a / ratio lower than that of the biosphere. Dating considerations The variation in the / ratio in different parts of the carbon exchange reservoir means that a straightforward calculation of the age of a sample based on the amount of it contains will often give an incorrect result. There are several other possible sources of error that need to be considered. The errors are of four general types: variations in the / ratio in the atmosphere, both geographically and over time; isotopic fractionation; variations in the / ratio in different parts of the reservoir; contamination. Atmospheric variation In the early years of using the technique, it was understood that it depended on the atmospheric / ratio having remained the same over the preceding few thousand years. To verify the accuracy of the method, several artefacts that were datable by other techniques were tested; the results of the testing were in reasonable agreement with the true ages of the objects. Over time, however, discrepancies began to appear between the known chronology for the oldest Egyptian dynasties and the radiocarbon dates of Egyptian artefacts. Neither the pre-existing Egyptian chronology nor the new radiocarbon dating method could be assumed to be accurate, but a third possibility was that the / ratio had changed over time. The question was resolved by the study of tree rings: comparison of overlapping series of tree rings allowed the construction of a continuous sequence of tree-ring data that spanned 8,000 years. (Since that time the tree-ring data series has been extended to 13,900 years.) In the 1960s, Hans Suess was able to use the tree-ring sequence to show that the dates derived from radiocarbon were consistent with the dates assigned by Egyptologists. This was possible because although annual plants, such as corn, have a / ratio that reflects the atmospheric ratio at the time they were growing, trees only add material to their outermost tree ring in any given year, while the inner tree rings don't get their replenished and instead start losing through decay. Hence each ring preserves a record of the atmospheric / ratio of the year it grew in. Carbon-dating the wood from the tree rings themselves provides the check needed on the atmospheric / ratio: with a sample of known date, and a measurement of the value of N (the number of atoms of remaining in the sample), the carbon-dating equation allows the