I. Birth and Education
1. Early Years
2. Trinity College and Dunsink Observatory
3. Life at the Observatory
II. Ray Optics
4. The "Theory of Systems of Rays"
5. Creating the "Theory of Systems of Rays"
6. Conical Refraction
7. Philosophical Romance
8. Helen Bayly
IV. Light and Dynamics
9. Theories of Light
10. Optics at the British Association
11. The Luminiferous Aether
12. The Metaphysical Foundations of Mechanics
13. The General Method in Dynamics
14. The Fate of the Optical-Mechanical Analogy
V. Politics and Religion
15. Reform and Religious Turmoil
16. In and Out of the Oxford Movement
VI. "Algebra as the Science of Pure Time"
17. The Foundations of Algebra and the Coleridgean View of Science
18. "Algebra as the Science of Pure time"
19. The Kantian Content of the "Essay on Algebra as the Science of Pure Time"
20. The Equation of the Fifth Degree
21. From Algebraic Couples to Quaternions
22. The Creation of Quarternions
23. The Fate of Quarternions
24. The Hodograph and the Icosian Calculus
VIII. Last Years
25. Catherine Disney Barlow
26. The End of a Career
27. Hamilton and Nineteenth-Century Science
Appendix: The Equations of Conjugation and Logarithms of Number Couples
Abbreviations Used in the Notes
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