ABSTRACTThis paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to (...) initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the ‘abstract algebra’ and ‘abstract geometry’ of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to ‘algebraical geometry’ and ‘geometrical algebra’ of the second generation of ‘scientific’ symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s–1840s. (shrink)

In the second half of the nineteenth century, gas discharge research was transformed from a playful and fragmented field into a new branch of physical science and technology. From the 1850s onwards, several technical innovations – powerful high-voltage supplies, the enhancement of glass-blowing skills, or the introduction of mercury air-pumps – allowed for a major extension of experimental practices and expansion of the phenomenological field. Gas discharge tubes served as containers in which resources from various disciplinary contexts could be brought (...) together; along with the experimental apparatus built around them the tubes developed into increasingly complex interfaces mediating between the human senses and the micro-world. The focus of the following paper will be on the physicist and chemist Johann Wilhelm Hittorf , his educational background and his attempts to understand gaseous conduction as a process of interaction between electrical energy and matter. Hittorf started a long-term project in gas discharge research in the early 1860s. In his research he tried to combine a morphological exploration of gas discharge phenomena – aiming at the experimental production of a coherent phenomenological manifold – with the definition and precise measurements of physical properties. (shrink)