Historiographically, this work seeks to transcend the customary field versus particle dualism utilised by historians of physics with respect to Maxwell’s greatest contributions: the theory of electromagnetism and the kinetic theory of gases. By avoiding this traditional presentation, Harman allows a more contextualised analysis responsive to Maxwell’s own evolving conceptualisations. To this end, his explicit aim is ‘to describe the structure of Maxwell’s physical worldview. . . and to elucidate its architecture by tracing the motifs which thread their way through his natural philosophy’ (p. 10). These recurring themes give the book its structure.

The introductory chapters discuss the context of Maxwell’s place within the history of classical physics (Ch. I) and the formative influences engendered by Edinburgh experimental physics and metaphysics and Cambridge mathematics and philosophy of science (Ch. II, Ch. III). Maxwell’s early researches on the theory of colour vision and the motion of Saturn’s rings exemplified his ability to synthesize experimental and mathematical skills. Subsequent chapters stress the principal themes of Maxwell’s physical worldview including: ‘Physical and geometrical analogy’ (Ch. IV), ‘Models and mechanisms’ (Ch. V), and ‘Dynamical and statistical explanation’ (Ch. VI). Among motifs characterizing Maxwell’s natural philosophy, Harman discerns three fundamental relationships: 1) between physical analogies and mechanical models; 2) between models and more general dynamical principles; and 3) between dynamical laws and statistical explanations. By exploring these relationships, Harman illustrates how Maxwell evolved as a natural philosopher, always concerned to develop a comprehensive worldview.

While stressing thematic organisation, Harman skillfully weaves together the broad changes in nineteenth-century mathematics, physical sciences, and philosophy with Maxwell’s evolution as a natural philosopher. Lifelong interests in methodological and philosophical problems crucially shaped Maxwell’s science. Largely due to the influence of Edinburgh professor of Logic and Metaphysics William Hamilton, he embraced the power of analogy and the intelligibility of scientific concepts. Also linking him to the Scottish ‘common sense’ school were his preference for geometrical models and cautious attitude toward hypotheses. Concepts of intelligibility and clarity, expressed via geometrical models, characterised much of Maxwell’s work. At Cambridge, he also adopted and adapted methodological concepts, such as William Whewell’s ‘fundamental ideas.’

Permeating Harman’s account are the diverse ways in which Maxwell utilised the interacting concepts of geometry, intelligibility, and analogy. Sparked by William Thomson’s use of ‘mathematical analogy’ between electrostatic attraction and heat conduction, Maxwell’s initial attack on electricity conceptually transformed the work of both Thomson and Michael Faraday. ‘On Faraday’s lines of force’ (1856) appealed to a ‘physical analogy’ between electricity and an imaginary incompressible fluid flowing in tubes. Using this tactic, Maxwell obtained physical ideas without adopting a physical theory. In his view, the inherently geometrical imagery of ‘lines of force’ gave them intelligibility. Avoiding the adoption of physical properties, this model’s primary function was of mathematical resemblance.

Upon reading papers on gas theory by Rudolf Clausius, Maxwell developed a different type of ‘physical analogy’ comparing properties of gas molecules with colliding elastic spheres. Although meant as a physical explanation, his ‘Illustrations of the dynamical theory of gases’ (1860) warned that gas molecules could also be treated as ‘centres of force’ with identical results. Despite this caveat, Maxwell clearly intended to generate a physical account of gases.

Encouraged perhaps by his successful use of ‘physical analogy’ in describing properties of gases, the four-part ‘On physical lines of force’ (1861-62) sought a similar explanation for electromagnetism. Inspired by Thomson’s use of ‘molecular vortices’ to account for the magneto-optical effect, Maxwell identified his hypothesis of ‘molecular vortices’ with the mechanics of an etherial field. As Harman clearly illustrates, Maxwell extended mechanical modeling in different parts of the paper through innovations such as the ‘idle wheels’, ‘elastic cells’, and the ‘displacement current,’ the last leading to the electromagnetic theory of light. At each step, Maxwell emphasized the provisional, yet mechanically conceivable nature of his models and the need for intelligibility. Although increasingly cautious in later work, he firmly retained the belief that physical reality was ‘dynamical’ in nature (i. e., matter in motion).

Chapters seven and eight illustrate Maxwell’s steadfast adherence to the reality of an underlying medium, yet trajectory away from using specific mechanical models. Though moving toward Lagrangian mathematical formalism in later work, he always insisted that abstract mathematics must be conjoined with physical meaning. Maxwell’s application of William Rowan Hamilton’s quarternions, for example, provided a geometrical, and therefore intelligible, representation of electromagnetic quantities. Also utilising concepts from the newly developed science of energy, Maxwell proposed energy transformations as the physical basis for field theory in his magnum opus Treatise on Electricity and Magnetism (1873). German action-at-a-distance theories, he contended, were inconsistent with the propagation of energy in an ethereal medium. Using spectrographic evidence, Maxwell similarly abandoned models of colliding elastic spheres in the paper, ‘On the dynamical theory of gases’ (1867). Further innovations led him to introduce probabilistic and statistical concepts into his macroscopic descriptions of gas molecules. In this work, Maxwell avoided assumptions about the behavior of individual molecules and the nature of matter. From this emerged Maxwell’s statistical interpretation of the second law of thermodynamics.

Harman’s final chapter focuses on Maxwell’s critiques of philosophical naiveté and scientific materialism. Accepting the limitations of scientific explanation, Maxwell combined enormous philosophical sophistication with traditional goals of harmonising scientific and religious beliefs. Harman nicely summarizes these issues, but provides no concluding summary, therefore the book ends rather abruptly. Despite the sometimes distracting and lengthy use of direct quotations, The Natural Philosophy of James Clerk Maxwell provides a concise examination of the overarching themes of Maxwell’s worldview and the scientific context in which his natural philosophy arose.

ROBINSON M. YOST