where "exp" refers to the base of the natural logarithm system, e = 2.71828 ..., and t1/2 is called the half-life of the radioisotope, the time after which one can expect that half the atoms of N0 will have decayed so that N/N0 = V2.

The most important of the radioisotope applications for archaeology is the measurement of the decay of the radioisotope of carbon, 14C, with half-life of ~5700 y, which allows a rough dating of objects that contain carbon. 14C is produced by several nuclear reactions, the most important being the interaction of neutrons with an atmospheric atom of nitrogen: 14N + n = 14C + 1H (the neutron most likely originates from the interaction of cosmic rays with particles in the atmosphere, which produces cascading showers of particles; the cosmic ray flux oscillates over an 11-year cycle, reaching a minimum, "Forbush decrease," at solar cycle maximum). Minor fluctuations in the production of radioactive carbon may be determined by checking tree-ring dates against 14C dates. The carbon may also be directly measured in the ice layers of the Greenland ice cap. In §6 and elsewhere, when we refer to 14C dates, we will use "b.c." to indicate uncor-rected and "b.c." to indicate corrected calendar dates.

As useful as it is, 14C dating is not the only way. There are a variety of other, specialized techniques that may be useful in dating artifacts.

The Earth's magnetic field varies with time in both strength and direction, both of which may be used in dating. When iron-bearing rocks (often ferrous clays) are heated above the Curie point, the temperature at which the local magnetic domains in the material are free to align themselves along ambient magnetic field lines, they do so align themselves. As the material cools, the prevailing geomagnetic field is "frozen" in, creating a record of the geomagnetic field at that time. Thus, archaeomagnetism is a way to date fired sites, such as hearths and kilns, or buildings and even cities destroyed in conflagrations. The temporal variations in the direction of magnetic north and in the strength of the magnetic field allow the establishment of local chronologies wherever there are adequate samples that have been fired in place.

Another age-determining process that makes use of previously fired materials is thermal luminescence. In this technique, the pottery, fired flint, or hearth is reheated. Free electrons, which were released as a consequence of low-level

Thus, one may plot measured samples of the quantity on the left-hand side of (4.23) against a (N/NDs). The plot is a straight line with zero point equal to the relative initial abundance of the daughter isotope and a slope from which the time t, the age of the sample, can be calculated. Thus, for the decay of 87Rb (a radioisotope of rubidium with half-life equal to 48.8Gy) into 87Sr, relative to the stable isotope of strontium,

86Sr, the Soko-Banja chondritic meteorite is determined to have an age of 4.45 ± 0.02 Gy and an initial ratio, 87Sr/86Sr = 0.69959 ± 0.00024 (Minster and Allegre 1981, cited in Wasson 1985, p. 52).

radioactivity in the material, are trapped in the matrix material; the reheating permits recombination and interactions that result in light emission, the intensity of which is related to the time since previous heating.

One dating technique involves measurement of annual "rings" in glass materials due to the effects of sunlight on the glass surface. The formation of surface layers in glass is particularly important in dating artifacts made from obsidian, a naturally occurring glass of volcanic origin.

The development of styles of a historical sequence of pottery, weapons, jewelry, and other artifacts in association with certain layers of debris in an archaeological site provides a basic method of relative dating. A less exact method involves measurement of the degree of curl in archeologi-cally recovered skins, including parchments. Although providing only rough dates, the technique is adequate to distinguish between medieval and Roman materials and was used to verify the age of the Dead Sea scrolls.

Altogether there are of the order of 70 archeological-geophysical techniques of dating objects and sites.

Finally, a linguistic technique, glottochronology, is useful in determining the history of the development of languages, sometimes correlated with archaeological evidence. The technique is based on the discovery that there is a statistically regular loss of vocabulary from a specified list of words in the basic vocabulary. This brief listing is intended to point out that archeologists now have a substantial body of techniques to determine dates.

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