearance of issues: as Crawford has put it, "Of two hoards with some issues in common, that which is later will contain issues which do not occur in the other hoard and which are less worn [sc. than other coins in the hoard]. A relative order of issues follows automatically." The principle can be extended as far as the number of hoards will permit, and the resulting chronology can complement or correct information gleaned from style or dies, or even stand on its own.

Where it is abundant, the evidence of hoards is second only to that of die links in importance, with the caveat that it is even more susceptible to adulteration in modern times than to honest distortion in antiquity. Since finds from strictly controlled contexts are infrequent, there is almost always some doubt about the integrity of lots, even when they seem intrinsically plausible. A find outside a controlled excavation will almost always find its way to a dealer. He will always have the opportunity, and almost always the inclination, to withhold rare issues in any condition, and extremely fresh coins whether rare or not, because of the commercial premium such pieces demand. For the one case, this is unfortunate because the documentation of sparse issues is by definition poor: only in the last dozen years, for example, has the first of the famous EID MAR denarii (whose antiquity has sometimes been doubted) been recorded in a secure ancient context; in the second case, removal of an extremely fine coin may take with it the firm post quem we would like. Equally, the dealer may have occasion to purge his stock by tossing in extraneous material to fill out a lot. These are evils that have to be abided, since even tainted hoards frequently provide valuable new raw material for the study of under-documented series, and occasionally even fill gaping holes in our knowledge.

3.4. Archaeological Finds

Hoards can provide us with the individual's (or, occasionally, the state's) store of wealth, and generally hoards can be placed in time with more or less certainty. archaeological finds are another matter, since they represent individual coins that were lost casually without intent of recovery, and there is no sound way, except in sealed deposits dateable on other grounds, to determine the terminus ante quem of loss. A corollary to this is that site-finds tend to reflect the petty currency of the day: since hoards represent money intended for recovery, they consist of high-value coins; archaeological finds represent, in the main, coins whose recovery was a matter of indifference.14

Coins are invariably among the most numerous artefacts found in excavation contexts, and almost always the most precisely dateable ones. While this draws the archaeologist's attention, he is unlikely to be much further interested in the numismatic significance of the object, and the record of sites from which the coins have been published in usable detail is disgraceful. Here we may make an unbiased exception for American teams, whose publications have included model studies of Athens, Corinth, Troy, Sardis, Dura, Antioch, and more recently Carthage.

In archaeological finds, what is lost in terms of chronological control is regained in spatial control. For the numismatist, an exact locus is seldom the objective, and in fact association by locus is often pressed too hard, by both numismatists and archaeologists, given the disturbance of rigid stratification in modern times. For the numismatist the larger picture is important: what circulated at a site, and in what quantities? Excavations themselves confirm that their bulk consists of local issues; this can be important in dealing with coins whose mintage is unknown, and on occasion the exceptions can be taken to demonstrate lines of commercial contact. Another general principle is that in any system of multiple mints, the mints will be represented in direct relationship to their distance from the site. The late Byzantine finds from Athens have been subjected to new scrutiny in recent years with a view toward a better definition of the output of Thessalonica.

The systematic investigation of a site can also tell a great deal about how its inhabitants perceived and used money, and about the mint that provided it for them. Ancient Carthage provides a good example. The site, which had never been investigated for the Byzantine period, revealed a phenomenon that had not been noticed elsewhere: a strong preference for the nummus, a tiny copper coin easy to lose, difficult to recover and of negligible value, to the exclusion of virtually all larger denominations.

These came up by the hundreds at Carthage, although they are all but absent from other sites. The denomination had been introduced only in the early fifth century, and its minting at Carthage continued through the Vandal occupation of 428-532. When the Vandals were driven out by Belisarius, a denomination that had developed independently in the Byzantine system (and had almost been phased out by Anastasius I) began to be struck under imperial auspices even as the Vandal coins remained in circulation. The vitality of the coin continued there into the seventh century, long after it had fallen into disuse elsewhere, for reasons that can only be guessed at.

Secondly, the Carthage finds did a great deal to eliminate a strongly anti-Western bias in Byzantine mint studies. Simply by making available so many coins (Dumbarton Oaks, one of the world's largest Byzantine collections, has only 69 coins of Constans II, far fewer than were recovered in the Michigan digs alone) the excavations helped to rewrite the history of the mint and of coin use at the site.

