Newton’s De gravitatione: a review and reassessment

The widely accepted supposition that Newton’s De gravitatione was written in 1684/5 just before composing the Principia is examined. The basis for this determination has serious difficulties starting with the failure to examine the numerical estimates for the resistance of aether. The estimated range is not nearly nil as claimed but comparable with air at or near the earth’s surface. Moreover, the evidence provided most likely stems from experiments by Boyle, Hooke, and others in the 1660s and does not use evidence available in the late 1684. The document supports Newton’s contention that the aether medium incorporates very large voids thereby proving that body and space differ but does by no means completely reject its corporeal nature or eliminate its resistance. Newton’s use of the term inertia provides no conclusive evidence for a late date as often claimed and his definition of gravitas is difficult to reconcile with a late one.     

Borelli’s edition of books V–VII of Apollonius’s Conics,and Lemma 12 in Newton’s Principia

To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (Principia, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s Conics before the printing of the Principia.

     

The coming-to-be of Hansen’s method

This article by Curtis Wilson is an account of the origin of Hansen’s powerful systematic method for finding contributions of higher order perturbations in celestial mechanics. Hansen’s method was developed in the course of improving on Laplace’s treatment of the mutual perturbations of Jupiter and Saturn. This method, an entirely new way of doing celestial mechanics when it first appeared, later made possible the successful treatment of the complicated motions of our moon (see Wilson 2010). In this paper Wilson gives a brief historical introduction followed by an account of relevant technical details of the Laplacian background, an account illustrating technical details in Hansen’s initial development in his Disquisitions of 1829, and a treatment illustrating details contributing to the achievement of Hansen’s more refined development in his Untersuchung of 1831. These details include conditional equations Hansen provides for checking the accuracy of calculations. Wilson also includes a detailed assessment showing the extraordinary improvement in empirical accuracy of Hansen’s treatment over the best earlier treatment of the Jupiter-Saturn  interactions.     

Isaac Newton’s ‘Of Quadrature by Ordinates’

In Of Quadrature by Ordinates (1695), Isaac Newton tried two methods for obtaining the Newton–Cotes formulae. The first method is extrapolation and the second one is the method of undetermined coefficients using the quadrature of monomials. The first method provides $n$ -ordinate Newton–Cotes formulae only for cases in which $n=3,4$ and 5. However this method provides another important formulae if the ratios of errors are corrected. It is proved that the second method is correct and provides the Newton–Cotes formulae. Present significance of each of the methods is given.     

The law of refraction and Kepler’s heuristics

Archive for History of Exact Sciences - Johannes Kepler dedicated much of his work to discover a law for the refraction of light. Unfortunately, he formulated an incorrect law. Nevertheless, it was...     

Deducing Newton’s second law from relativity principles: A forgotten history

In French mechanical treatises of the nineteenth century, Newton’s second law of motion was frequently derived from a relativity principle. The origin of this trend is found in ingenious arguments by Huygens and Laplace, with intermediate contributions by Euler and d’Alembert. The derivations initially relied on Galilean relativity and impulsive forces. After Bélanger’s Cours de mécanique of 1847, they employed continuous forces and a stronger relativity with respect to any commonly impressed motion. The name “principle of relative motions” and the very idea of using this principle as a constructive tool were born in this context. The consequences of Poincaré’s and Einstein’s awareness of this approach are analyzed. Lastly, the legitimacy and significance of a relativity-based derivation of Newton’s second law are briefly discussed in a more philosophical vein.

     

The Principia’s second law (as Newton understood it) from Galileo to Laplace

Archive for History of Exact Sciences - Newton certainly regarded his second law of motion in the Principia as a fundamental axiom of mechanics. Yet the works that came after the Principia, the...     

The potter’s wheel: the host’s role in sculpting its microbiota

Animals, ranging from basal metazoans to primates, are host to complex microbial ecosystems; engaged in a symbiotic relationship that is essential for host physiology and homeostasis. Epithelial surfaces vary in the composition of colonizing microbiota as one compares anatomic sites, developmental stages and species origin. Alterations of microbial composition likely contribute to susceptibility to several distinct diseases. The forces that shape the colonizing microbial composition are the focus of much current investigation, and it is evident that there are pressures exerted both by the host and the external environment to mold these ecosystems. The focus of this review is to discuss recent studies that demonstrate the critical importance of host factors in selecting for its microbiome. Greater insight into host–microbiome interactions will be essential for understanding homeostasis at mucosal surfaces, and developing useful interventions when homeostasis is disrupted.     

The story of ‘Scientist: The Story of a Word’

This examination of an important paper by Sydney Ross is the first in a projected series of occasional reflections on ‘Annals of Science Classic Papers’ that have had enduring utility within the field of history of science and beyond. First the messages of the paper are examined, some well known but others, particularly Ross's own contemporary concerns about the use of the word ‘scientist’, less so. The varied uses made of the paper by scholars are then traced before Ross's biography is examined in order to try to understand how a figure professionally marginal to the field of history of science came to write such a significant piece. Ross’s interest in the topic appears to have been informed by a romantically tinged scientific progressivism and a deep concern with the importance of linguistic precision in science and in public affairs. The inspirations of the author and the interests of his audience have been only partially aligned, but the paper's insights remain of broad historical interest and have wider ramifications since the denotation ‘scientist’ and its proper application are much debated today in contests over the authority of science.     

