Furthermore, the ratio is known to fluctuate significantly over relatively short periods of time (e.g.
Unfortunately the ratio of carbon-12 to carbon-14 has yet to reach a state of equilibrium in our atmosphere; there is more carbon-14 in the air today than there was thousands of years ago.
Because it is radioactive, carbon 14 steadily decays into other substances.
This argument was popularized by Henry Morris (1974, p.164), who used some calculations done in 1968 by Melvin Cook to get the 10,000-year figure. Whitelaw, using a greater ratio of carbon-14 production to decay, concluded that only 5000 years passed since carbon-14 started forming in the atmosphere!
The argument may be compared to filling a barrel which has numerous small holes in its sides.
Even for the first investigation, there was a possibility of using radiocarbon dating to determine the age of the linen from which the shroud was woven.
The size of the sample then required, however, was ~500cm, which would clearly have resulted in an unacceptable amount of damage, and it was not until the development in the 1970s of small gas-counters and accelerator-mass-spectrometry techniques (AMS), requiring samples of only a few square centimetres, that radiocarbon dating of the shroud became a real possibility. The shroud was separated from the backing cloth along its bottom left-hand edge and a strip (~10 mm x 70 mm) was cut from just above the place where a sample was previously removed in 1973 for examination.
The barrel represents the earth's atmosphere in which the carbon-14 accumulates.