Sometimes numismatics and archaeology work hand in hand. The most dramatic example is perhaps Morgantina, a site in Sicily that was excavated by Princeton for several seasons beginning in 1955, and is still under investigation today. Its remains pointed to a vaguely third century date, but the place had no name -- it was known as Serra Orlando, the modern name, until association with reports in Livy which seemed to correlate with two Roman destructions of Morgantina, a town that had admitted Hannibalic garrisons, in 214 and 211 B.C. These dates were pretty securely established by the coins themselves, which ran right through Hieronymus (215-214 B.C.) and which were consistent with other finds of ceramics, glass, and statuary. All the coins, that is, except for several that belonged to the earliest Roman denarial issues, which on the chronology of that day belonged fully thirty years later. As Greek coins had dated the site, however, Morgantina itself has come to date the introduction of the denarius, especially as subsequent investigation had demonstrated the tightly die-linked character of the Roman material, thus reinforcing the impression of its early place in the denarius series--and nothing further has come to light which would suggest alternative dates for the two destruction levels of the city.15

3.5. Documents

The most important documents for numismatists are those generated in the creation and the functioning of a mint. Since mints are extensions of governmental apparatus, they have their own bureaucracies and their own paper work; but since they literally have a "license to print money", that work must be carefully controlled. The coins themselves prove that this was so: coins are marked with magistrates' and issue marks, and in the Roman world with types which indicate the issuer and his authority. Presumably this was intended to control flow and smelting of bullion, protect against adulteration and peculation, and in the worst case to follow a paper trail to the individual responsible. Potentially the comparison of documents with coins can check die survival, illustrate the internal organization of the mint from intake of bullion to dissemination of coin, and provide the economic historian with that most valuable piece of information, the amount of money generated. Unfortunately, virtually all the official documents from antiquity have been lost.16 For later periods, mint records often survive, and valuable information is also contained in law codes, governmental decrees, trial records and records of private transactions.

Documents of private utterance--papyri, merchants' exchange books, receipts, and the like--can be of great value for showing what was being traded in a given time and place; they also fulfill their original purpose in stating the relative values of currencies. Thus even where this cannot be determined through finds and analyses, it can sometimes be reconstructed from the documents.

Another kind of documentary evidence is provided by inscriptions, military diplomas, and the like: prosopographical information about those individuals who performed some function in the mint. Since these people were generally no more than low-level bureaucrats (and in some cases the production personnel were slaves), history has not preserved a great deal of information about them; but an individual's career, often detailed in epitaphs, may often be placed in the context of the history of a mint.

3.6. Literature

The literary and historical tradition is of a value which has to be estimated on a case-by-case basis. For most of history, those who wrote it down did not understand more than the bare rudiments of economic and exchange theory (Diocletian's Maximal Edict, given a millennium's background of money and prices, was foredoomed). On the other hand, coins and money were taken for granted, so that it is only the exceptional coin or event that merited mention. It is mere accident that we have any idea where the mint of Rome was located, for example; the first use of silver coin is probably misdated; references to denominations are often silently "updated" to use terms current in the writer's day, and in general ancient historians wrote from a biased point of view that suggested retrojection of innovations and a national proprietariness about them. Such factors render Pliny's account of Roman coinage in Natural History book 33 -- the only fairly connected one we have -- a tissue of error and misunderstanding. Mentions of coins are perhaps on firmer ground when events such as the infamous "revolt of the moneyers" had significant social or political implications, but in virtually every case such writings as survive to us were produced after a considerable lapse of time. Chroniclers also frequently display bias in reporting on past coinage changes, which are often characterized as attempts to steal from the populace, whatever their actual intent may have been. The literary sources can hardly ever be employed as a starting point of inquiry, except in the later medieval and modern periods.

3.7. Metrology

For purposes of this definition, metrology may be divided into two categories: weight and content. The weight of the individual coin may be helpful in determining its authenticity or its attribution: a seriously under- or over-weight coin should arouse suspicion. To make either determination, however, one must know the standard to which it is struck; put another way, the tabulation of large numbers of like coins can determine the standard to which they were struck.

Mean, median, and mode are all useful measures for this purpose. The mean weight is particularly useful for baser coins, where the point was not necessarily to strike all coins to a precise standard, but merely to produce a certain number per weight unit, e.g. a denarius of 45 to the pound. The mean can tell us how many, and the standard deviation how closely the standard was adhered to; but both methods give undue weight to anomalous coins. By far the most useful measurement is the mode; this will reveal anomalies at once. Usually numismatists employ frequency tables, which show how many coins cluster around a given weight in a range defined by the coinage itself. This will not only refine the precision of the standard, but will reveal whether or not there was an alteration of standard within an issue. A truly regular coinage will show only a single mode; one in which there were variations with time or place might show two or more modes. All these methods, obviously, depend on the assemblage of as many weights as possible.

