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G. N. Cantor. Optics after Newton. Theories of light in Britain and Ireland, 1704–1840 . Manchester: Manchester University Press, 1983. Pp. ix + 257. ISBN 0-7190-0938-3. £20.

Faced with the 'Euler phenomenon' (Fellmann's own phrase) most authors have confined themselves to surveying Euler's work, taking on the work of his contemporaries as it impinged on Euler himself. This is also the traditional approach of the editors of Euler's works. Few have taken the opportunity, as Truesdell so usefully did in 1960, of attempting an overview of their patch as it developed in Euler's time. Moreover, those authors who do consider Euler in context are constrained rather too much by the shortage of space available, and on these occasions most of their scholarship is in the footnotes in the form of further reading that expands upon their essays. When in due course the eighteenth century receives more attention then it has had of late, what will we need and how will this book help us? I think we will need to develop a conceptual language with which to distill and not just to chop down the problems. For example, in his pure mathematics Euler was highly algebraic, his organizing concept was that of function, his interest in foundational questions limited to a naive use of infinitesimals. He re-created the calculus as he derived it from Leibniz and Newton, and extended it greatly by his investigation of the calculus of several variables. The role of differential equations in organizing mathematics and mathematical physics is one of his greatest perceptions, as numerous authors here attest. But if what Euler did is clear, it is still not obvious how we should organize our analysis of it, how to structure it, how to perceive and present its central problems. Beyond the definitions, beyond the off-quoted passages and the pertinent correspondence, what was the shifting core of the action? Can one find a way of describing how Euler gradually discovered a theory of numbers beneath the sparkle of disparate problems (here well described by Weil and Scharlau) which does not instead make it too intentional, but exhibits Euler's intuitions at their proper level? Or will the sprawling nature of history defeat us? The matter is more urgent in applied mathematics, where we have to deal with eighteenth century concepts we now find muddled, even flawed. Euler's success with the moon is well-known, and nicely told here by Volk, but Euler's theoretical dynamics invokes the mysterious vis (In this connection, see also I Szabo: Geschichte der mechanischen Principien und ihrer wichstigsten Anwendungen, Birkhaiiser, Basel, 1979). Cross's essay, drawn from work in progress on potential theory, will be a way in to the history of physical ideas that goes beyond exhuming attractive pieces of mathematics. We need a way of formulating scientific practise as an always imprecise debate with nature that does not lapse into metaphysics. As we grope our way towards it, this book will help us get started, and to measure our simplicities against the century's greatest pioneer. The ocean of scholarship, in which even good work can drown in neglect, has been usefully contracted by this book, we are in the editors' debt.