Archive for History of Exact Sciences最新文献

Among the most influential and well-known experiments of the 19th century was the generation and detection of electromagnetic radiation by Heinrich Hertz in 1887–1888, work that bears favorable comparison for experimental ingenuity and influence with that by Michael Faraday in the 1830s and 1840s. In what follows, we pursue issues raised by what Hertz did in his experimental space to produce and to detect what proved to be an extraordinarily subtle effect. Though he did provide evidence for the existence of such radiation that other investigators found compelling, nevertheless Hertz’s data and the conclusions he drew from it ran counter to the claim of Maxwell’s electrodynamics that electric waves in air and wires travel at the same speed. Since subsequent experiments eventually suggested otherwise, the question arises of just what took place in Hertz’s. The difficulties attendant on designing, deploying, and interpreting novel apparatus go far in explaining his results, which were nevertheless sufficiently convincing that other investigators, and Hertz himself, soon took up the challenge of further investigation based on his initial designs.

In my 2018 article in this journal, I described 15th-century Italian astronomer Giovanni Bianchini’s treatment of the problem of stellar coordinate conversion in his Tabulae primi mobilis, the first correct European solution. In this treatise Bianchini refers to a book he had written previously, containing the same error that had plagued his predecessors’ work on the problem. In this article, we announce the discovery of this earlier treatise. We compare its canons and tables to Bianchini’s later work, noting the places where the contents overlap (roughly one quarter of the text). We analyze his mathematical methods and the unique tables he constructed for converting stellar coordinates, including the earliest known European arc sine table, that he would abandon only a few years later.

From 1873 to 1878, the American physicist Josiah Willard Gibbs offered to the scientific community three great articles that proved to be a milestone for the science of thermodynamics. On the other hand, between 1886 and 1896, the French physicist Pierre Maurice Marie Duhem translated thermodynamics into the language of Lagrange’s analytical mechanics. At the same time, he expanded its scope to include thermal phenomena, electromagnetic phenomena, and all kinds of irreversible processes. Duhem formulated a version of thermodynamics characterized by the conceptual unification of mechanics, physics, and chemistry. Overall, the work of both physicists on thermodynamics is tremendous, full of axioms, theorems, corollaries, proofs, and hundreds of equations. Therefore, it would be a utopian aim to provide a short analysis of their work. Instead, the present study will attempt to give a brief outline of the main tools and concepts used by the two physicists. I will argue that each scientist approaches thermodynamics in a new and unique way, which reveals their scientific styles as reflected in their personalities, the writing styles, their behavior toward publicity, and their inclination for publication. Finally, I will examine the influence of their theories on the development of chemical thermodynamics.

We report on an unpublished and previously unknown manuscript of John von Neumann and contextualize it within the development of the theory of shock waves and detonations during the nineteenth and twentieth centuries. Von Neumann studies bombs comprising a primary explosive charge along with explosive booster material. His goal is to calculate the minimal amount of booster needed to create a sustainable detonation, presumably because booster material is often more expensive and more volatile. In service of this goal, he formulates and analyzes a partial differential equation-based model describing a moving shock wave at the interface of detonated and undetonated material. We provide a complete transcription of von Neumann’s work and give our own accompanying explanations and analyses, including the correction of two small errors in his calculations. Today, detonations are typically modeled using a combination of experimental results and numerical simulations particular to the shape and materials of the explosive, as the complex three dimensional dynamics of detonations are analytically intractable. Although von Neumann’s manuscript will not revolutionize our modern understanding of detonations, the document is a valuable historical record of the state of hydrodynamics research during and after World War II.

This article describes the emergence of formal methods in theory of partial differential equations (PDE) in the French school of mathematics through Janet’s work in the period 1913–1930. In his thesis and in a series of articles published during this period, Janet introduced an original formal approach to deal with the solvability of the problem of initial conditions for finite linear PDE systems. His constructions implicitly used an interpretation of a monomial PDE system as a generating family of a multiplicative set of monomials. He introduced an algorithmic method on multiplicative sets to compute compatibility conditions, and to study the problem of the existence and the uniqueness of a solution to a linear PDE system with given initial conditions. The compatibility conditions are formulated using a refinement of the division operation on monomials defined with respect to a partition of the set of variables into multiplicative and non-multiplicative variables. Janet was a pioneer in the development of these algorithmic methods, and the completion procedure that he introduced on polynomials was the first one in a long and rich series of works on completion methods which appeared independently throughout the twentieth-century in various algebraic contexts.

