Before 1600 the most common method of division used in Europe was the galley, batello, or scratch method, and this was still popular up to the end of the eighteenth century. This method is commonly supposed to be of Hindu origin, being based on a method found in India about the fourth century. It will be shown that the Hindu method is identical to the Chinese method of division (ch'u) mentioned in very early Chinese texts such as the Chiu Chang Suan Shu (Nine Chapters on the Mathematical Art, c. first century a.d.). The earliest detailed description of this method is found in the Sun Tzŭ Suan Ching (The Mathematical Manual of Master Sun, third century a.d.).

As has become evident from historical studies, science does not proceed in the coherent and predictable way that basic science texts would have us believe. I will argue that an excellent counter-example is an episode from the historical development of quantum mechanics in which the incompatibility of the particle and the wave representations of the electron and light were destined to be encompassed by two mathematically equivalent, but conceptually quite different theories.

I shall argue that the appearance of two such different, yet equivalent, quantum theories was not surprising at all and I claim even predictable. As Einstein himself wrote in 1909: ‘It is my opinion that the next phase in the development of theoretical physics will bring us a theory of light that can be interpreted as a kind of fusion of the wave and the [particle] theory.’ Certainly, the interpretative content of Werner Heisenberg's and Erwin Schrödinger's theories could not have been more different. By mid-1926, the theoretical foundations had been laid for a scientific and emotional battleground between the particle and the wave. I suggest that an important element in the debate was not the incompatibility itself but actually coming to terms with ambiguity in science. For, in the end, ambiguous and vague interpretations of the same phenomena became part of science, where science was supposed to give a clear and unambiguous description of nature.

Built in Greenwich in 1675–1676, the Royal Observatory was situated outside the capital but was deeply enmeshed within its knowledge networks and communities of practice. Scholars have tended to focus on the links cultivated by the Astronomers Royal within scholarly communities in England and Europe but the observatory was also deeply reliant on and engaged with London's institutions and practical mathematical community. It was a royal foundation, situated within one government board, taking a leading role on another, and overseen by Visitors selected by the Royal Society of London. These links helped develop institutional continuity, while instrument-makers, assistants and other collaborators, who were often active in the city as mathematical authors and teachers, formed an extended community with interest in the observatory's continued existence. After outlining the often highly contingent institutional and personal connections that shaped and supported the observatory, this article considers the role of two early assistants, James Hodgson and Thomas Weston. By championing John Flamsteed's legacy and sharing observatory knowledge and practice beyond its walls, they ensured awareness of and potential users for its outputs. They and their successors helped to develop a particular, and ultimately influential, approach to astronomical and mathematical practice and teaching.

This paper throws light on the development of experimental zoology in Britain by focusing on the establishment of the British Journal of Experimental Biology (BJEB) and the Society for Experimental Biology (SEB) in 1923. The key actors in this story were Lancelot T. Hogben, Julian S. Huxley and Francis A.E. Crew, who started exploring the possibility of establishing an experimentally oriented zoological journal in 1922. In order to support the BJEB and further the cause of the experimental approach, Hogben, Crew, Huxley and their colleagues decided to found a society, which led to the formation of the SEB. From its inception the journal was plagued with difficulties that led to the merger of the BJEB and the Biological Proceedings of the Cambridge Philosophical Society in the autumn of 1925. Also discussed are the views that the leading proponents of experimental zoology in Britain in the 1920s expressed towards morphology and how their views further complicate the already much modified ‘revolt from morphology’ thesis.

The Cambridge school of animal morphology dominated British zoology in the late nineteenth century. Historians have argued that they were very successful until the death of their leader F. M. Balfour in 1882, when the school all but died with him. This paper argues that their initial success came about because their work fitted well with the university in the 1870s and 1880s. They attempted to trace evolutionary trees by studying individual development. To do this they needed access to species they considered primitive. Balfour made use of his social networks to aid the school and to collect the specimens they needed for their work. The school has been portrayed as failing in the 1890s when students rejected dry laboratory-bound studies. However, a new generation of researchers who followed Balfour had to travel extensively if they were to obtain the organisms they needed. International travel was popular amongst zoologists and the Cambridge school developed their own extensive networks. A new breed of adventurer–zoologists arose, but because of the school's tenuous position within the university they were unable to equal Balfour's success.

