As a ‘Stop Press!’ postscript to *The Keys to Avalon*, Blake and Lloyd refer to an article by Keith Nurse in *History Today* for August 1999, called ‘New dating for Wat’s Dyke’. They assume that it revolutionises our understanding of the date of the earthwork. It is based on a radiocarbon determination of the date of carbonised wood from a hearth excavated beneath the Dyke at Maes-y-Clawdd. I will start by giving the basic details of the date and then move on to its implications.

The date, as supplied by the radiocarbon laboratory of Queen’s University, Belfast on 7 July 1997 (sample number UB-4158), is 1571 ± 69 years BP (Before Present). ‘Present’ in terms of radiocarbon dates means 1950; the ± symbol gives us an indication of the sampling errors in determining the age, expressed as a statistical ‘standard deviation’. Unfortunately, ‘radiocarbon years’ are not the same as calendar years, and need to be calibrated against samples of known age. The calibrated date can be calculated as AD 486 ± 75; what this means is that there is a 68% chance that the true calendar age of the carbonised wood from the hearth falls into the period AD 411 to 561; increase the range to two ‘standard deviations’ and there is a 95% chance that the age falls into the range AD 268 to 630.

In technical language, the dates are:

- 1571 ± 69 BP (UB-4158)
- 1σ range Cal AD 411-561 (Cal BP 1539-1389)
- 2σ range Cal AD 268-630 (Cal BP 1682-1320)

So, the radiocarbon date tells us that a hearth constructed on the ground surface contained wood that came from a plant that was alive some time between the mid-third century and the earlier seventh century. One thing we can be absolutely certain about is that this part of Wat’s Dyke was built after the time of Septimius Severus, who died in 211. What it does not tell us is that Wat’s Dyke was built in the fifth century, even less that it was built AD *c* 446, as Blake and Lloyd suggest.

Firstly, the ‘date’ is not a date in the everyday sense of the word. We can state that Septimius Severus died on 4 September 211 and know that the earth was in a particular position in the sky, that the moon and planets appeared in certain constellations and so on. That is a true historical date. A radiocarbon determination, on the other hand, is a statistical approximation to the *age* of a sample. It tells us how old it is relative to the date at which the determination was made. This is known as a ‘relative date’, because calculating it depends on knowing the starting point (in other words, the historical date of the radiocarbon test).

But worse, working out the age of a sample is done by calculating the relative proportions of two isotopes of carbon: C^{12}, which is stable, and C^{14}, which is radioactive and decays at a known rate (currently thought to be about 1% every 83 years). Both types of carbon are absorbed from the environment by living organisms and once formation of the cellular structures ceases (usually at death), the proportion of radioactive C^{14} in a sample begins to decrease. The proportion of the two isotopes in the environment is in the region of 670,000,000,000 to 1 (in European numbers, this is six hundred and seventy thousand million to one; in American numbers, six hundred and seventy billion to one), so the measurement of proportions in samples is far from precise and always lower than this. Moreover, we cannot count all of the atoms, so an approximation is made based on the weight of the sample and either the evidence of radioactive decay measured by means such as a Geiger counter (a technique known as beta counting), or by spectroscopic analysis of charged carbon ions in a particle accelerator (known as accelerator mass spectrometry). The reliability of the age calculated in this way depends on how many atoms of C^{14} were present in the original sample (the older the sample, the fewer the radioactive atoms and the greater the difficulty of spotting them), the size of the sample (the smaller the sample, the fewer the number of atoms available to count) and the length of time available for counting (the shorter the time, the fewer the ‘blips’ recorded by the Geiger counter). An assessment of the reliability is given in the ‘margin of error’ figure that accompanies the dates; the quoted figure is a statistical ‘standard deviation’.

These techniques give an assessment of the age of the sample based on how far the proportion of radioactive C^{14} has declined from its assumed starting point of 1 in 670,000,000,000. However, this assumes that the proportion of C^{14} in the environment has always remained at the same level. We now know that, for a variety of reasons, this is not the case. The proportion has varied considerably over time, so that the starting ratios of the two isotopes will also have varied. A technique is needed to determine changes in the proportions of the two isotopes over time. Such a technique has been available since the late 1960s, when it was found that by radiocarbon dating growth rings from trees, which can be assigned to a particular calendar year, a consistent pattern emerges which shows times when there has been more C^{14} in the environment and other times when there has been less. Of course, the assessments of radiocarbon dates of tree rings is also subject to a margin of error, so the margin of error for the age of a sample will increase when the age is calibrated.

Then there is the question of exactly what is being dated. If it is part of a human being (an Egyptian mummy, say), we will get a determination of the date of death for that individual. If it is a piece of timber, we will get a date for the formation of the particular group of growth rings being tested. This is where problems can occur. Structural timbers are often reused many times over the centuries, so a radiocarbon determination of timber needs to take this into account. Wood used in a hearth (which is what was dated at Maes-y-Clawdd) may derive from recently felled timber or it may have come from a building that was centuries old.

There is finally the problem that ‘a single date is no date’: the potential for contamination, reuse of old materials, laboratory error and so on is so great that a single radiocarbon determination is next to useless. It is good practice to date a number of samples whenever possible, ensuring that a good range of materials is represented, minimising the risks outlined. This is why the Shroud of Turin was subjected to a number of separate tests by different laboratories and why we can be certain that the shroud was made between the mid thirteenth century and the late fourteenth: numerous samples, all giving the same general age, can be combined to increase the accuracy of the determination, and determinations from different laboratories reduce the effects of experimental error, laboratory contamination and so on.

It is interesting to look at the alleged early date of Wat’s Dyke. What we have is a radiocarbon date from a hearth built on the ground surface beneath the Dyke at Maes-y-Clawdd. Wood used in the hearth was growing between the late third and early seventh century, but it most certainly does not date Wat’s Dyke. There is the basic archaeological principle of the *terminus post quem*: the ‘date after which’. The Dyke was constructed after the hearth was in use; the hearth was in use after the tree that supplied its fuel had been felled. That is what the radiocarbon date tells us. It has nothing to do with the construction of the Dyke, but rather tells us that the Dyke must be later, and there is no reason why it could not be many centuries later.