The most discussed and mysterious column within the Babylonian astronomy is column Φ. It is closely connected to the lunar velocity and to the duration of the Saros. This paper presents new ideas for the development and interpretation of column Φ. It combines the excellent Goal-Year method (for the prediction of Lunar Six time intervals) with old ideas and practices from the “schematic astronomy”. Inspired by the old “TU11” rule for prediction of times of lunar eclipses, it proposes that column Φ, in a similar way, used the sum of the Lunar Four to predict times of lunar eclipses as well as the duration of one, 6, and 12 months by means of what usually is called “R–S” schemes. It also explains fully the structure and development of such schemes, a fact that strongly supports the new interpretation of column Φ.

The assumption that Ptolemy adopted star coordinates from a star catalog by Hipparchus is investigated based on Hipparchus’ equatorial star coordinates in his Commentary on the phenomena of Aratus and Eudoxus. Since Hipparchus’ catalog was presumably based on an equatorial coordinate system, his star positions must have been converted into the ecliptical system of Ptolemy’s catalog in his Almagest. By means of a statistical analysis method, data groups consistent with this conversion of coordinates are identified. The found groups show a high degree of agreement between Hipparchus’ and Ptolemy’s data. The value of the obliquity of the ecliptic underlying the conversion is estimated by adjustment and statistically agrees with Ptolemy’s value of this parameter. The results allow the assumption that Ptolemy’s coordinates were determined from Hipparchus’ coordinates by an accurate star globe or even by calculation. For a calculative derivation of ecliptical coordinates from equatorial ones, possible calculation methods are discussed considering the mathematics of the Almagest.

Tycho Brahe was not just an observer; he was a skilled theoretical astronomer, as his lunar and solar models show. Still, even if he is recognized for proposing the Geoheliocentric system, little do we know of the technical details of his planetary models, probably because he died before publishing the last two volumes of his Astronomiae Instaurandae Progymnasmata, which he planned to devote to the planets. As it happens, however, there are some extant drafts of his calculations in Dreyer’s edition of Tycho’s Opera Omnia under the name Calculi ad Corrigenda Elementa orbitae Saturni, which, to the best of my knowledge, have not yet been analyzed before. In these manuscripts, Tycho starts with calculations based on the Prutenic Tables and makes a series of adjustments to the mean longitude, the longitude of the apogee, and the eccentricity to fit a series of observations of oppositions. In doing that, Tycho (1) describes and applies a new method for obtaining accurate values for the parameters of the superior planets, he (2) develops a divided eccentricity (not bisected) model of Saturn, similar to the one we know Longomontanus and Kepler applied to Mars, and finally (3) he realizes that the true position of the Sun somehow affects the motion of Saturn around the zodiac and develops a method to correct the position of Saturn as a function of solar equation of anomaly. So, a close analysis of the calculations reveals details of the Tychonic planetary models unknown until now. The present study analyzes these drafts.

In this paper, we discuss Babylonian observations of a “massing of the planets” reported in two Astronomical Diaries, BM 32562 and BM 46051. This extremely rare astronomical phenomenon was observed in Babylon between 20 and 30 March 185 BC shortly before sunrise when all five planets were simultaneously visible for about 10 to 15 min close to the horizon in the eastern morning sky. These two observational texts are not only interesting as records of an extremely rare planetary configuration, but also because (1) the observers appear to be confused by the presence of all planets simultaneously and mix them up in their reports, and (2) the two reports of the same observations are so different that we are forced to conclude that they were carried out by two different observers. There is an additional astronomical event which makes this planetary configuration even more unique: the exact conjunction of the planets Mars and Jupiter in the afternoon of 25 March 185 BC. An exact conjunction, where two planets are so close together that they appear as one object in the sky, is also extremely rare. Although this exact conjunction between Mars and Jupiter occurred during the day so that it was not observable, it was correctly predicted by the Babylonian scholars: a remarkable achievement and a nice illustration of their astronomical craftsmanship. Finally, our study clearly exposes one of the limitations of Babylonian naked-eye astronomy. When first appearances of the planets Mercury, Mars and Saturn are expected around the same date, it is nearly impossible to correctly identify them because their expected positions are only approximately known while they have about the same visual magnitude so that they become visible at about the same altitude above the horizon.