Many fragments of the meteorite iron have been found around the crater, and it is reasonable to assume that this is the kind of iron we would expect to find in the core of the earth. Like the core iron, it is mixed with a little lead, which can be isolated and analyzed in a mass spectrometer for its isotopic composition. This lead is found to be much less contaminated with radiogenic lead, and hence is much more primitive than the oldest leads found on earth. Thus, meteorites presumably are as close as we can get to true primordial lead—the lead of the time when the earth (and the protoplanet) first formed. Once these measurements were available, it was easy to write the Houtermans equation for present-day and primordial leads in this way: ((²⁰⁶Pb)/(²⁰⁴Pb)) present - ((²⁰⁶Pb)/(²⁰⁴Pb)) primordial ------------------------ -------------------------- ((²⁰⁷Pb)/(²⁰⁴Pb)) present - ((²⁰⁷Pb)/(²⁰⁴Pb)) primordial = 137.7 ((e^{λ}238^{t} - 1))/((e^{λ}235^{t} - 1)) The present ratio of ²³⁸U to ²³⁵U is 137.7. e = the base of natural logarithms λ = the DECAY CONSTANT of each isotope of uranium t = the age of the earth. Substituting the best experimental lead isotope ratios into the equation and solving for t, Patterson was able to calculate that the earth is 4550 million years (4.55 aeons) old. Subsequent calculations based on other procedures generally have confirmed that result. Analytical Techniques Each method of nuclear age determination involves a different sequence of sample preparation. Wood, peat, charcoal, bones, or shells are cleaned for carbon-14 dating in order to remove every trace of possible contamination by modern carbon as well as extraneous old carbon. Rocks are crushed and ground, minerals are separated according to what is needed in any particular study, and the desired elements are extracted and separated by chemical procedures. Often there may be several different ways of doing the same thing; different laboratories use different procedures. In every case, however, long and complicated procedures must be followed before results are obtained from which an age can be calculated. There is no such thing as a black box into which you can throw a rock and read its age on a dial! Of all the elements that are part of the useful parent-daughter systems, only potassium is common enough to be analyzed by conventional chemical techniques. All the other elements, especially the radiogenic ones, are present in such small quantities that special processes had to be developed to measure them. The most valuable and generally used process is called ISOTOPE DILUTION. Isotope Dilution This is a process for analyzing an unknown material by incorporating uniformly into it a small amount of a radioactive test substance and determining how much the tracer radioactivity is altered by dilution in the original material.