With the death of Joseph Needham on 24 March 1995 the world of learning lost one of the greatest scholars in this or any country, of this or any century. For more than thirty years Needham had been the greatest sinologist in the West, having previously achieved an international status as a research biochemist and as a historian. Intellectually a bridge-builder between science, religion and Marxist socialism, and supremely so between East and West, he has been called the Erasmus of the twentieth century. A sober assessment suggests that with the passage of time he will be recognized as a greater figure than the scholar from Rotterdam.

In 1878, amid a rapidly proliferating social interest in public health and cleanliness, a group of sanitary scientists and reformers founded the Parkes Museum of Hygiene in central London. Dirt and contagion knew no social boundaries, and the Parkes's founders conceived of the museum as a dynamic space for all classes to better themselves and their environments. They promoted sanitary science through a variety of initiatives: exhibits of scientific, medical and architectural paraphernalia; product endorsements; and lectures and certificated courses in practical sanitation, food inspection and tropical hygiene. While the Parkes's programmes reified the era's hierarchies of class and gender, it also pursued a public-health mission that cut across these divisions. Set apart from the great cultural and scientific popular museums that dominated Victorian London, it exhibited a collection with little intrinsic value, and offered an education in hygiene designed to be imported into visitors’ homes and into urban spaces in the metropole and beyond. This essay explores the unique contributions of the Parkes Museum to late nineteenth-century sanitary science and to museum development, even as the growth of public-health policy rendered the museum obsolete.

The catalogues of mid-eighteenth-century mathematical instrument makers included not only instruments in the sense ‘tools of science’ but also devices intended primarily for educational use. Among the latter would be found mechanical models of the solar system, in varying degrees of complexity and under various names; for convenience such models may be, and often were, loosely called orreries.

Freemasonry was the most widespread form of secular association in eighteenth-century England, providing a model for other forms of urban sociability and a stimulus to music and the arts. Many members of the Royal Society and the Society of Antiquaries, for instance, were Freemasons, while historians such as Margaret Jacob have argued that Freemasonry was inspired by Whig Newtonianism and played an important role in European Enlightenment scientific education. This paper illustrates the importance of natural philosophy in Masonic rhetoric and utilizes material from Masonic histories, lodge records and secondary works to demonstrate that scientific lectures were indeed given in some lodges. It contends, however, that there were other sources of inspiration for Freemasonry besides Newtonianism, such as antiquarianism, and that many other factors as well as the prevalence of Masonic lodges determined the geography of English scientific culture. Although the subject of Freemasonry and natural philosophy has great potential, as Jacob has demonstrated so well, much further work, especially in the form of prosopographical studies of provincial lodges, is required before the nature of the relationship between the two can be fully appreciated.

The metamathematical framework of the early modern period is primarily determined by two presuppositions stemming from the Aristotelian tradition: (1) mathematical objects are abstracted from sensible matter; (2) imagination is a reproductive faculty exclusively connected with the sensible realm. The recovery of the works of the Greek commentators confronted the early modern readers with rivalling philosophical–mathematical views that explicitly called into question some of their previously undisputed assumptions. In this article I will argue that Francesco Piccolomini (1523–1607) in his Academicae contemplationes brings about an original fusion of these colliding horizons, by transposing the synthesis established by (?)Simplicius between Aristotelian abstractionism and Neoplatonic innatism into the sixteenth century.

Only weeks following Queen Victoria's ascension to the throne on 20 June 1837, a controversy brewed over the naming of the ‘vegetable wonder’ known today as Victoria amazonica (Sowerby). This gargantuan lily was encountered by the Royal Geographical Society's explorer Robert Schomburgk in British Guyana on New Year's Day, 1837. Following Schomburgk's wishes, metropolitan naturalists sought Victoria's pleasure in naming the flower after her, but the involvement of multiple agents and obfuscation of their actions resulted in two royal names for the lily: Victoria regina (Gray) and Victoria regia (Lindley). To resolve the duplicity in names, the protagonists, John Edward Gray and John Lindley, made priority claims for their respective names, ultimately founding their authorities on conventions aligned with gentlemanly manners and deference to nobility. This article will analyse the controversy, hitherto unexamined by historians, and argue for its significance in repositioning Queen Victoria – and nobility generally – as central agents in the making of authority in early Victorian science.

Frederick Soddy's productive pure research ended with the outbreak of World War I. Before that time Soddy was internationally acknowledged as a great scientist. He had, with Rutherford, produced the atomic disintegration theory and, in association with Ramsay, had proved it experimentally. He had been one of the first men to elucidate the nature of isotopes, and it was he who gave them their name. After the war he was dismissed as a man who had forsaken his science to propound wild theories of monetary reform.

In the Annual Report of University College London (UCL) for 1946–47 it is stated that ‘the Department of History and Philosophy of Science played a leading part in the formation of the British Society for the History of Science’ and that four members or former members of the department were serving on its Council, one of them as the founder president. A brief account of the early history of the department may therefore be of interest to members of the Society.

The Century between the death of Copernicus (1543) and the birth of Newton (1642) witnessed a major reshaping of traditional ways of viewing the universe. The Ptolemaic system was challenged by Copernican heliocentrism, the Aristotelian world was assailed by Galilean physics and revived atomism, and theology was troubled by the progressive distancing of God from the daily operation of His creation. Besides earning this era the title of ‘the Scientific Revolution’, the intellectual ferment of these times offered many world systems as successors to the throne of crumbling Aristotelianism.

There existed between Charles Lyell and Roderick Impey Murchison, the two most prominent British geologists of the mid-nineteenth century, a rivalry that was personal, professional, and theoretical. This rivalry, which was for the most part friendly, was most keenly felt by Murchison, who was always envious of the popular and professional success of Lyell's theories. Although both were born in Scotland and raised in England, where they lived most of their lives, their early lives were considerably different. Murchison's early career as an army officer and fox hunter contrasts rather strongly with Lyell's academic life at Oxford and as a law student. Each was the eldest child of a well-to-do Scottish family. Although Lyell's family was much the wealthier, Murchison personally always had more money than Lyell since Murchison ultimately inherited the estates of his father, father-in-law, and uncle, while Lyell's inheritance waited until his father's death in 1849, at which time the estate was left in trust for the many Lyell children.

When Charles Lyell was writing his Principles of geology early in 1830, he interpolated five chapters between a recently written historical account of the science and the main body of textual material whose structure had long been determined. These added chapters contained not only Lyell's effort ‘to express the consequences of the uniformity of nature in the history of the earth’, but also his general arguments against the catastro-phic-progressionist interpretation, which he felt obliged to refute. In Chapter IX, the final one in the introductory sections, Lyell chose as representative of the progressionist view, Sir Humphry Davy, ‘a late distinguished writer’ who had ‘advanced some of the weightiest of these objections’ to Lyell's own steady-state view of the earth. No other defender of the progressionist history of the earth was named in Lyell's chapter, and we might well ask, why Humphry Davy? Was he merely an easy target for Lyell's refutations, a straw man set up by Lyell for his own rhetorical convenience?

The following essay is adapted from one with the same title read to the British Society for the History of Science on 20 October 1958—the anniversary, by a striking coincidence, of the birth of W. H. Young (1863–1942). To his memory I dedicated the talk, and now rededicate its publication, not only because I am his daughter and of all that means, but because he invented a method, the method of monotone sequences, which shows the powerfulness of inequalities as a mathematical tool supremely.

The paper is an attempt to set the social and historical background against which the Royal Institution was founded, and to trace the events in its very early history. The founder of the Institution was Benjamin Thompson, Count Rumford, that soldier of fortune who took service with the Elector Palatine of Bavaria, and it was in the course of his duties in Munich that his interest in the practical problems of philanthropy was aroused.

In London, in the concluding years of the eighteenth century, he was drawn into the group of philanthropists and reformers among whom William Wilberforce was the leading figure, and Sir Thomas Bernard, Treasurer of the Foundling Hospital, one of the most active members. The focus of their activities was the Society for Bettering the Condition and Increasing the Comforts of the Poor, and to this Society Rumford submitted his proposals for a new scientific institution in London, designed to improve the lot of the poor and the working classes by the application of science to useful purposes.

It was decided to make an appeal for funds, Rumford's proposals were circulated, and the Count succeeded in interesting the President of the Royal Society, Sir Joseph Banks, who took the Chair at the early meetings and allowed them to be held at his house, 32 Soho Square. At a meeting held there on 7 March 1799, the new institution was formed by resolution of the subscribers of 50 guineas each, who became the first Proprietors of the Royal Institution of Great Britain, as it was afterwards named in its Royal Charter.