Establishing Weight Systems in Bronze Age Scandinavia
Sperber, Erik, Antiquity
A further statistical study of the weights of distinctive objects from the Scandinavian Bronze Age finds, again, a system of standardized units, and looks as far as Egypt for an identity of pattern.
Mats Malmer (1992) advocates the existence of a weight system in late Bronze Age Scandinavia where the weights would be bronze figurines, 'Goddesses of Wealth'. The golden arm rings (called oath rings by allusion to an Icelandic saga) would also constitute a system. These finds, 22 in all, are concentrated in Denmark and southern Sweden.
By plotting the present weight of these artefacts Malmer could visualize the weight system used and also establish the identity of the weight system of the 'Goddesses' with that of the golden oath rings by a common unit of about 107 g. Weights of 2/4, 3/4, 5/4 and 7/4 of the unit appear.
In his paper, Malmer also points to the Fardrup axes, which may have been used as standards of value, although using the 'common sense' method, he was not able to reveal the units of the systems.
Holm's index, a statistical method for revealing the modules of such unit systems in complex and fairly inaccurate samples of weights or other experimental data, was developed a few years ago by Holm (1987). His method, easily transformed for computer use, uses the analogy between a weight system where the weight pieces appear at regular intervals and a sine curve which moves from -1 to +1 likewise at regular intervals. A search for a module system can be made by letting a tentative unit weight vary and plotting the sum of deviations of the sinus curve from zero, here called 'Holm's index'. When the tentative unit weight coincides with the unit of the present set, a minimum of the index appears. If the weight set is accurate, the minimum is deep and sharp. For ancient sets, the minima are very often blunt. For a minimum found it is possible to ask: 'Is this a statistically significant "unit weight" of the set?' and also to give the significance of the answer.
There is never one single unit for a parameter: a millimetre, a metre or a kilometre are equivalent units of length, although only the metre is defined by independent external standards. For weight sets the same is true, but in archaeological work we usually have to confine ourselves to sets covering only a small range, mostly less than one order of magnitude.
Very important is the property of a set that when you have found a certain unit, 1/2, 1/3, 1/4 etc. of that same unit are also unit weights of the set. The index may show several minima which we may call 'harmonics' of a superior unit weight. The minimum corresponding to half the unit weight is the 1st harmonic, etc. From these minima a superior weight of the set can be found out and it may be possible to draw some conclusions from it. It is by no means necessary for the weight set to contain a real weight piece corresponding to the unit found or to any one of the minima.
Corrosion during thousands of years in the soil is a factor to be kept in mind. For bronze, the tin component on corrosion forms a film of insoluble tin dioxide near the original surface of the artefact, slowing down further corrosion. Copper oxides and verdigris often adhere well to the surface and dissolve only slowly in the ground water, provided it does not contain aggressive carbon dioxide. Further, our objects are heavy and compact in shape, which limits the relative surface of the artefact. The weight pieces may have kept their weight fairly well through the years, probably within a few per cent (Sperber 1991: 164). It was therefore decided not to try to apply any corrections to the weights given by Malmer.
The 'Goddesses of Wealth' and the golden
The following minima were obtained when Holm's index was applied to the 'Goddesses'
The only minimum of TABLE 1 that is statistically significant with a probability of around 98% is at 26 g. …