Muḥyī al-Dīn al-Maghribī’s lunar measurements at the Maragha observatory

This paper is a technical study of the systematic observations and computations made by Mu?yī al-Dīn al-Maghribī (d. 1283) at the Maragha observatory (north-western Iran, c. 1259–1320) in order to newly determine the parameters of the Ptolemaic lunar model, as explained in his Talkhī? al-majis?ī, “Compendium of the Almagest.” He used three lunar eclipses on March 7, 1262, April 7, 1270, and January 24, 1274, in order to measure the lunar epicycle radius and mean motions; an observation on April 20, 1264, to determine the lunar eccentricity; an observation on August 29, 1264, to test the model; and another on March 15, 1262, for measuring the lunar parallax. In the second period of activity at the Maragha observatory, Shams al-Dīn Mu?ammad al-Wābkanawī (c. 1254–1320) adopted all of al-Maghribī’s parameter values in his Zīj, but decreased his value for the mean longitude of the moon at epoch by 0;13,11 $^{\circ }$ . By comparing the times of the new moons and lunar eclipses in the period of 1270–1320 as computed from the astronomical tables of the Maragha tradition with the true modern ones, it is argued that this correction was very probably the result of actual observations.     

Kepler,Tycho, and the ‘Optical Part of Astronomy’: the genesis of Kepler's theory of pinhole images

In the last half of the 16^th century, the method of casting a solar image through an aperture onto a screen for the purposes of observing the sun and its eclipses came into increasing use among professional astronomers. In particular, Tycho Brahe adapted most of his instruments to solar observations, both of positions and of apparent diameters, by fitting the upper pinnule of his diopters with an aperture and allowing the lower pinnule with an engraved centering circle to serve as a screen. In conjunction with these innovations a method of calculating apparent solar diameters on the basis of the measured size of the image was developed, but the method was almost entirely empirically based and developed without the assistance of an adequate theory of the formation of images behind small apertures. Thus resulted the unsuccessful extension of the method by Tycho to the quantitative observation of apparent lunar diameters during solar eclipses. Kepler's attention to the eclipse of July 1600, prompted by Tycho's anomalous results, gave him occasion to consider the relevant theory of measurement. The result was a fully articulated account of pinhole images. Dedicated to the memory of Ronald Cameron Riddell (29.1.1938–11.1.1981)     

Swedenborg's Lunars

The celebrated Swedish natural philosopher and visionary theologian Emanuel Swedenborg (1688–1772) devoted major efforts to the establishment of a reliable method for the determination of longitude at sea. He first formulated a method, based on the astronomical observation of lunar position, while in London in 1710–12. He issued various versions of the method, both in Latin and in Swedish, throughout his career. In 1766, at the age of 78, he presented his scheme for judgment by the Board of Longitude in London. The rich archive of Swedenborg's career allows an unusually detailed historical analysis of his longitude project, an analysis rather better documented than that available for the host of contemporary projectors who launched longitude schemes, submitted their proposals to the Board of Longitude, and have too often been ignored or dismissed by historians. This analysis uses the longitude work to illuminate key aspects of Swedenborg's wider enterprises, including his scheme to set up an astronomical observatory in southern Sweden to be devoted to lunar and stellar observation, his complex attitude to astronomical and magnetic cosmology, and his attempt to fit the notion of longitude into his visionary world-view. Swedenborg's programme also helps make better sense of the metropolitan and international networks of diplomatic and natural philosophical communication in which the longitude schemes were developed and judged. It emerges that his longitude method owed much to the established principles of earlier Baroque and Jesuit natural philosophy while his mature cosmology sought a rational and enlightened model of the universe.     

‘Land-marks of the universe’: John Herschel against the background of positional astronomy

John Herschel (1792–1871) was the leading British natural philosopher of the nineteenth century, widely known and regarded for his work in philosophy, optics and chemistry as well as his important research and popular publications on astronomy. To date, however, there exists no extended treatment of his astronomical career. This paper, part of a larger study exploring Herschel's contributions to astronomy, examines his work in the context of positional astronomy, the dominant form of astronomical practice throughout his lifetime. Herschel, who did not himself practice positional astronomy and who was known for his non-meridional observations of specific stellar objects, was nonetheless a strong advocate for positional astronomy—but for very different reasons than the terrestrial applications to which it was most often put. For Herschel, the star catalogues of positional astronomy were the necessary observational foundation upon which information about the stars as physical objects could be constructed. Positional astronomy practiced in the great national observatories was not about navigation or timekeeping; it was a way to standardize stellar observations and make them useful data for constructing theories of the stars themselves. For Herschel, the seeds of the new astronomy emerged from the practices of the old.     

The ‘Società degli Spettroscopisti Italiani’: birth and evolution

The anniversary of the death of Pietro Tacchini (1838–1905), one of the pioneers of solar physics in Italy, is commemorared by this account of his major creation, the Società degli Spettroscopisti Italiani (1871). Established to promote cooperation among solar spectroscopists engaged in the study of the solar chromosphere, it was the first scientific Society devoted to spectroscopy and its astronomical applications. Its journal, the Memorie, collected most of the important works on solar physics by Angelo Secchi SJ (1818–1878), Tacchini himself, and many other protagonists of the newly born astrophysics. A brief history of the Society and its development draws on many previously unexploited archival sources, in order to show its role in raising astrophysics to the status of a scientific discipline, in the context of the astronomical research of that time in Italy and abroad, especially in the USA.     

