Archive for History of Exact Sciences最新文献

Planck’s pioneering contributions to special relativity have received less consideration than one might expect in the historiography and philosophy of physics. Although they are celebrated in isolation, they are mostly not understood as integral to an overarching project. This paper aims (a) to provide a historically accurate overview of Planck’s contributions to the early history of relativity that is reasonably accessible to today’s reader, (b) to demonstrate how these contributions can be presented against the background of Planck’s ‘Helmholtzian’ vision of relativistic general dynamics based on the principle of relativity and principle of least action, and (c) to argue that Planck’s general dynamics serves as an illuminating example of the use of ‘principles’ in physics.

Between 1873 and 1876, Felix Klein published a series of papers that he later placed under the rubric anschauliche Geometrie in the second volume of his collected works (1922). The present study attempts not only to follow the course of this work, but also to place it in a larger historical context. Methodologically, Klein’s approach had roots in Poncelet’s principle of continuity, though the more immediate influences on him came from his teachers, Plücker and Clebsch. In the 1860s, Clebsch reworked some of the central ideas in Riemann’s theory of Abelian functions to obtain complicated results for systems of algebraic curves, most published earlier by Hesse and Steiner. These findings played a major role in enumerative geometry, whereas Plücker’s work had a strongly qualitative character that imbued Klein’s early studies. A leitmotif in these works can be seen in the interplay between real curves and surfaces as reflected by their transformational properties. During the early 1870s, Klein and Zeuthen began to explore the possibility of deriving all possible forms for real cubic surfaces as well as quartic curves. They did so using continuity methods reminiscent of Poncelet’s earlier approach. Both authors also relied on visual arguments, which Klein would later advance under the banner of intuitive geometry (anschauliche Geometrie).

Antonio Signorini’s contribution to the constitutive theory of non-linear elasticity is reconstructed and analyzed. Some uninformed opinions suggesting he had a minor role, lacking of significant results, are discussed and refuted. It is shown that Signorini should be rightly credited for being among the first scholars aware of the central problem of non-linear elasticity: the determination of the general form of the elastic potential.

Ptolemy reports three dated lunar eclipses observed by Hipparchus, and also refers to two more, without identifying them, which Hipparchus compared with two earlier counterparts (apparently, observed in Mesopotamia) to assess the validity of the Babylonian period relations of the lunar motion. Also, in Pliny the Elder’s Historia naturalis, we are told that a horizontal lunar eclipse (selenelion) at sunrise and moonset was reported (observed?) by Hipparchus. Reviewing a paper by G.J. Toomer in 1980, it is shown that the pairs of the eclipses were, almost certainly, the ones occurring on “31 January 486 b.c. and 27 January 141 b.c.” and “19 November 502 b.c. and 14 November 157 b.c.”; and if Hipparchus observed from St. Stephen’s Hill in Rhodes, the most probable candidate for the selenelion at moonset was the lunar eclipse of 7 February 142 b.c., although he also had the chance to observe any of the four others, occurring on 3 July 150 b.c., 10 April 145 b.c., 26 November 139 b.c., and 15 November 138 b.c., on a sufficiently elevated mountain on the island.

Ibn al-Zarqālluh (al-Andalus, d. 1100) introduced a new inequality in the longitudinal motion of the Moon into Ptolemy’s lunar model with the amplitude of 24′, which periodically changes in terms of a sine function with the distance in longitude between the mean Moon and the solar apogee as the variable. It can be shown that the discovery had its roots in his examination of the discrepancies between the times of the lunar eclipses he obtained from the data of his eclipse observations over a 37-year period in the latter part of the eleventh century and the predictions made on the basis of the lunar theories in the Mumta(textit{d{h}})an zīj (Baghdad, ca. 830) and al-Battānī’s zīj (Raqqa, d. 929), which were available to him at the time. What Ibn al-Zarqālluh found is, in fact, a special case of the annual equation of the Moon, which is applicable in the oppositions and, thus, in the lunar eclipses. The inequality was discovered independently by Tycho Brahe (d. 1601) and Johannes Kepler (d. 1630). As Ibn Yūnus (d. 1009) reports in his (textit{d{H}})ākimī zīj, Ibn al-Zarqālluh’s medieval Middle Eastern predecessors, the Persian astronomers Māhānī (d. ca. 880) and Nayrīzī (d. 922) as well as ‘Alī b. Amājūr (fl. ca. 920), were already acquainted with the problem of the eclipse timing errors, but it had remained unresolved until Ibn Yūnus provided a provisional, and incorrect, solution by reducing the size of the lunar epicycle. As we argue, the diverse ways to tackle the same problem stem from two different methodologies in astronomical reasoning in the traditions developed separately in the Eastern and Western regions of the medieval Islamic domain.

