Whether there's a data point on the Y-axis or not, the Y-intercept of the line doesn't change as the slope of the isochron line does (as shown in Figure 5).Therefore, the Y-intercept of the isochron line gives the initial global ratio of could be subtracted out of each sample, and it would then be possible to derive a simple age (by the equation introduced in the first section of this document) for each sample.An additional nice feature of isochron ages is that an "uncertainty" in the age is automatically computed from the fit of the data to a line.A routine statistical operation on the set of data yields both a slope of the best-fit line (an age) and a variance in the slope (an uncertainty in the age).
(The range of uncertainty varies, and may be as much as an order of magnitude different from the approximate value above.
This will be discussed in more detail in the section on Gill's paper below.
The "generic" method described by Gonick is easier to understand, but it does not handle such necessities as: (1) varying levels of uncertainty in the X- versus Y-measurements of the data; (2) computing an uncertainty in slope and Y-intercept from the data; and (3) testing whether the "fit" of the data to the line is good enough to imply that the isochron yields a valid age.
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.
Now that the mechanics of plotting an isochron have been described, we will discuss the potential problems of the "simple" dating method with respect to isochron methods.