Achaeometrical Research in Hungary II., 1988
ANCIENT TECHNOLOGY - László BARTOSIEWICZ: A quantitative assesment of red deer antler as raw material
proportions change along with increasing size, the decimal logarithms of the variables available for study provided the linear regression equations summarised in Table 3. Table 3 Parameters of allometric equations expressing the relative growth of antler parts (independent variable: antler beam length) Variable Coefficient of determination Integration coefficient Allometric coefficient eye tine length 1.000 0.818 0.810 bez tine length 0.876 0.624 0.858 trez length 0.980 2.582 0.557 burr circumference 0.992 1.169 0.660 lower beam circumference 0.990 0.668 0.663 upper beam circumference 0.986 0.401 0.764 number of points in crown 0.984 0.069 0.848 antler weight 0.988 0.017 1.170 Of the parameters listed in Table 3, coefficients of determination (i. e. squared coefficients of correlation) show that the large number of cases in the reference sample guarantee the statistical significance (P<0.00J) of relationships established here. They express the biological fact that correlations between lateral beam length and other metric traits of the antler are by definition high (HABERMEHL 1985: 35, Tabelle 3). Coefficients of integration show the intersection between the regression line and the "y" axis, representing measurements chosen as dependent variables. More importantly from the viewpoint of practical interpretation, allometric coefficients correspond to the slope of the regression line. They express the different rates of relative growth by which each variable follows the longitudinal growth of antler beam. Allometric coefficients equalling 1 would be indicative of isometry. Isometry means that both studied measurements increase with the same absolute intensity. As is shown by the results in Table 3, however, all studied antler dimensions grow more slowly than the independent variable, lateral beam length. The only exception, antler weight, naturally increases progressively relative to antler length. Its allometric coefficient, however, is not as intensive as might be predicted on the basis of the dimensional difference between weight and length. In principle, weight grows isometrically with volume, but as a function of a single dimensional, linear trait such as beam length it could result in an allometric coefficient as great as 3 {Volume = length 3 ). The 1.170 value obtained for antler weight in Table 3 reflects the slender structure of antler, in which longitudinal growth unquestionably dominates. Tine lengths as well as circumferences of the antler grow more slowly than beam length. The relative growths of more proximally located eye and bez tines (0.810 and 0.858) are more intensive than that of the trez tine (0.557). On the other hand, the relative thickening of the antler beam, expressed by the allometric coefficients of the three circumferences studied, is less intensive in the antler's proximal portion (0.660 and 0.663) than in the upper section of the beam (0.764). The relative increase in the number of points in the antler's crown is comparable to the allometric growths of eye tine and bez tine lengths. These relationships are summarised in Figure 1. 220
