7.3 Trend surface analysis

The second type of visualisation evaluating the chronological model is based on the measured proportion of tin in artefacts made primarily of copper. Generally it is accepted that tin started to be used in copper metallurgy increasingly throughout the Early Bronze Age. For some time, the process went on in parallel with the declining production of the so-called arsenic bronze, but in the later EBA arsenic bronze gave way to tin-enriched alloys. Spectral analysis of chemical composition conducted on metal objects from Holešov in the 1970s produced only semi-quantitative results that lack the precision of more advanced analytical methods. No high values of tin presence were detected, as these are more common in artefacts of the Bronze Age proper (around 10% of tin in alloy). Small proportions (around 1–3%) of tin identified in Holešov are usually regarded as random admixtures indicating no deliberate intent (Págo 1985, 177; Bertemes 1989, 158-62; Muhly 1993). However, we will see that the spatial pattern of this attribute is relatively strong and therefore deserves more attention. Even a slightly increased tin ratio in the material may in fact indicate a change in raw materials used, new experiments in the technological process or simply mixing pure copper with higher-content tin bronze imported from other regions to produce new artefacts.

No metal objects were found with the Bell Beaker burials from Holešov. A total of 224 measurements have been taken on Early Bronze Age artefacts from 103 graves (Págo 1985). Only one Holešov grave containing copper or bronze items lacks any data on their metal composition. Original semi-quantitative classes of tin presence were transformed into an ordinal scale (values 1–5) that is more convenient for data processing. Then each grave could be assigned a 'mean' value, calculated from the particular measurements of its tin content. This result does not represent the true arithmetic mean of measured values since it stems from ordinal data, where distances between any two values cannot be measured. From a mathematical point of view this approach can provide only approximate results, but it is useful if we understand it as proxy data for the comparison and ordering of the larger spatial zones of the whole site area.

Despite the circumstances that can make the mean value misleading (such as a possible metal degradation, less precise analytical method, different kinds of alloys combined in one burial assemblage, tin proportion as a technological and not chronological factor), chronological spatial development can on a general level be revealed by means of trend analysis. It can be demonstrated that 'bronze' artefacts combined in one burial assemblage are not composed of alloys with widely differing tin proportions. Amounts of each assemblage tend to vary closely around the mean value, indicating some kind of meaningful structuring (Šmejda 2004, fig. 12).

Figure 12
Figure 12: A plan of Holešov cemetery showing the spatial trend of tin content in metal objects (Global Polynomial Interpolation method). Image credit: L. Šmejda.

The search for spatial patterning has been conducted with the help of trend surface analysis (Hodder and Orton 1976; Wheatley and Gillings 2002). The cubic variant (a third-order polynomial regression fitting) of this method has been applied to the data and the result clearly shows the propensity of the values to increase from north to south and also from the centre to periphery (Figure 12). The area typical for low tin amounts is in the same part of the site as the area rich in chipped stone. The values representing an average tin ratio are generally spreading southwards and eastwards, which correlates with the increase of absolute numbers of metal objects in these zones.

We have seen that the chronological progress from the north to the south-east is revealed also by the spatial trend analysis, which produced a polynomial surface derived from the proportion of tin in metal artefacts. The assumption that the ratio of tin to copper in the metal composition increased through the Early Bronze Age seems to be in accordance with other evidence (cultural determination of more characteristic finds, distribution of stone and metal objects).