The treatment of observations in early astronomy

Communicated by Curtis Wilson     

Geminus and the concept of mean motion in Greco-Latin astronomy

Conclusion Geminus account of lunar motion in chapter 18 of hisIntroductio astronomiae is, in our view, an important contribution to Greco-Latin astronomy because, in attempting to reconstruct arithmetically (the parameters of) the Moon's motion in longitude, he undermines the task astronomers had hitherto set for themselves. This undermining of a commonly acknowledged view of the purpose of astronomy is articulated in a whole new set of questions concerning the nature and place of both observation and mathematical reasoning in the science of the heavens. Yet, one must not overlook the fact thatGeminus reconstruction also indicates resources for addressing these questions. Of these resources, the most powerful proved to be the idea that irregular motion could be quantified as a systematic departure from a mean motion, and the idea that observational data could be organized and structured by means of genetic arithmetical reconstructions.But, since we limit our attention to extant treatises and decline to speculate about works or parts of works that have not survived, we must say that it would takePtolemy to discern the new direction for astronomy thatGeminus opened up and to pursue it. In part, this involved straightening out the conflated conception of mean motion in chapter 18 — the qua arithmetic mean daily displacement can only be anapparent lunar motion in longitude and not one the Moonreally makes, but the same need not be true of the qua periodic mean daily displacement — and determining its proper relation to real and apparent planetary motion. Indeed,Ptolemy's genius lay, we think, in seeing that even though, in assimilating Babylonian astronomy, earlier and contemporary Greco-Latin writers betrayed a confused, inconsistent, and unsophisticated grasp of the proper role of arithmetic, geometry, and observation in astronomical argument [seeBowen 1994], the solution lay in a mathematical reconstruction of the observed celestial motions, in which mean motion played an essential role.     

The intelligibility of motion and construction: Descartes’ early mathematics and metaphysics, 1619-1637

I argue for an interpretation of the connection between Descartes’ early mathematics and metaphysics that centers on the standard of geometrical intelligibility that characterizes Descartes’ mathematical work during the period 1619 to 1637. This approach remains sensitive to the innovations of Descartes’ system of geometry and, I claim, sheds important light on the relationship between his landmark Geometry (1637) and his first metaphysics of nature, which is presented in Le monde (1633). In particular, I argue that the same standard of clear and distinct motions for construction that allows Descartes to distinguish ‘geometric’ from ‘imaginary’ curves in the domain of mathematics is adopted in Le monde as Descartes details God’s construction of nature. I also show how, on this interpretation, the metaphysics of Le monde can fruitfully be brought to bear on Descartes’ attempted solution to the Pappus problem, which he presents in Book I of the Geometry. My general goal is to show that attention to the standard of intelligibility Descartes invokes in these different areas of inquiry grants us a richer view of the connection between his early mathematics and philosophy than an approach that assumes a common method is what binds his work in these domains together.     

Electric charge in hyperbolic motion: the early history

The study of an electric charge in hyperbolic motion is an important aspect of Minkowski’s geometrical formulation of electrodynamics. In “Space and Time”, his last publication before his premature death, Minkowski gives a brief geometrical recipe for calculating the four-force with which an electric charge acts on another electric charge. The subsequent work of Born, Sommerfeld, Laue, and Pauli filled in the missing derivation details. Here, we bring together these early contributions, in an effort to provide a more modern, accessible, and unified exposition of the early history of the electric charge in hyperbolic motion.

