The Language of Physics

I: Introduction.- Mathematics and Modern Physics.- Modern Physics.- Earlier Historical Approaches to Modern Physics.- Mathematics as Language.- Organization of the Text.- I: Eighteenth-Century Science.- II: Vibrating Strings and Eighteenth-Century Mechanics.- Mathematics from Physics.- Ignoring Physics.- Eighteenth-Century Mechanics and the History of Physics.- III: Eighteenth-Century Physics and Mathematics: A Reassessment.- Physics as Experimental Philosophy.- The Practice of Mathematics.- The Intellectual Geography of Physics and Mathematics.- The Social Geography of Physics and Mathematics.- II: Transitions, 1790–1830.- IV: “Empirical Literalism”: Mathematical Versus Experimental Physics in France, 1790–1830.- Changes in Social Geography, 1790–1830.- Experimental Physics.- Electricity and Magnetism.- Heat.- Light and Elasticity.- French Mathematics and Physics c. 1830: Some Conclusions.- V: On the Margins: Experimental Physics and Mathematics in the German States, 1790–1830.- Prologue.- Physics and Mathematics in the German States, 1790–1830.- University Reform and Career Opportunities.- Changes in Physics in the 1820s.- Changes in Mathematics in the 1820s.- VI: On the Margins: Experimental Philosophy and Mathematics in Britain, 1790–1830.- Social Institutions.- Natural Philosophy and the Universities.- Intellectual Organization of Research, 1800–1820.- Mathematics in Britain, 1790–1820.- Natural Philosophy and Mathematics in the 1820s.- III: Transformations, 1830–1870.- VII: From Natural Philosophy and “Mixed Mathematics” to Theoretical and Experimental Physics: Britain, 1830–1870.- Keywords.- The Crucial Turn: the 1830s.- Cambridge University, the Cambridge Mathematical Journal, and Theoretical Physics.- William Thomson.- George Gabriel Stokes.- James Clerk Maxwell.- VIII: Physics and Mathematics in the German States, 1830–1870.- Mathematical Physics as Mathematics.- The Transformation of Physics: The First Generation.- Franz Neumann.- Wilhelm Weber.- Clausius and Helmholtz.- IV: Conclusions and Epilogue.- IX: Physics About 1870 and the “Decline” of French Physics.- The “Decline” of French Physics.- Some Conclusions.- X: Epilogue: Forging New Relationships: 1870–1914.- The Limitations of Autonomy.- Mathematics in Physics.- Beyond the Calculus.- Physicists Versus Mathematicians.