The slope of the line determines the date, and the closeness of fit is a measure of the statistical reliability of the resulting date.
Technical details on how these dates are calculated are given in Radiometric dating. As with any experimental procedure in any field of science, these measurements are subject to certain "glitches" and "anomalies," as noted in the literature.
The method was developed by Willard Libby in the late 1940s and soon became a standard tool for archaeologists.
For example, creationist writer Henry Morris [Morris2000, pg.The simplest form of isotopic age computation involves substituting three measurements into an equation of four variables, and solving for the fourth.The equation is the one which describes radioactive decay: If one of these assumptions has been violated, the simple computation above yields an incorrect age.The latest high-tech equipment permits reliable results to be obtained even with microscopic samples.Radiometric dating is self-checking, because the data (after certain preliminary calculations are made) are fitted to a straight line (an "isochron") by means of standard linear regression methods of statistics.
The older a sample is, the less (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples.