On Jacobi’s transformation theory of elliptic functions

The main interpretative challenge set by the Fundamenta Nova Theoriae Functionum Ellipticarum lies in Jacobi’s transformation theory upon which the entire theoretical edifice of the treatise depends. Unfortunately, Jacobi did not convey any indication of how he attained his general formulae for rational transformations of elliptic functions. He limited himself to providing a posteriori verification of the validity of his claims. The aim of this paper is precisely to describe the heuristic path by which in 1827 Jacobi succeeded in finding these transformation formulae. The proposed historical reconstruction will hopefully shed new light upon the emergence in Jacobi’s work of the inversion process of elliptic integrals of the first kind and thus of the elliptic function sinam \(u\) itself.     

Structural differences of cone ‘oil-droplets’ in the light and dark adapted retina ofPoecilia reticulata P.

Summary The vast majority of oil-droplets in the dark and light-adapted retinal twin-cones ofPoecilia reticulata is of the matrix-type. In bright light (day light+overhead strip light) there occurs in some regions a very pronounced numerical change from matrix to cristate-type, whereas other regions remain unaffected. The functional significance of these differences is discussed.     

What's nu? A re-examination of Maxwell's ‘ratio-of-units’ argument,from the mechanical theory of the electromagnetic field to ‘On the elementary relations between electrical measurements’

This re-examination of the earliest version of Maxwell's most important argument for the electromagnetic theory of light—the equality between the speed of wave propagation in the electromagnetic ether and the ratio of electrostatic to electromagnetic measures of electrical quantity—establishes unforeseen connections between Maxwell's theoretical electrical metrology and his mechanical theory of the electromagnetic field. Electrical metrology was not neutral with respect to field-theoretic versus action-at-a-distance conceptions of electro-magnetic interaction. Mutual accommodation between these conceptions was reached by Maxwell on the British Association for the Advancement of Science (BAAS) Committee on Electrical Standards by exploiting the measurement of the medium parameters—electric inductive capacity and magnetic permeability—on an arbitrary scale. While he always worked within this constraint in developing the ‘ratio-of-units’ argument mathematically, I maintain that Maxwell came to conceive of the ratio ‘as a velocity’ by treating the medium parameters as physical quantities that could be measured absolutely, which was only possible via the correspondences between electrical and mechanical quantities established in the mechanical theory. I thereby correct two closely-related misconceptions of the ratio-of-units argument—the counterintuitive but widespread notion that the ratio is naturally a speed, and the supposition that Maxwell either inferred or proved this from its dimensional formula.     

Pensions for ‘Cultivators of Science’

The occasional (and belated) concern of the British Government with science in the nineteenth century is a matter of potential interest to historians of science, yet many previous studies have tended to range over a variety of different aspects of the question. There have been too many vague allusions to financial support as ‘money for science’ in general. It is time that particular parts of the problem were unpacked. For example, the award of money (from the 1820s) to pay a few people of independent means for apparatus was quite distinct from the provision (from the 1830s) of an occasional pension. Even then, to speak of ‘pensions’ uncovers unfortunate ambiguities. For too long science in Britain was regarded as no more than a private hobby for the well-to-do. As late as 1856 an official government statement seemed to make this attitude official. The English attitude to pensions differed remarkably from the French, who established a precedent in the reward of savants, sometimes quoted enviously by British men of science. In 1837 Robert Peel virtually admitted that, in awarding pensions to ‘cultivators of science’, he was following the French practice. It may also be useful to emphasise the contrast between the English (often led by Cambridge professors) and the Scots, mostly from Edinburgh, mainly represented here by Whewell and Brewster, respectively. Babbage had a different role in this story from that usually told. A large part in supporting men of science of modest means could have been played by the British Association for the Advancement of Science but it consistently refused to do so, although it supported an elite among its own members.     

Lebesgue’s criticism of Carl Neumann’s method in potential theory

In the 1870s, Carl Neumann proposed the so-called method of the arithmetic mean for solving the Dirichlet problem on convex domains. Neumann’s approach was considered at the time to be a reliable existence proof, following Weierstrass’s criticism of the Dirichlet principle. However, in 1937 H. Lebesgue pointed out a serious gap in Neumann’s proof. Curiously, the erroneous argument once again involved confusion between the notions of infimum and minimum. The objective of this paper is to show that Lebesgue’s sharp criticism of Neumann’s proof was only partially justified.