Displaced tables in Latin: the Tables for the Seven Planets for 1340

The anonymous set of astronomical tables preserved in Paris, Bibliothèque nationale de France, MS lat. 10262, is the first set of displaced tables to be found in a medieval Latin text. These tables are a reworking of the standard Alfonsine tables and yield the same results. However, the mean motions are defined differently, the presentation of the tables is unprecedented, and some new functions are introduced for computing true planetary longitudes. The absence of any instructions as well as unusual technical terms in the headings make it difficult to appreciate the cleverness that went into the construction of these tables that are extant in a unique copy. In this article we provide a detailed analysis of these tables and their underlying parameters. The displaced tables are typical of a pervasive tendency in Islamic science to provide extensive and elegant numerical tables for the convenience of practitioners. The underlying astronomical theory is neither questioned nor affected. Edward S. Kennedy      

The lunar and Paschal tables of De ratione paschali attributed to Anatolius of Laodicea

Summary of conclusions The seven MS lunar and Paschal tables of De ratione paschali fall into two distinct groups which we have classified as Sirmond-type and Padua-type respectively, and from these we have restored the tables of their archetype. The Sirmond-type tables preserve a unique lunar year, which we term the Anatolian lunar year, and they first emerge in the context of a larger computus which was assembled in southern Ireland c. 658, a copy of which Wilfrid had evidently obtained by the time of the Synod of Whitby. The weight of circumstantial evidence supports the hypothesis that it was he who then instigated the corruption of both the tables and the patristic authorities of De ratione paschali, a copy of which subsequently passed to Bede and thence to the Sirmond group of MSS. The Padua-type tables on the other hand are represented only by the Padua MS, and they appear to have originated from within Insular circles on the Continent. These too were crudely corrupted, first by changing their lunar year from Anatolian to Roman and moving their ferial data from January to December and changing some Paschal data, and then secondly by collation with Sirmond-type tables. In the case of both types the objective was clearly to weaken the relationship between the lunar and Paschal tables and to try and obscure the Paschal principles that they preserve and thereby undermine the position of those followers of the Insular latercus who relied on the authority of De ratione paschali for their Pasch. These conclusions naturally give a rather different colour to the events of Whitby from that given by Bede, who places them completely in a theological context. However in material terms what was really at stake at Whitby was the transfer of the patronage of the entire kingdom of Northumbria from the Celtic to the Roman church. Here then was sufficient motivation to justify the most ruthless of expedients.     

The Lunar Theories of Tycho Brahe and Christian Longomontanus in the Progymnasmata and Astronomia Danica

Tycho Brahe's lunar theory, mostly the work of his assistant Christian Longomontanus, published in the Progymnasmata (1602), was the most advanced and accurate lunar theory yet developed. Its principal innovations are: the introduction of equant motion for the first inequality in order to separate the determination of direction and distance; a more accurate limit for the second inequality although requiring a more complex calculation; additional inequalities of the variation and, in place of the annual inequality in Tycho's earlier theory, a reduction in the equation of time; in the latitude theory a variation of the inclination of the orbital plane and an inequality of the motion of the nodes; a reduction in the range of variation of distance, parallax, and apparent diameter. Some of these were already present in Tycho's earlier lunar theory (1599), but all were changed in notable ways. Twenty years later Longomontanus published a modified version of the lunar theory in Astronomia Danica (1622), for the purpose of facilitating the calculation through new correction tables, and also explained his reasons for parts of the theory in the Progymnasmata. This paper is a technical study of both lunar theories.     

The Jalālī Calendar: the enigma of its radix date

The Jalālī (or Malikī) Calendar is well known to Iranian and Western researchers. It was established by the order of Sulṭān Jalāl al-Dīn Malikshāh-i Saljūqī in the 5th c. A.H. (The dates which are designated with A.H. indicate the Hijrī Calendar.)/11th c. A.D. in Isfahan. After the death of Yazdigird III (the last king of the Sassanid dynasty), the Yazdigirdī Calendar, as a solar one, gradually lost its position, and the Hijrī Calendar replaced it. After the rise of Islam, nonetheless, Iranians preferred various solar calendars to the Hijrī one. The Jalālī Calendar must be considered the culmination of such efforts. The present article deals with the riddle of the radix date (epoch) of the Jalālī Calendar. The author examines the problem through a historical approach and provides a novel solution to the question.