The analysis of what makes up a coin is an area that has only yielded usable results in recent times and one that is still in a state of flux and evaluation. Until the 1940s it was necessary to destroy a coin in order to capture the detailed information it could provide regarding alloys and fineness; this naturally discouraged large-scale analysis of the kind necessary to yield meaningful results, particularly for precious-metal coins. Since then, techniques involving spectroscopy or irradiation and which do minimal damage, if any, have become progressively cheaper, and this has encouraged further investigation. Sophisticated methods are capable of detecting trace elements in minute quantities, and this holds out the hope of identifying the sources of metals used in certain coinages; in vast series that must have consisted heavily of recoined metal, it is important to establish the relative silver or gold content of successive issues by analyzing as many specimens as possible. Both approaches have been tried with more or less success, and both represent a great advance over the laborious and time-consuming technique of specific gravity, which is wholly non-destructive and usually duplicable, but useful only for binary alloys and even then mainly those including gold.

There is no one "recommended" method; the method of choice depends upon the kind of result sought, the material involved, and the precision necessary.17

Problems remain with sampling techniques (both from the coin population and from the individual coin), and with the comparability of results achieved by different methods. Nonetheless it is doubtful whether any future mint study, for example, can rightly omit analysis as one of its features, and the day may not be far off when "AV", "AR", and "AE" are replaced by more scientific descriptions of coin content. For most individuals and institutions, the greatest barrier is the expense. (The British Museum has its own laboratory, which can perform analyses on request, and laboratories at Oxford were used to analyze virtually all the silver coins in the Ashmolean Museum's collection; in contrast, such ANS coins as have been analyzed have been done by individuals with their own access to laboratories, with risk to the security of the objects. We still have no ready means of regular analysis.)

3.8. Statistics

The use of statistics is certainly not exclusive to numismatists, but the science has had practical applications in our context only since the Second World War. Its major application has been in the area of calculating mint output.18

As indicated above, the simple counting of known specimens is a poor guide to the original volume of an issue. This is so for a variety of reasons. If we were to begin from museum collections-they do, after all, represent our most permanent repositories of coins-we would quickly find that the population is distorted by modern preference and selection. The bias is almost always in favor of issues that were originally extremely rare, or series with a great deal of variety. The curator (or for that matter the collector on whose beneficence curators have come to depend) is usually not inclined to celebrate last year's acquisition of the 100th duplicate denarius of Trajan, or his 2500th tornesello--nor even, in most circumstances, will he seek out well-known varieties which only fill gaps in his own collection. Money is too scarce, and especially in a universalist collection such as this one we cannot afford the luxury of indulging our own preferences.

Even hoards and excavations can be misleading. Quite apart from the problem of modern contamination discussed above, we have no way of knowing what factors govern the deposit or loss of coins, or what lost coins have been recovered since antiquity.

A check against this may be provided by population sampling. Working from the principle that the number of dies used to produce an issue provides an index to its size, we could in theory count all dies for all issues; but life is short, the work is unattractive, and the picture is altered almost daily by the appearance of heretofore unknown specimens, whether fresh out of the ground or back in "circulation" as the result of a collection's dispersal. How do we know when to stop counting?

It stands to reason that as the number of coins in a sample increases, the ratio of coins to dies will start to increase from its beginning at 1:1, and further that the relative rate of increase will give a key to the size of the original sample. (That is, you are closer to having a complete sample of dies if you find 25 different obverses in the first 100 coins than if you find 50 or 90.) The point at which you can stop counting-and calculating-is when statistical formulae tell you that the predicted range of x, where x is the unknown original number of dies used, has ceased to increase.

