The history of the magic lantern provides a privileged case study with which to explore the histories of projection, demonstration, illusion and the occult, and their different intersections. I focus on the role of the magic lantern in the work of the Jesuit Athanasius Kircher and the French Cartesian Abbé de Vallemont. After explaining the various meanings of the seventeenth-century concept of illusio, I propose a new solution for the long-standing problem that Kircher added the ‘wrong’ illustrations to his description of the lantern. The complex interaction between text, image and performance was crucial in Kircher's work and these ‘wrong’ figures provide us with a key to interpreting his Ars Magna. I argue that Vallemont used the magic lantern in a similar rhetorical way in a crucial phase of his argument. The magic lantern should not be understood merely as an illustrative image or an item of demonstration apparatus; rather the instrument is employed as part of a performance which is not meant simply to be entertaining. Both authors used a special form of scientific demonstration, which I will term ‘analogical demonstration’, to bolster their world view. This account opens new ways to think about the relation between instruments and the occult.

Sol fons lucis universi, vas admirabile, opus Excelsi, divinitatis thalamus, risus coeli, decor, & pulchritudo mundiA. Kircher

For one of those Gnostics, the visible universe was an illusion or, more precisely, a sophism. Mirrors and fatherhood are abominable because they multiply it and extend it.J. L. Borges

In early nineteenth-century London audiences flocked to a variety of lectures and shows on astronomical topics. While the religious and social positions of the lecturers and showmen varied significantly, the vast majority adopted a Newtonian cosmology incorporating a belief in the plurality of worlds. This paper focuses on Isaac Frost's 1846 book Two Systems of Astronomy in an attempt to gain a fuller understanding of how some thinkers in plebeian London responded to and resisted this emergent astronomical orthodoxy. Central to this analysis is research that reveals how changes in the intellectual world of Frost and his Muggletonian co-religionists prompted this formerly non-proselytizing Protestant sect to become increasingly vocal during the nineteenth century. This research is based upon a thorough examination of the Muggletonian archive in the British Library together with a collection of approximately thirty Muggletonian letters deposited in the Oxfordshire Records Office in 1993 and not examined by previous historians. It is concluded that the unorthodox or anti-Newtonian cosmologies advanced by several early nineteenth-century thinkers were often intellectually coherent and embodied in receptive social contexts.

Today the economic diagram is employed universally in teaching and research by professional economists. Yet the history of its construction shows that much that has been regarded as distinctive of twentieth-century visual culture was prefigured in the nineteenth. This paper will place the construction of the first economic diagrams by Alfred Marshall in the context both of contemporary visual technologies developed in other moral sciences, and of his wider theory of industrial production. The paper will argue that an understanding of the background to the historical graphs, constructed by the Cambridge political economist from the late 1860s onwards, will necessitate a revision of the narrative of modern visual reasoning, as recently advanced by Lev Manovich.

As one of the most tireless advocates of Modernism in the Church of England, Ernest William Barnes (1874–1953) was the subject of both veneration and scorn. The position Barnes adopted on evolution during the inter-war years, the period during which he was installed as the Bishop of Birmingham, has been the focus of recent scholarship. In particular, his spiritual agenda departed from those of most Modernists in that it encouraged the faithful to accept the precepts of evolution and Mendelism while it repudiated Lamarckian progressivism. Indeed, his unadulterated appreciation of neo-evolutionary theories makes it easier to understand his willingness to promote eugenic principles.

Another unusual aspect of Barnes's Modernist theology, however, remains to be examined in any detail – namely its mathematical underpinnings. Before rising to his bishopric, Barnes was elected a Fellow of the Royal Society on the strength of his mathematical research. Further, his reputation as one knowledgeable in both modern mathematical and biological investigations provided an authoritative legitimacy that was meant to enhance his efforts at reconciliation, including his Gifford Lectures of 1927 to 1929. This paper examines Barnes's promotion of Riemannian geometry, especially as it relates to the consolation he found in the concept of a finite universe. Ultimately it asserts that mathematics made essential contributions to a cosmological perspective integral to his Modernism.