Prolegomena to Late Cypriot Weight Metrology

Abstract

The systems of weight measurement used in prehistoric Cyprus have never been studied comprehensively. The group of artifacts here examined consists of several dozen Late Bronze Age stone balance weights from Enkomi, Ayia Irini, Idalion and the Cape Gelidonya shipwreck which share a characteristic sphendonoid (i.e., sling bullet) shape. It is shown, using simple statistical procedures, that one system, decimal in structure, is represented in these objects. This system was used throughout the eastern Mediterranean area during the late second millennium B.C., and appears to have been of Egyptian origin. In a monumental study that appeared nearly sixty years ago, Petrie presented a corpus of several thousand stone and metal balance weights from archaeological sites throughout the ancient eastern Mediterranean.' His was the first attempt to synthesize the empirical evidence then available into a coherent interpretation of the systems of mensuration in use from predynastic times in Egypt to the Roman Imperial period. His approach differed from that of earlier students of ancient metrology in its reliance on the balance weights themselves rather than on contemporary historical testimonia to indicate absolute masses of, and relationships among, the many weight standards in use in the ancient world. Petrie presented a neat and superficially cogent, if somewhat simplified, picture of the economic relations among peoples in this area in antiquity. He calculated precise upper and lower limits for each of the standard units of mass used in this very large region, and argued that-as if by international agreement-the major local units were fixed relative to one another to such a degree of precision that there was virtually no overlap in absolute mass. Further analysis of Petrie's raw data reveals that the masses of the international standards were quite fluid through time, and that the overall picture of economic relationships was extraordinarily complex. Dozens of names of ancient units of weight survive in historical sources; moreover, ancient balance weights themselves occasionally bear inscriptions which name their units and proclaim their denominations. Such clues are of primary importance in recovering ancient metrical systems, but are, of course, restricted to literate cultures of the historical period. The next best source for the recovery of a system comes from simple markings (e.g., strokes, dots or circles) engraved into the weights. With even a small sample, it is often possible to derive a relative scale from individual pieces, even though the names of the standard units are unknown to us (this is particularly helpful for the earlier prehistoric periods2). The most difficult systems to recover are those whose balance weights typically bear no markings whatever; in such cases, the credibility of attributions of individual pieces in a system must rest on the incidence of statistically significant clusters of absolute masses and on simple and practical ratios in mass among the pieces. It follows that the larger the sample, the greater is the likelihood that a system can be recovered, assuming that the only balance weights used in the metrological analysis are those which are in an excellent state of preservation and seem to reflect accurately their originally intended masses. I have elsewhere presented a detailed metrological analysis of a remarkably cohesive group of balance weights from Aegean Middle and Late Bronze Age sites.3 This article, which follows as much as possible the principles developed for that work, presents and elucidates the metrical and cognitive significance of a much more problematic group of balance weights from four Late Bronze Age sites in the eastern Mediterranean. The aim is to recover both the absolute mass on which the system was based and the mathematical design which inspired the system and governed its use. The sample considered here is admittedly small, and has been deliberately limited, but the * I would like to thank my colleagues Alice Hausman (Department of Archaeology) and Stephen Meeks (Department of Mathematics) at Boston University for reading versions of this article and improving it with their suggestions. Responsibility for errors, computational or other, is solely mine. 'W.M. Flinders Petrie, Ancient Weights and Measures (London 1926). Petrie had had a long-term interest in metrology, empirical as well as theoretical (see also his Inductive Metrology [London 1877]). Noteworthy earlier studies in ancient metrology include F. Hultsch, Griechische und ramische Metrologie (Berlin 1882) and Die Gewichte des Alterthums (Leipzig 1898); RE Suppl. 3 (1918) 587-654 s.v. Gewichte (C. Lehmann-Haupt); and O. Viedebantt, Antike Gewichtsnormen und Miinzfiisse (Berlin 1923). 2 On this see, e.g., K. Petruso, Marks on Some Minoan Balance Weights and their Interpretation, Kadmos 17 (1978) 26-42. 3 K. Petruso, Systems of Weight in the Bronze Age Aegean (Diss. Indiana University 1978). Revised version forthcoming as a volume of the Keos excavations final reports.