Astrophysics and Nucleosynthesis

Having now examined attempts to explain the nature of the elements and the periodic system in a theoretical manner, it is necessary to backtrack a little in order to pick up a number of important issues not yet addressed. As in the preceding chapters, several contributions from fields outside of chemistry are encountered, and the treatment proceeds historically. So far in this book, the elements have been treated as if they have always existed, fully formed. Nothing has yet been said about how the elements have evolved or about the relative abundance of the isotopes of the elements. These questions form the contents of this chapter. It also emerges that different isotopes show different stabilities, a feature that can be explained to a considerable extent by appeal to theories from nuclear physics. The study of nucleosynthesis, and especially the development of this field, is intimately connected to the development of the field of cosmology as a branch of physical science. In a number of instances, different cosmological theories have been judged according to the degree to which they could explain the observed universal abundances of the various elements. Perhaps the most controversial cosmological debate has been over the rival theories of the big bang and the steady-state models of the universe. The proponents of these theories frequently appealed to relative abundance data, and indeed, the eventual capitulation of the steady-state theorists, or at least some of them, was crucially dependent upon the observed ratio of hydrogen to helium in the universe. Chapters 2, 3, and 6 discussed Prout’s hypothesis, according to which all the elements are essentially made out of hydrogen. Although the hypothesis was initially rejected on the basis of accurate atomic weight determinations, it underwent a revival in the twentieth century. As mentioned in chapter 6, the discoveries of Anton van den Broek, Henry Moseley, and others showed that there is a sense in which all elements are indeed composites of hydrogen.

Homeomeric Lines in Greek Mathematics

ArgumentThis article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical property, a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context.