The planetary increase of brightness during retrograde motion: An explanandum constructed ad explanantem

In Ancient Greek two models were proposed for explaining the planetary motion: the homocentric spheres of Eudoxus and the Epicycle and Deferent System. At least in a qualitative way, both models could explain the retrograde motion, the most challenging phenomenon to be explained using circular motions. Nevertheless, there is another explanandum: during retrograde motion the planets increase their brightness. It is natural to interpret a change of brightness, i.e., of apparent size, as a change in distance. Now, while according to the Eudoxian model the planet is always equidistant from the earth, according to the epicycle and deferent system, the planet changes its distance from the earth, approaching to it during retrograde motion, just as observed. So, it is usually affirmed that the main reason for the rejection of Eudoxus' homocentric spheres in favor of the epicycle and deferent system was that the first cannot explain the manifest planetary increase of brightness during retrograde motion, while the second can. In this paper I will show that this historical hypothesis is not as firmly founded as it is usually believed to be.     

The astronomical tables of Jacob ben David Bonjorn

Communicated by J. North     

Length of the year in pre-epicyclic planetary theory

An estimate is made of the length of the year implied in the pre-epicyclic planetary theory of the Pañcasiddhntik. It is shown that this could be the same as the year-length of the corresponding Babylonian theory.     

Epicycles,eccentrics, and ellipses: The predictive capabilities of Copernican planetary models

A theoretical analysis of the potential accuracy of early modern planetary models employing compound circles suggests that fairly simple extensions of those models can be sufficiently accurate to meet the demands of Tycho Brahe's observations in both ecliptic longitude and latitude. Some of these extensions, such as the substitution of the true sun for the mean sun, had already been taken by Kepler before he abandoned circular models. Other extensions, involving one or two extra epicycles, were well within the mathematical capabilities of sixteenth-century and seventeenth-century astronomers. Hence neither the failure of astronomers before Kepler to correct errors in planetary positions nor Kepler's decision to abandon circular models was a consequence of inherent limitations in those models.     

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.     

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 herbicide Eptam® 6-E: A selective female chemosterilant for the Egyptian cotton leafworm,Spodoptera littoralis

Zusammenfassung Das herbizide Thiolcarbamat Eptam® hemmt die Entwicklung der Weibchen der ägyptischen BaumwollraupeSpodoptera littoralis. Die schlüpfenden Weibchen sind relativ klein und legen keine oder nur sterile Eier.