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They used pottery and other materials in sites to date 'relatively'.They thought that sites which had the same kinds of pots and tools would be the same age.The C14 method has been and continues to be applied and used in many, many different fields including hydrology, atmospheric science, oceanography, geology, palaeoclimatology, archaeology and biomedicine.All plants and animals on Earth are made principally of carbon.Rasmus Nyerup's quote reminds us of the tremendous scientific advances which have taken place in the 20th century.
Most of the carbon on Earth exists in a slightly different atomic form, although it is chemically speaking, identical to all carbon.
In the 1940s, scientists succeeded in finding out how long it takes for radiocarbon to disappear, or decay, from a sample of carbon from a dead plant or animal.
Willard Libby, the principal scientist, had worked in the team making the nuclear bomb during World War 2, so he was an expert in nuclear and atomic chemistry.
We know that it is older than Christendom, but whether by a couple of years or a couple of centuries, or even by more than a millenium, we can do no more than guess." [Rasmus Nyerup, (Danish antiquarian), 1802 (in Trigger, 19)].
The person who wrote these words lived in the 1800s, many years before archaeologists could accurately date materials from archaeological sites using scientific methods.