     

‘Holding’ and ‘endorsing’ claims in the course of scientific activities

My principal aims are to show that holding, adopting and endorsing (definitions of which I provide) are distinct cognitive attitudes that may be taken towards claims at different moments of scientific activities, and that none of them are reducible to acceptance (as defined by Jonathan Cohen); to explore in detail the differences between holding and accepting, using the controversies about GMOs to provide illustrations; and to draw some implications pertinent to democratic decision-making concerning public policies about science and technology, and to the responsibilities that scientists thereby incur.     

Lagrange’s theory of analytical functions and his ideal of purity of method

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline.     

Britton’s theory of the creation of Column $$\varPhi $$ in Babylonian System A lunar theory

The following article has two parts. The first part recounts the history of a series of discoveries by Otto Neugebauer, Bartel van der Waerden, and Asger Aaboe which step by step uncovered the meaning of Column \(\varPhi \), the mysterious leading column in Babylonian System A lunar tables. Their research revealed that Column \(\varPhi \) gives the length in days of the 223-month Saros eclipse cycle and explained the remarkable algebraic relations connecting Column \(\varPhi \) to other columns of the lunar tables describing the duration of 1, 6, or 12 synodic months. Part two presents John Britton’s theory of the genesis of Column \(\varPhi \) and the System A lunar theory starting from a fundamental equation relating the columns discovered by Asger Aaboe. This article is intended to explain and, hopefully, to clarify Britton’s original articles which many readers found difficult to follow.     

‘Action substances’ of peripheral nerve re-visited

Fifty years ago, four action substances were described as being liberated from peripheral nerve in the course of activity. An attempt has been made to update this information. Confirmatory evidence is available that acetylcholine and thiamine do play a role in the course of activity. However, the question of the relationship in time between their release and the electrical events, and the possible effect on specific ionic gating mechanisms, remains unclarified. The liberation of potassium has been found to be a transmembrane K efflux, and the question of the existence of another substance similar to thiamine has not been pursued.a member of the Editorial Board of EXPERIENTIA from 1974 to 1982     

An ‘ecobox’ with a discontinuous temperature gradient and a continuous light intensity gradient

Summary An apparatus is described for culturing micro-algae in a discontinuous temperature gradient and a continuous light intensity gradient. The apparatus provides 100 different combinations of these abiotic factors at 1 time. The crossgradient culture apparatus is called ecobox.     

Temperature-induced reversal of dominance of variegation in ‘Ornamental kale’

Résumé La transmission de l'albinisme panaché deBrassica oleracea L. ne dépend que d'un seul facteur. Chez les hétérozygotes ce caractère apparaît à basse température (7°C), mais pas à haute température (21°C). Chez les homozygotes le caractère se manifeste probablement toujours, tout en restant peu prononcé à des températures plus élevées. Ainsi il y a une inversion du caractère dominant avec changement de température.     

Burnside’s engagement with the “modern theory of statistics”

The group theorist William Burnside devoted much of the last decade of his life to probability and statistics. The work led to contact with Ronald Fisher who was on his way to becoming the leading statistician of the age and with Karl Pearson, the man Fisher supplanted. Burnside corresponded with Fisher for nearly three years until their correspondence ended abruptly. This paper examines Burnside’s interactions with the statisticians and looks more generally at his work in probability and statistics. I am grateful to June Barrow-Green and Tony Mann for showing me important letters, to Susan Woodburn, Elise Bennetto and Jeniffer Beauchamps of the University of Adelaide for help with letters to Fisher and to Jonathan Harrison of St. John’s Cambridge for help with letters to Baker and White. Peter Neumann, the editor and a referee made helpful comments on an earlier draft.     

Studies on the hypoglycemic effect of ‘Vincamin’

Zusammenfassung Nach Verabreichung von Vincamin sinkt bei akuten Versuchen an Ratten der Blutzuckerspiegel. Die nach Dextroseverfütterung verursachte Hyperglykämie wird durch Vincamin verhindert, der Blutzuckeranstieg jedoch bleibt nach Adrenalin unbeeinflusst.     

‘Chromatoid body’ in the spermatogenesis of scorpions

Zusammenfassung Die von früheren Autoren als «Chromatoidkörper» bezeichnete Struktur der Spermatozoiden von Skorpionen,Palamnaeus bengalensis, ist kein wirklicher «Chromatoidkörper», sondern ein Hilfskörper lipoprotonischer Natur ohne jegliche RNA.