The natures of numbers in and around Bombelli’s L’algebra

The purpose of this article is to analyse the mathematical practices leading to Rafael Bombelli’s L’algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the fourteenth to sixteenth centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra.     

The evolution of X chromosome inactivation in mammals: the demise of Ohno’s hypothesis?

Ohno’s hypothesis states that dosage compensation in mammals evolved in two steps: a twofold hyperactivation of the X chromosome in both sexes to compensate for gene losses on the Y chromosome, and silencing of one X (X-chromosome inactivation, XCI) in females to restore optimal dosage. Recent tests of this hypothesis have returned contradictory results. In this review, we explain this ongoing controversy and argue that a novel view on dosage compensation evolution in mammals is starting to emerge. Ohno’s hypothesis may be true for a few, dosage-sensitive genes only. If so few genes are compensated, then why has XCI evolved as a chromosome-wide mechanism? This and several other questions raised by the new data in mammals are discussed, and future research directions are proposed.     

The semantic conception and the structuralist view of theories: A critique of Suppe’s criticisms

Different conceptions of scientific theories, such as the state spaces approach of Bas van Fraassen, the phase spaces approach of Frederick Suppe, the set-theoretical approach of Patrick Suppes, and the structuralist view of Joseph Sneed et al. are usually put together into one big family. In addition, the definite article is normally used, and thus we speak of the semantic conception (view or approach) of theories and of its different approaches (variants or versions). However, in The Semantic Conception of Theories and Scientific Realism (Urban and Chicago: University of Illinois Press, 1989), starting from certain remarks already made in “Theory Structure” (in P. Asquith and H. Kyburg (Eds.), Current Research in Philosophy of Science, East Lansing: Philosophy of Science Association, 1979, pp. 317–338), Frederick Suppe excludes the structuralist view as well as other “European” versions from the semantic conception of theories. In this paper I will critically examine the reasons put forward by Suppe for this decision and, later, I will provide a general characterization of the semantic family and of the structuralist view of theories in such a way as to justify the inclusion of the structuralist view (as well as other “European” versions) as a member of this family.     

Superposition: on Cavalieri’s practice of mathematics

Bonaventura Cavalieri has been the subject of numerous scholarly publications. Recent students of Cavalieri have placed his geometry of indivisibles in the context of early modern mathematics, emphasizing the role of new geometrical objects, such as, for example, linear and plane indivisibles. In this paper, I will complement this recent trend by focusing on how Cavalieri manipulates geometrical objects. In particular, I will investigate one fundamental activity, namely, superposition of geometrical objects. In Cavalieri’s practice, superposition is a means of both manipulating geometrical objects and drawing inferences. Finally, I will suggest that an integrated approach, namely, one which strives to understand both objects and activities, can illuminate the history of mathematics.     

The ‘Chemistry of Space’: The Sources of Hermann Grassmann's Scientific Achievements

Albert Lewis's article (Annals of Science, 1977) analysing the influence of Friedrich Schleiermacher on Hermann Grassmann, stimulated many different studies on the founder of n-dimensional outer algebra.

Following a brief outline of the various, sometimes diverging, analyses of Grassmann's creative thinking, new research is presented which confirms Lewis's original contribution and widens it considerably. It will be shown that:

i.?Grassmann, although a self-taught mathematician, was at the centre of a hitherto understated intellectual trend, which was defining for Germany. Initiated by Pestalozzi's concept of elementary mathematical education and culminating in the modern mathematics of the late 19th Century, it was reflected in the contributions of Grassmann, Riemann, Jacobi and Eisenstein.

ii.?Hermann Grassmann, his father Justus, and his brother Robert were all demonstrably influenced by Schleiermacher's dialectic; however the two brothers responded to it in very different ways.

iii.?Whilst the more philosophical parts of Hermann's 1844 Extension Theory are characterised by the influence of Schleiermacher and also by the mathematical knowledge of his father, the entire development of this work is the unfolding of a single idea based on the father's interpretation of combinatorial multiplication as a ‘chemical conjunction‘, which was developed largely dialectically by Hermann.     

The role of inflammation in sporadic and familial Parkinson’s disease

The etiology of Parkinson’s disease (PD) is complex and most likely involves numerous environmental and heritable risk factors. Interestingly, many genetic variants, which have been linked to familial forms of PD or identified as strong risk factors, also play a critical role in modulating inflammatory responses. There has been considerable debate in the field as to whether inflammation is a driving force in neurodegeneration or simply represents a response to neuronal death. One emerging hypothesis is that inflammation plays a critical role in the early phases of neurodegeneration. In this review, we will discuss emerging aspects of both innate and adaptive immunity in the context of the pathogenesis of PD. We will highlight recent data from genetic and functional studies that strongly support the theory that genetic susceptibility plays an important role in modulating immune pathways and inflammatory reactions, which may precede and initiate neuronal dysfunction and subsequent neurodegeneration. A detailed understanding of such cellular and molecular inflammatory pathways is crucial to uncover pathogenic mechanisms linking sporadic and hereditary PD and devise tailored neuroprotective interventions.