Abstract

This collection belongs to a distinguished series and contains a number of outstanding essays. Some of the essays, notably those by Alan Shapiro, Michael Nauenberg, and George Smith, expand on work published in The Foundations of Newtonian Scholarship, edited by Richard H. Dalitz and Nauenberg , which can be seen as a companion volume.Jed Buchwald and I. Bernard Cohen identify two strands of contemporary Newtonian research. The first, “Motivations and Methods,” opens with an essay by Maurizo Mamiani on the sources for the Regulae Philosophandi in Book 3 of Newton's Principia. Relying on his previous critical edition of Newton's Treatise on the Apocalypse, Mamiani shows that “Robert Sanderson's [1631] Logicae Artis Compendium is the primary source of Newton's rules” . Thus circa 1672 Newton adapted Sanderson's laws first to biblical exegesis and later to the investigation of nature. Cohen compares Newton's Opticks with Huygens's Traité de la lumière, shedding light on the history of their editions. Shapiro's study on diffraction presents a detailed analysis of Newton's experimental investigations, with particular emphasis on quantitative methods. Shapiro argues that not only Robert Hooke's role but also “Newton's inability to conclude the part [of the Opticks] on diffraction was a principal reason” for the delay of its publication until 1704 . Mordechai Feingold outlines a picture of the Royal Society where, a few years after its foundation, two factions emerge, the naturalists and the mathematicians. His interpretation provides a convincing key for interpreting events at the society in Newton's time and beyond.The second strand, “Celestial Dynamics and Rational Mechanics,” opens with an essay by Bruce Brackenridge on the interplay among Newton's three different ways to represent curves, which he calls the “polygonal, parabolic, and the curvature methods.” Essays by Nauenberg and Curtis Wilson provide starkly contrasting perspectives on Newton's investigations on lunar motion in relation to those of later mathematicians. According to Nauenberg, the perturbation method developed by Newton in the Portsmouth papers is remarkable and “corresponds” to later methods developed by Leonhard Euler and George W. Hill: “The evidence presented here indicates that [Newton] could have succeeded in his quest to evaluate correctly higher‐order terms to the motion of the lunar apogee had he continued to pursue his method more carefully, particular[ly] in regard to the dependence on the orbit's eccentricity” . By contrast, Wilson emphasizes the differences between Newton's and later contributions. A crucial section in his essay addresses the same problem that is at the center of Nauenberg's work but reaches opposite conclusions. The section is titled “Why It Is Unlikely that Newton Would Ever Have Solved the Problem of the Moon's Apsidal Motion Correctly” . In his remarkable study, Wilson identifies several important differences between Newton and his successors, such as the shift from geometrical to analytic methods. The problem of the apsidal motion can only be solved in a “blind, iterative” algorithmic fashion, one Newton did not prefer. Moreover, Wilson argues that whereas the solutions by Leonhard and Johann Albrecht Euler and by Hill “started from differential equations that stated exactly the conditions of the problem” and allowed a close check of the approximations adopted, “Newton's calculative procedure … provides no internal check on the accuracy of [his] assumptions or of his results” . Although both Nauenberg and Wilson employ modern notation, Wilson is more careful in conveying the sense of Newton's style and original way of proceeding. Michel Blay's fine essay identifies the main aim of Newton's Principia as determining how one can “achieve mathematical rigor in the transition from the discontinuous to the continuous” . Traditionally historians have identified the laws of motion, especially the second law, as the intellectual cornerstone of Newton's masterpiece. Blay's conclusion, however, is that “the real driving force of Newton's dynamics, the coherence of the Principia, resides in the lemmas of Section 1” .George Smith's essay on Book 2 of the Principia is probably the most original and innovative contribution to this volume and one of the most important studies of Newton's work. It will become a classic in the field. Smith, a philosopher and engineer by profession, has the technical skills and the historicophilosophical sophistication to deal with the complex issues of motion in resisting media and to analyze Newton's problematic experiments and theories. Book 2 has traditionally been little studied and bracketed off as a rather cumbersome and unfortunate aside in Newton's oeuvre. Smith's work sheds new light on it and at the same time shows the profound links with better‐known aspects of Newton's research. A useful appendix to his essay contains a translation of those passages on fluid resistance from the first edition that were replaced or removed in the later editions. Finally, an essay by the late Sam Westfall analyzes the background to the mathematization of nature in the sixteenth and seventeenth centuries, focusing on four technologies: water management, military engineering, navigation, and cartography. Westfall's conclusion relates to his interest in patronage and argues that the advances in seventeenth‐century mathematics are “perhaps partly” due to a “greater demand for mathematical expertise than any previous society ever had” . His article is accompanied by an eloge by Cohen.I very much hope that a paperback edition will make this important volume available to a wider audience