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3ª parte
The calendar-age ranges which correspond to the radiocarbon confidence limits are show in Table 3. These were determined from the high-precision curve of Stuiver and Pearson 5 based on dendrochronological dating. Method A (the intercept method) in revision 2.0 of the University of Washington Quaternay Isotope Laboratory Radiocarbon Calibration Program 15 was used. In this method, the error in the calibration curve is first incorporated into the radiocarbon error, thus widening the limits on the radiocarbon scale slightly; calendar ages are then found that correspond to these limits, without transforming the complete probability distribution of radiocarbon dates. No additional uncertainty has been added to take account of the short growth period of textile samples. There is little published guidance on this, although it has been suggested that 15 years should be added in quadrature to the overall uncertainty in the radiocarbon date for samples of growth period less than one year, such as linen. In general, such additional uncertainty would widen the 95% calendar limits by ~ 2 - 4 years at either end, except for sample 3 where the 9 cal BC limit would be changed to 34 cal BC.
The 95% limits for the shroud are also illustrated in Fig. 2, where it is apparent that the calibration of the radiocarbon date for sample 1 gives a double range. The correct transformation of probability distributions from the radiocarbon to the calendar scale is still subject to debate, there being two different methods of dealing with multiple intercepts. However, both methods agree that the major probability peak lies in the earlier of the two ranges, in the 68% range at the end of the thirteenth century. Sample 4 has a very narrow calendar range: this is due to the steep slope in the calibration curve at this point, and is an occasional instance of calibration reducing rather than increasing a confidence range. Sample 3 compares well with the date obtained by conventional radiocarbon dating; there is no evidence for a difference between the two results. The dates for samples 2 and 4 agree with the historical evidence, which places them in the eleventh to twelfth centuries and late thirteenth/early fourteenth centuries AD respectively.
The results, together with the statistical assessment of the data prepared in the British Museum, were forwarded to Professor Bray of the Istituto di Metrologia 'G. Colonetti', Turin, for his comments. He confirmed that the results of the three laboratories were mutually compatible, and that, on the evidence submitted, none of the mean results was questionable.
Conclusions
The results of radiocarbon measurements at Arizona, Oxford and Zurich yield a calibrated calendar age range with at least 95% confidence for the linen of the Shroud of Turin of AD 1260 - 1390 (rounded down/up to nearest 10 yr). These results therefore provide conclusive evidence that the linen of the Shroud of Turin is mediaeval.The results of radiocarbon measurements from the three laboratories on four textile samples, a total of twelve data sets, show that none of the measurements differs from its appropriate mean value by more than two standard deviations. The results for the three control samples agree well with previous radiocarbon measurements and/or historical dates.
We thank Cardinal Anastasio Ballestrero for allowing us access to the shroud, Professor L. Gonella for his help and support throughout the project and Professor A. Bray for commenting on our statistical assessment of the data. We also thank Miss E. Crowfoot, T. G. H. James, Dr J. Evin, M. Prevost-Macillacy, G. Vial, the Mayor of Saint-Maximin and the Egypt Exploration Society for assistance in obtaining the three known-age control samples. Oxford thank P. H. South (Precision Process (Textiles) Ltd, Derby) for examining and identifying the cotton found on the shroud sample; R. L. Otlet (Isotopes Measurement Laboratory, AERE, Harwell) for stable isotope ratio measurements on two samples; J. Henderson and the Department of Geology, Oxford Polytechnic for undertaking scanning electron microscopy, and SERC for the Special Research Grant which provided the primary support for the Radiocarbon Accelerator Unit. Zurich thank the Paul Scherrer Institut (PSI, CH-5234 Villigen) for technical and financial support. The AMS Programme at Arizona is partially supported by a grant from the NSF.
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