half of the initial will remain; a quarter will remain after 11,400 years; an eighth after 17,100 years; and so on. The above calculations make several assumptions, such as that the level of in the atmosphere has remained constant over time. In fact, the level of in the atmosphere has varied significantly and as a result, the values provided by the equation above have to be corrected by using data from other sources. This is done by calibration curves (discussed below), which convert a measurement of in a sample into an estimated calendar age. The calculations involve several steps and include an intermediate value called the "radiocarbon age", which is the age in "radiocarbon years" of the sample: an age quoted in radiocarbon years means that no calibration curve has been used − the calculations for radiocarbon years assume that the atmospheric / ratio has not changed over time. Calculating radiocarbon ages also requires the value of the half-life for . In Libby's 1949 paper he used a value of 5720 ± 47 years, based on research by Engelkemeir et al. This was remarkably close to the modern value, but shortly afterwards the accepted value was revised to 5568 ± 30 years, and this value was in use for more than a decade. It was revised again in the early 1960s to 5,730 ± 40 years, which meant that many calculated dates in papers published prior to this were incorrect (the error in the half-life is about 3%). For consistency with these early papers, it was agreed at the 1962 Radiocarbon Conference in Cambridge (UK) to use the "Libby half-life" of 5568 years. Radiocarbon ages are still calculated using this half-life, and are known as "Conventional Radiocarbon Age". Since the calibration curve (IntCal) also reports past atmospheric concentration using this conventional age, any conventional ages calibrated against the IntCal curve will produce a correct calibrated age. When a date is quoted, the reader should be aware that if it is an uncalibrated date (a term used for dates given in radiocarbon years) it may differ substantially from the best estimate of the actual calendar date, both because it uses the wrong value for the half-life of , and because no correction (calibration) has been applied for the historical variation of in the atmosphere over time. Carbon exchange reservoir Carbon is distributed throughout the atmosphere, the biosphere, and the oceans; these