Work on statistical formulae has been in progress since the 1960s; important names you in this context include C. S. S. Lyon, Giles Carter, and Ludovico Brunetti. Warren Esty has contributed an annotated survey of formulae.19 Any of these can estimate the predicted number of dies, given the size of sample and the number of dies recorded; and while the range of error is very high as the ratio of coins:dies approaches 1:1, it is very low when it approaches 3:1 on almost all methods, and can be used for coinages that fall in between. In a study of Hadrian's cistophori published some years ago Lyon's formula was applied to a sample of 463 coins which represented 309 obverses and 410 reverses, or roughly 1.5:1 for obverses and 1.1:1 for the reverses. The value of x for the obverses could be calculated as likely to fall between 477 and 601 obverses in 90 percent of cases, with the likeliest figure in that range being 537. For the reverses the range was, naturally, much higher, 1597 to 2436 with the likeliest being 1852. These ranges seem uselessly broad, but they compared well with results achieved by similar methods for the cistophoric coinage of Augustus; thus it was possible to say that the two coinages were comparable in scale. When methods can be checked against more completely-documented coinages, such as that of Syracuse (E. Boehringer) or the Lincoln mint (Mossop) they bear out the validity of the formulae.

All this is a slow business, and students have tried to recognize reality and escape the tedium of studying the dies of one series after another by comparing related issues, one of which has been treated in detail and the other not. Their relative frequency in hoards selected for representativeness can be compared, and a hypothetical number of dies calculated for the uncounted issue. In its combination of two methods which already have their own built-in (and rather large) tolerances for error, this simply multiplies the error factor further, and the results achieved have been attacked; but it represents a creative stopgap measure until more series can be studied in full.20

