[Illustration: _Tracks of uranium fission from a fossil antelope bone fragment from Hopefield, Cape Province, South Africa._] The fission clock method works this way: A cleavage face or a polished surface of a crystal or glass fragment is etched with a suitable solvent. Different acids work best for different materials, and a suitable procedure must be developed especially for each substance. The etching brings out the fission tracks so they can be seen (usually as little conical pits) and counted under a microscope. After this, the sample is exposed to a known amount of slow neutrons[15] in a nuclear reactor. New fissions are produced, but this time only in ²³⁵U (which is present in all natural uranium in the proportion of 1 atom of ²³⁵U to 137.7 atoms of ²³⁸U), because slow neutrons do not produce fissions in ²³⁸U. After the neutron irradiation, the same surface is etched again, and the new tracks counted. The old tracks, having been etched twice, now appear larger and thus can be distinguished from the new ones that were caused by ²³⁵U fission. The rate at which ²³⁸U decays by fission, λ_{f}, is known, as are the rate it decays by alpha decay, λ_{α}, and the total number of slow neutrons, _n_, to which the sample was exposed in the reactor. The age of the crystal or glass can then be calculated: t = (1)/(λ_{α}) ln (1 + (_n_N_{s})/(N_{i}) × constant) where ln = the natural logarithm (log to the base _e_), N_{s} = the number of atoms in the sample. N_{i} = the number of atoms of ²³⁵U in the irradiated sample, and the constant has the value: ½ (λ_{α} × 582 × 10⁻²⁴)/(λ_{f} × 137.7) = 4.25 × 10⁻¹⁸ Fission-track dating is a brand new technique, still only partly developed. It has enormous range and is applicable to numerous minerals; these advantages imply that it is likely to become very useful. [Illustration: _An atomic absorption spectrophotometer is used to measure the amount of potassium in samples of mica dissolved in acid._] Plumbology The most complicated and therefore probably the most interesting decay scheme of all is the decay of uranium to lead, discovered well over half a century ago and still intensively studied. There are several reasons for the interest. First, uranium and lead are geochemically separated to a high degree, not only on the small scale of an ore deposit but also on the scale of the earth as a whole. Second, natural uranium has two isotopes with half-lives that are neither too long nor too short to be useful (the greater half-life almost exactly equaling the age of the earth), and these half-lives differ from each other by a factor of about 6.3. That leads to very important consequences, as we shall see. Third, uranium and lead are both common, and techniques are available for extracting them in measurable quantities from almost any natural material.