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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.
In a separate article (Radiometric dating), we sketched in some technical detail how these dates are calculated using radiometric dating techniques.
Here is one example of an isochron, based on measurements of basaltic meteorites (in this case the resulting date is 4.4 billion years) [Basaltic1981, pg. Skeptics of old-earth geology make great hay of these examples.
For example, creationist writer Henry Morris [Morris2000, pg.
by Tas Walker A geologist works out the relative age of a rock by carefully studying where the rock is found in the field.
The field relationships, as they are called, are of primary importance and all radiometric dates are evaluated against them.