1. The American Numismatic Society was itself founded in 1858, at which time it was known as the American Numismatic and Archaeological Society.
2. The classic source for all numismatic vocabulary is F. von Schrötter, Wörterbuch der Münzkunde (Berlin-Leipzig, 1930); in English there are A. R. Frey, Dictionary of Numismatic Names (New York, 1917) (reprint editions include a multilingual glossary prepared by Mark Salton), and R. G. Doty, The Macmillan Encyclopedic Dictionary of Numismatics (New York, 1982).
3. The issue of copper alloys is particularly relevant to the study of the non-precious metal coins of the Roman empire issued following the reforms of the Emperor Augustus in the late first century BC. Lower denomination coins, including Asses and Quadrantes, were issued in pure copper, whereas the Sestertius and Dupondius were issued in orichalcum, the name given by numismatists to the alloy of copper and zinc. In modern parlance, this alloy is called brass. Bronze, when used precisely, refers to an alloy of copper and tin.
4. The best discussion of technique as an outgrowth of manufacturing methods for Greek coins is that of C.M. Kraay, Archaic and Classical Greek Coins (Berkeley and London, 1975) pp. 1-19.
5. For a remarkable treatment of style in Greek coinage, beginning from the premise that "Greek coins are the grammar of Greek art," see B. V. Head, Historia Numorum, Second Edition (London, 1911) pp. lxi-lxiv. C. H. V. Sutherland, "What is Meant by `Style' in Coinage," American Numismatic Society Museum Notes 4 (1950) pp. 1-12, comments on the inadequacy of Head's approach, and gives some insight into the history of the term and the proper application of the criterion. See also H. A. Cahn, "Analyse et interprétation du style," Congrès international de numismatique Paris 6-11 juillet 1953 II. Actes (Paris, 1953) pp. 37-42.
6. Compare the remarks of Harold Mattingly (Roman Coins, Second Edition [London, 1960] p. 42): "If two or three scholars readily agree on what they see, they obviously are seeing something that is really there, even if other scholars fail to see it;" and "Style by itself can hardly prove mintage, widely different styles might exist together in the same mint. But, when differences of fabric reinforce differences of style, the case can become much stronger."
7. With reference to die study see the concise discussion of L. Mildenberg, The Coinage of the Bar-Kochba War (Aarau, 1984) pp. 18-20.
8. C. A. Hersh, "A Study of the Coinage of the Moneyer C. Calpurnius Piso L. f. Frugi," Numismatic Chronicle 7 16 (1976) pp. 7-63.
9. There have been some experiments that attempt to replicate ancient minting conditions, notably those of Sellwood and Beer; and other attempts to match known dies with documentary evidence to achieve a coin-per-die ratio; but the (often unknown) physical nature of the dies and variation in minting procedures caution against the facile extrapolation of such data from one series to another.
10. The methodology of die study has been extended and its theory refined in several ways.
  1. Punches. Some mints--most of them mediaeval and modern, but there are some arguable ancient cases--employed punches to speed the manufacture of dies. These punches could include letters or parts of letters, decorative elements, or even busts in silhouette. Like whole dies, punches can be linked and their relationship charted. A punch link has many of the same implications that a die link does.
  2. Hubs. In modern times, hubs have carried the process of die manufacture back a step further: whole dies are made from masters cut in relief and used to manufacture an intaglio image in a die; this explains why modern coins all look alike. The theory of hubbing has been extended to pre-modern series as well, since the economy of manufacture is obvious; but in no case has it been demonstrated, and in no case has it been seriously argued that dies were not retouched afterwards. Thus the question, while interesting for ancient coinage, seems not to impair the validity of die study.
  3. Recut dies. Since dies were often the masterworks of their engravers, and presumably expensive to produce, they were often recut or retouched, either to correct flaws or to amend dates. Scholars have often designated recut dies with superscript or subscript letters to designate different "states" of dies or phases of their use. When discriminating dies it is important to consider that what appears to be a different die might be a reworked version of an earlier one.
11. For a general discussion, see Casey (below, n. 10) pp. 51-67. For a succinct treatment of the method for chronological purposes, and then its application, see M. H. Crawford, Roman Republican Coin Hoards (RNS Special Publication 4, London, 1969), esp. p. 1 (better than the treatment in the same author's Roman Republican Coinage).
12. See Margaret Thompson, "Athens Again," Numismatic Chronicle 7 2 (1962) pp. 301-333. The excellent discussion of problems relating to hoard analysis on pp. 308-310 has value independent of her defense of the now-abandoned chronology for the New Style silver coinage of Athens.
13. These three hoards are selected as being of great importance in the Greek, Roman, and early modern fields. The Asyut hoard established synchronisms among late archaic and classical Greek silver coins; Dorchester revealed, through the distribution of coin types, the organization of the mint in the mid-third century A.D.; and the Lohe hoard showed that distribution of coins in hoards could reflect very precisely actual numbers put into circulation. See M Price and N. Waggoner, Archaic Greek Coinage. The Asyut Hoard (London, 1975); H. Mattingly, "The great Dorchester hoard of 1936," Numismatic Chronicle 5 19 (1939) pp. 21-61; and B. Thordeman, "The Lohe Hoard: a contribution to the methodology of numismatics," Numismatic Chronicle 6 18 (1948) pp. 188-204.
14. P. J. Casey, Understanding Ancient Coins: An Introduction for Archaeologists (Norman and London, 1986); P. J. Casey and R. Reece, Coins and the Archaeologist (2nd revised edition, London, 1988) collects exemplary papers relating to the Roman world.
15. See T. V. Buttrey, "The Morgantina Excavations and the Date of the Roman Denarius," Congresso Internazionale di Numismatica Roma 1961 II.Atti (Rome, 1965), pp. 261-267.
16. Some exceptions from the Greek world are the Athenian currency decree and the Currency Law of 375/4; from the Roman world, the Trajanic inscriptions relating to the mint and the relatively recent inscription from Aphrodisias reflecting Diocletian's retariffing of his own reformed copper.
17. The most useful compendium of studies, by a variety of methods, remains E. T. Hall and D. M. Metcalf, eds., Methods of Chemical and Metallurgical Analysis of Ancient Coinage (Royal Numismatic Society Special Publication 4, London, 1970). The volume contains a full bibliography of earlier analyses. An irregular series, Metallurgy in Numismatics, is now edited by Metcalf.
18. A useful, though somewhat uneven, treatment of statistics and computers, as well as various methods of metal analysis, can be found in vol. II of M. Price et al., eds., A Survey of Numismatic Research 1978-1984 (London, 1986) pp. 961-1076. See also C. Carcassone and T. Hackens, eds., Statistique et numismatique. Table ronde organisée par le Centre de Mathematique Sociale de l'École des Hautes Études en Sciences Sociales de Paris et le Seminaire de Numismatique M. Hoc de l'Université Catholique de Louvain. Paris, 17-19 septembre 1979 (PACT 5, Strasbourg, 1981). An excellent introduction to statistics, in comprehensible language, is provided by R. D. Drennan, Statistics for Archaeologists. A Commonsense Approach (New York, 1996).
19. W. W. Esty, "Estimation of the Size of a Coinage: A Survey and Comparison of Methods," Numismatic Chronicle 146 (1986) pp. 185-215.
20. The whole question has become very controversial. See in particular T. V. Buttrey, "Calculating ancient coin production: facts and fantasies," Numismatic Chronicle 153 (1993) pp. 335-351; and "Calculating ancient coin production II: why it cannot be done," Numismatic Chronicle 154 (1994) pp. 341-352. See in response F. De Callataÿ, "Calculating ancient coin production: seeking a balance," Numismatic Chronicle 155 (1995) pp. 289-311.

The Staff of the American Numismatic Society. Date:
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