     

Before words: reading western astronomical texts in early nineteenth-century Japan

SUMMARY

In 1803, the most prominent Japanese astronomer of his time, Takahashi Yoshitoki, received a newly imported Dutch translation of J. J. Lalande's ‘Astronomie’. He could not read Dutch, yet he dedicated almost a year to a close examination of this massive work, taking notes and contemplating his own astronomical practices. How did he read a book he could not read? Following the clues Yoshitoki left in his notes, we discover that he found meanings not only in words, but also in what are often taken for granted or considered to be auxiliary tools for data manipulation, such as symbols, units, tables, and diagrams. His rendering of these non-verbal textual elements into a familiar format was crucial for Yoshitoki's reading, and constituted the initial step in the process of integrating Lalande's astronomy into Japanese astronomical practices, and the subsequent translation of the text into Japanese.     

Chemistry and meteorology, 1700–1825

In 1639–1640 Benedetto Castelli (1577–1643) wrote a treatise on the loadstone which is quite unlike any of its contemporaries. In it are the origins of the notion of elementary magnets sharing a common alignment, the idea that all materials are magnetic in different ways, and the first intimation of the conception of magnetic domains. Castelli did not publish his treatise. Nevertheless his work was noted during his life-time, and may have exerted an influence on the development of magnetic theory in the 17th century. The treatise was published in 1883. Since then, however, it has either been neglected or not appreciated. It deserves being rescued from the neglect of more than three centuries.     

François Viète’s revolution in algebra

Archive for History of Exact Sciences - Françios Viète (1540–1603) was a geometer in search of better techniques for astronomical calculation. Through his theorem on angular...     

Viète's Controversy with Clavius Over the Truly Gregorian Calendar

Some twenty years after the Gregorian calendar reform, towards the end of his life, François Viète published his own calendar proposal. This treatise contains a sharp attack against the Jesuit scholar Clavius, the mathematical mind behind the reform. Understandably enough, Clavius prepared a negative reply. Viète heard of it and exploded in a fit of rage, ``I demonstrated that you are a false mathematician [ . . . ], and a false theologian.'' Sadly, Clavius' rejection, added as a chapter to his monumental apology of the Gregorian reform, appeared when Viète had already passed away.Viète seriously believed that the true aim of the Gregorian reform has been betrayed and he was furious about some logical inconsistencies which he claimed to have found in Clavius' calendar. Clavius apparently confused solar day and epactal day (or ``tithi''), the thirtieth part of a lunar month. This is the very core of Viète's attack against Clavius whom he accused of having introduced a false lunar period (``falsa periodus lunaris''). But his own work has some logical inconsistencies too. For instance, he reproaches Clavius for having introduced lunar months of 31 days which, indeed, are unrealistic. Grievously, his own rules can likewise give rise to lunations of unnatural lengths.In order to understand these subtle twists reader and author must work largely through both Clavius and Viète's methods of Easter reckoning. The fruit of all those efforts might be an insight into Viète's clear mathematical thinking. His calendar, however, was never considered.     

Studies in Babylonian lunar theory: part III. The introduction of the uniform zodiac

This paper is the third of a multi-part examination of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton, AHES 61:83–145, 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies, accomplished in the construction of the System A lunar theory early in the fourth century B.C. Part II (Britton, AHES 63:357–431, 2009) examines the accomplishment of this separation by the construction of a successful theory depicting the variations due to lunar anomaly in System A and its subsequent adaptation in System B. The present paper examines the introduction of the uniform zodiac, necessary for any theory depicting variations depending on the position of syzygy. It addresses three questions: (1) In light of all available evidence, what is the magnitude of the constant term in the expression Δλ* = C ? 1.3828°Y, describing the difference between the Babylonian sidereal longitudes and modern tropical longitudes? (2) What considerations governed the placement of the Babylonian sidereal zodiac relative to the fixed stars? (3) When was the uniform zodiac introduced? To the first question it finds C = 3.20° ± 0.1°, scarcely different from Huber’s (Centaurus 5:192–208, 1958) estimate of 3.08°, essentially confirming Huber’s result obtained from much less data. For the second it shows that accommodating the three asterisms comprising Taurus limited the placement of the zodiac to within 3°, while the prominence of half sign multiples among the measured intervals between prominent Normal Stars led irresistibly to the choice adopted. Finally, it finds that the zodiac was introduced between ?408 and ?397 and probably within a very few years of ?400.     

Master Georg Dörffel and the rise of cometary astronomy

This paper examines the purport of epact tables encountered on scientific instruments, and explains their use. The epact is a valuable chronological aid for calculating the age of the moon. In handbooks of chronology, usually two types of epacts are distinguished: the epact used in medieval times, and the so-called Lilian epact used after 1582 in the Gregorian perpetual calendar. By examining the rules for calculating the age of the moon, it turns out that the Julian and Gregorian epacts encountered on instruments must be distinguished from the medieval and Lilian epacts. It is shown that the Julian epact was already in use in 1478, and that, by adjusting for the shift of ten days in the date of the vernal equinox, the Gregorian epact was derived from it in 1582. The common association of the latter with the Lilian epact employed in the Gregorian perpetual calendar is incorrect. It is further shown that in contrast to the medieval and Lilian epacts, which served purely ecclesiastical purposes, the Julian and Gregorian epacts were mainly used to calculate the true age and zodiacal position of the moon. This knowledge was applied to secular interests such as ‘lunar astrology’, tidal computations, and the conversion of lunar into solar time.