A collection of public lectures by a leading nineteenth-century scientist surveys foundational scientific ideas and their practical and philosophical implications. Essays range from a memorial sketch of a colleague and an autobiographical sketch to explorations of the axioms underlying geometry, the connections between optics and painting (treating form, shade, colour, and harmony), theories of planetary formation, and the role of reflective thought in medicine. Contributions mix historical perspective, clear exposition of principles, and reflections on academic freedom and scientific method, aiming to make complex topics accessible to educated readers.