     

The American Philosophical Society and the rise of astronomy in the United States in the middle of the nineteenth century

Early geological investigations in the St David's area (Pembrokeshire) are described, particularly the work of Murchison. In a reconnaissance survey in 1835, he regarded a ridge of rocks at St David's as intrusive in unfossiliferous Cambrian; and the early Survey mapping (chiefly the work of Aveline and Ramsay) was conducted on that assumption, leading to the publication of maps in 1845 and 1857. The latter represented the margins of the St David's ridge as ‘Altered Cambrian’. So the supposedly intrusive ‘syenite’ was regarded as younger, and there was no Precambrian. These views were challenged by a local doctor, Henry Hicks, who developed an idea of the ex-Survey palaeontologist John Salter that the rocks of the ridge were stratified and had formed a Precambrian island, round which Cambrian sediments (now confirmed by fossil discoveries) had been deposited. Hicks subsequently proposed subdivision of his Precambrian into ‘Dimetian’, ‘Pebidian’, and (later) ‘Arvonian’, and he attempted correlations with rocks in Shropshire, North Wales, and even North America, seeking to develop the neo-Neptunist ideas of Sterry Hunt. The challenge to the Survey's work was countered in the 1880s by the Director General, Geikie, who showed that Hicks's idea of stratification in the Dimetian was mistaken. A heated controversy developed, several amateur geologists, supported by a group of Cambridge Sedgwickians, forming a coalition of ‘Archaeans’ against the Survey. Geikie was supported by Lloyd Morgan. Attention focused particularly on Ogof Lle-sugn Cave and St Non's Arch, with theory/controversy-ladenness of observations evident on both sides. Evidence from an eyewitness student record of a Geological Society meeting reveals the ‘sanit`ized’ nature of the official summary of the debate in QJGS. Field mapping early in the twentieth century by J. F. N. Green allowed a compromise consensus to be achieved, but Green's evidence for unconformity between the Cambrian and the Dimetian, obtained by excavation, can no longer be verified, and his consensual history of the area may need revision. Unconformity between the Cambrian and the Pebidian tuffs is not in doubt, however, and Precambrian at St David's is accepted. The study exhibits features of geological controversy and the British geological community in the nineteenth century. It also furnishes a further instance of the great influence of Murchison in nineteenth-century British geology and the side-effects of his controversy with Sedgwick.     

The geometry of burning mirrors in Greek antiquity. Analysis,heuristic, projections,lemmatic fragmentation

The article analyzes in detail the assumptions and the proofs typical of the research field of the geometry of burning mirrors. It emphasizes the role of two propositions of the Archimedean Quadratura parabolae, never brought to bear on this subject, and of a complex system of projections reducing a sumptōma of a parabola to some specific linear lemmas. On the grounds of this case-study, the much-debated problem of the heuristic role of analysis is also discussed.     

The history of science as the progress of the human spirit: The historiography of astronomy in the eighteenth century

In the eighteenth century, the historiography of astronomy was part of a wider discussion concerning the history of the human spirit. The concept of the human spirit was very popular among Enlightenment authors because it gave the history of human knowledge continuity, unity and meaning. Using this concept, scientists and historians of science such as Montucla, Lalande, Bailly and Laplace could present the history of astronomy in terms of a progress towards contemporary science that was slow and could be interrupted at times, but was still constant, regular, and necessary. In my paper I intend to explain how the originally philosophical concept of the human spirit was transferred to the history of astronomy. I also introduce the basic principles to which the development of the spirit is subject in astronomy, according to historians of astronomy. The third part of the paper describes how historians of astronomy took into account the effect of social and natural factors on the history of astronomy.     

Visual legitimisation of astronomy in the sixteenth and seventeeth centuries: Atlas, Hercules and Tycho’s nose

Images of the virtuous hero Hercules and the crowned King Atlas offered considerable potential for legitimising the new astronomy of the sixteenth and seventeenth centuries. The accomplishments of Hercules, a seeker after virtue, with his exceptional learning, his role as disseminator of knowledge, his significance as an example of ideal manhood and, in addition to all, his achievement of immortality, invited comparison with the endeavours of astronomers. Throughout the sixteenth and seventeenth centuries, Hercules and Atlas appear as the spiritual authorities of the discipline, and each was called into use to symbolise both the old and the new astronomy. Both figures embodied qualities that were decisive in struggles for patronage: they were politicised, especially Hercules, and used to legitimise claims to power.