In Accelerator Mass Spectrometry (AMS), for example, the number of radiocarbon atoms in a stream of atoms coming from the sample is counted.Thus there are statistical counting uncertainties proportional to the square root of the number of atoms counted.This idea is advanced, for example, in The Young Earth: C ratio was like before the industrial revolution, and all radiocarbon dating is made with this in mind.How do we know what the ratio was before then, though--say, thousands of years ago?The precision of a radiocarbon date tells how narrow the range of dates is.There are two main factors which determine the precision of a radiocarbon date.This Radiocarbon reference must originally have been translated from Russian and it is not unreasonable to suppose that there was some loss of descriptive clarity as a result.But it seems pretty clear that what is being described here is certainly not "Pennsylvanian coal".
Although no convincing argument for a change in the speed of light over time has been made, the question is irrelevant to the validity of tree-ring calibrated radiocarbon dates.Measurements can be made with a high degree of precision. Aardsma submitted a sample from a reed mat known to be over 5,000 years old.The measurement, before calibration, came back with an error bar of /- about 60 radiocarbon years. It should be noted that these measurement uncertainties do not increase linearly as one goes back in time.This is evident first of all by the fact that it is part of a date list which is broken into three parts: "geologic samples", "archaeological samples", and "fossil animals".Clearly, Pennsylvanian coal would be listed as a geologic sample, but this sample of "coal" is listed as an archaeological sample. In the original reference the sample is described as "scattered coals in a loamy rock in deposits of a 26-m [river] terrace".