This study examines Babylonian records of the new moon interval NA (sunset to moonset on the day of first lunar visibility) and the connection of this interval to the length of the moon. I show that the NA intervals in the Normal Star Almanacs were computed using the goal-year method and were then used in turn to predict the lengths of each month of the year. I further argue that these predicted month lengths, adjusted occasionally on the basis of observation in cases where the moon’s visibility was considered marginal, formed the basis of the Late Babylonian calendar.

The manuscripts and writings of the fifteenth-century astronomer and physician Lewis Caerleon (d. c. 1495) have been largely overlooked. To fill this gap, this article focuses on his writings and working methods through a case study of his canons and table for the equation of time. In the first part, an account of his life and writings is given on the basis of new evidence. The context in which his work on the equation of time was produced is explored in detail by reviewing the three key periods of his scientific production. His heavy reliance on Simon Bredon’s Commentum super Almagesti is also analyzed. The article also provides editions of Lewis Caerleon’s canons for calculating his table for the equation of time and a critical edition of Simon Bredon’s Commentum super Almagesti, III, 22–24. In the second part of this article, we analyze the table for the equation of time derived by Lewis around 1485. In addition to the final table, there is a unique table with intermediate results that records every step of his derivation. By following and discussing the details of this derivation, we shed a new light on tabular practices in mathematical astronomy. Following Lewis in his historical mathematical procedure, we argue, offers a novel historiographical approach that allows us to identify different sources and practices used by historical actors. Therefore, beyond the exchange of parameters residing in modern mathematical analysis, this novel approach offers a promising refinement for the analysis of the transmission of knowledge across space, time, and culture.

In 1646, Francesco Fontana (1580–1656) published his Novae Coelestium Terresriumque Rerum Observationes which includes discussions of optical properties of systems of lenses, e.g., telescope and microscope. Our study of the Novae Coelestium shows that the advance Fontana made in optics could not have been accomplished on the basis of the traditional spectacle optics which was the dominant practice at his time. Though spectacle and telescope making share the same optical elements, improving eyesight and constructing telescope are different practices based on different principles. The production of powerful astronomical telescopes demanded objective lenses with much longer focal length and eyepiece lenses with much shorter focal length than the range of focal length of lenses used for spectacles, respectively. Moreover, higher standard of precision and purity of the glass was required. The transition from the practice by which optical components were chosen from ready-made spectacle lenses to lenses which were produced according to predetermined specifications (e.g., calculation of focal length) was anything but straight forward. We argue that Fontana developed the optical knowledge necessary for improving the performance of optical systems. Essentially, he formulated—based on rich practical experience—a set of rules of calculation by which optical properties of a lens system could be determined and adjusted as required.

The efflux problem deals with the outflow of water through an orifice in a vessel, the flow over the crest of a weir and some other ways of discharge. The difficulties to account for such fluid motions in terms of a mathematical theory made it a notorious problem throughout the history of hydraulics and hydrodynamics. The treatment of the efflux problem, therefore, reflects the diverging routes along which hydraulics became an engineering science and hydrodynamics a theoretical science out of touch with applications. By the twentieth century, the presentation of the efflux problem in textbooks on hydraulics had almost nothing in common with that in textbooks on hydrodynamics.

This paper concerns late 1920 s attempts to construct unitary theories of gravity and electromagnetism. A first attempt using a non-standard connection—with torsion and zero-curvature—was carried out by Albert Einstein in a number of publications that appeared between 1928 and 1931. In 1929, Tullio Levi-Civita discussed Einstein’s geometric structure and deduced a new system of differential equations in a Riemannian manifold endowed with what is nowadays known as Levi-Civita connection. He attained an important result: Maxwell’s electromagnetic equations and the gravitational equations were obtained exactly, while Einstein had deduced them only as a first order approximation. A main feature of Levi-Civita’s theory is the essential use of the Ricci’s rotation coefficients, introduced by Gregorio Ricci Curbastro many years before. We trace the history of Ricci’s coefficients that are still used today, and highlight their geometric and mechanical meaning.