Tree-ring sequences

We, Libby and Pandolfi, have felt that a 1.5 percent uncertainty is tolerable within the limits of other errors inherent in the method, and therefore we have always analyzed whole wood in our study of isotope variations in tree-ring sequences. 

We hope that tree ring sequences will be prepared from trees of the southern hemisphere from which one could learn whether climate changes have been simultaneous in both hemispheres. There are large tree stumps in New Zealand, and perhaps similar material could be found in Australia and other southern lands, and there may be varve sequences as well in the southern hemisphere. 

The next problem was which trees to measure. Many tree ring sequences can be counted with an accuracy of about one year. Those which are not yet tied to modern sequences by overlapping ring patterns (said to be "floating"), can be dated in favorable cases with an accuracy of about 30 years by radiocarbon dating, depending on the age and the number of radiocarbon measurements which are made. 

We hope that analysis of stable isotopes in tree ring sequences will become an international undertaking, and that with the collaboration of many laboratories in many countries, the history of the climate in recent times, perhaps as far back as thirty thousand years, will be deduced, and that, from its determinatiop, the likely trends of climate in the near future will be predicted. 

Thus in our study of isotope variations in lengthy chronological sequences of tree rings, we are evaluating fluctuations in the sea surface temperatures, from which distilled the precipitation which nourished the trees and the sea surface temperatures, in turn, are affected by variations in the ultraviolet spectrum of the sun. 

It is a pleasure to thank Rudolph Black of the United States Advanced Research Projects Agency, who, in May 1971, funded our proposal that "temperature variations in past climates may be evaluated by measuring stable isotope ratios in natural data banks such as tree ring and varve sequences". We thank William Best of the U.S. Air Force Office of Scientific Research who monitored our study and Frank Eden of the U.S. National Science Foundation who subsequently provided further funds. 

Definition (Walk, path, cycle, ring, tree) Consider an m-multigraph on n nodes y th cot" responding bond graph y and a natural number k > 0. A sequence (fo,...,[Pg.56]

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