This article by Curtis Wilson is an account of the origin of Hansen’s powerful systematic method for finding contributions of higher order perturbations in celestial mechanics. Hansen’s method was developed in the course of improving on Laplace’s treatment of the mutual perturbations of Jupiter and Saturn. This method, an entirely new way of doing celestial mechanics when it first appeared, later made possible the successful treatment of the complicated motions of our moon (see Wilson 2010). In this paper Wilson gives (...) a brief historical introduction followed by an account of relevant technical details of the Laplacian background, an account illustrating technical details in Hansen’s initial development in his Disquisitions of 1829, and a treatment illustrating details contributing to the achievement of Hansen’s more refined development in his Untersuchung of 1831. These details include conditional equations Hansen provides for checking the accuracy of calculations. Wilson also includes a detailed assessment showing the extraordinary improvement in empirical accuracy of Hansen’s treatment over the best earlier treatment of the Jupiter-Saturn interactions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:120 HISTORY OF PHILOSOPHY Opera theologica quae latine edidit, 3 vols. (Roterodami, 1651-1660). His religious polemics with Amyrault and Grofius were famous. Paul Dibon, professor at the Ecole Pratique des Hautes Etudes, is the most prominent contemporary historian of seventeenth-century Dutch philosophy and intellectual life; he is perfectly aware of the fact that genuine history can only be founded on solid erudition, and this inventory is a first-class contribution (...) to it. Only those who ignore the difficulties of this kind of research will underestimate the enormous effort it involves--an effort which is, much more than a pedantic and mechanical listing of data, a kind of venatio, requiring a continuous alertness, a surprising amount of imagination and intelligence, a painstaking precision, and an enormous background of knowledge. The letters are arranged in chronological order (with the exception of a few which are undated). Each entry lists the date, the names and locations of the sender and addressee, and the opening words of the letter. The status of the letter (original/ minute/copy/printed) is indicated, as is the library in which the letter is located (and the call number), and/or, if the letter was published, the printed source. Thirty-two libraries were explored. GIORGIO TONELLI State University o/ New York at Binghamton Introduction to Newton's Principia. By I. Bernard Cohen. (Cambridge, Mass.: Harvard University Press, 1971. Pp. xxx+380. $30.00) Over the past dozen years or so Newtonian scholarship has burgeoned as never before, and a first and fundamental result has been the publication of more and more of the wealth of manuscript material and letters that Newton left as a legacy of potential insight and confusion to future scholars. To date, the most imposing of the undertakings in publication have been The Correspondence (1959- ), begun under the editorship of H. W. Turnbull and continued more recently under that of J. F. Scott, and the Mathematical Papers (1967- ), started and continuing under the editorship of D. T. Whiteside. Selected documents of importance have been published by I. Bernard Cohen, assisted by Robert E. Schofield, in Isaac Newton's Papers and Letters on Natural Philosophy... (1958), by A. R. Hall and Marie Boas Hall in Unpublished Scientific Papers o/ Isaac Newton (1962), and by J. W. Herivel in The Background of Newton's Principia (1965); additional documentary material has appeared in studies by Alexandre Koyr6, I. Bernard Cohen, Johannes A. Lohne, D. T. Whiteside, Richard S. Wesffall, J. E. McGuire and P. M. Rattansi, and still others--a full bibliography would run to considerable length. Nor, although the uncertainties in the interpretation of the documents are sometimes overwhelming, has this spate of publication merely served to replace one set of scholarly puzzles by another. The traditional, monolithic and impenetrable image of Newton "with his prism and silent face, / The marble index of a mind for ever / Voyaging through strange seas of Thought, alone..." has lost something of its hypnotic hold, and we begin to discern some of the steps, not to say jogs and leaps, in Newton's actual journey of thought and discovery. The volume here under review introduces another major enterprise in Newtonian scholarship, a "variorum" edition of the Principia. The edition itself, which has yet to appear, will consist primarily of a facsimile reproduction of the third edition (1726)-the last edition that Newton himself supervised----collated line by line with the variant readings in the two prior editions and in a manuscript of the first edition, and with the BOOK REVIEWS 121 corrections, improvements, and additions that Newton entered into copies of the first and second editions. This textual part of the edition was delivered to the press in 1966; additional parts are in various stages of preparation. There is to be a Commentary dealing with the prefaces, definitions, laws of motion, and the first three sections of Book I and most of Book III, along with English versions and modern analytical paraphrases of the sections dealt with, a glossary, and a number of short essays on such topics as the astronomical and physical data used by Newton, the mathematical background to the understanding of the Principia, and the analysis of... (shrink)

The present volume, like other volumes in this series, has the aim of introducing nonspecialists to the work of “a difficult and challenging thinker”. Galileo’s thought is often difficult to penetrate; scholars often clash in their interpretations of it.