In June 1847 William Thomson, later Lord Kelvin (1824–1907), met Joule at the Oxford meeting of the British Association for the Advancement of Science, and the encounter led Thomson to study Joule's papers on the mutual convertibility of heat and mechanical work. At the Oxford meeting Joule had read a paper describing his measurement of the temperature change in a fluid agitated by a paddle wheel that was turned by a descending hanging weight; he claimed to have determined the quantitative equivalence between the heat generated by the paddle wheel and the mechanical work required to generate that heat. Thomson found Joule's conclusions astonishing; and he reported Joule's work to his brother James Thomson (1822–92), who confessed that Joule's ‘Views have a slight tendency to unsettle one's mind’. The Thomsons' sense of intellectual disorientation arose from their belief, derived from the work of Sadi Carnot (1796–1832), that heat was conserved in the generation of mechanical work by heat engines. This theory seemed to contradict Joule's claim that heat must be consumed in the generation of work. The unravelling of the apparent contradiction between the theories of Carnot and Joule was to lead to the formulation of the science that in 1854 William Thomson was to term ‘thermo-dynamics’, the theory of the mechanical action of heat.

In his 1900 lecture ‘Nineteenth century clouds over the dynamical theory of heat and light’, William Thomson pointed to two problems facing the mechanical theory of nature: the failure to explain the mechanism of the motion of the earth through the ether, and the difficulty the concept of the equipartition of energy posed for the construction of molecular models. Thomson highlighted two ‘clouds’ that threatened his elaboration of mechanical models of physical phenomena, but there were wider dimensions to the difficulties that physicists perceived in the conceptual rationale of the mechanical theory of nature.

The traditional programme of mechanical explanation elicited diverse responses from physicists in the 1880s and 1890s. Thomson's ether models and Boltzmann's lectures on field theory continued the programme of elaborating detailed mechanical models of phenomena. Boltzmann strove to provide an exhaustive treatment of every detail of the structure and motions of his mechanical models of the electromagnetic field; and Thomson declared that the construction of a mechanical model of a phenomenon was the criterion of the intelligibility of that phenomenon. Nevertheless, the conceptual difficulties associated with the enunciation of mechanical models were well understood. Maxwell had pointed out that such models could not provide unique explanations of phenomena and had drawn attention to the dangers of confusing representation and reality, and though he remained committed to the ultimate aim of formulating a ‘complete’ mechanical theory of the field, in his Treatise he employed an analytical formulation of dynamics, rather than a specific mechanical model.

The physical constitution of matter appeared uncertain in the nineteenth century. Although an ontology of particles of matter in motion was fundamental to the programme of mechanical explanation and to the conceptual coherence of the science of thermodynamics, physicists were careful to distinguish between the general supposition of a particulate theory of matter and the adoption of more specific models of molecular structure. Though the mechanical view of heat as the motion of the particles of matter underlay the principle of the equivalence of heat and work, physicists found compelling evidence for a molecular theory of matter only with the development of the kinetic theory of gases in the 1850s. But the problem of explaining the phenomena of spectroscopy indicated the need to suppose complex internal molecular vibrations, and raised difficult questions about the formal coherence of the kinetic theory of gases. The problems of molecular physics raised crucial issues about the conflicting empirical constraints (from spectroscopy and the kinetic theory of gases) on the formulation of a coherent theory of the molecular structure of bodies. The problems of molecular physics shaped the development of thermodynamics: The statistical theory of molecular motions, which was formulated as a seminal feature of the kinetic theory of gases, led to the interpretation of the second law of thermodynamics as an irreducibly statistical law. For chemists, the problems of matter theory seemed equally complex, and the status of the atomic theory remained the subject of debate.

In the nineteenth century the term ‘physics’ acquired new and significant connotations. Although the term was still occasionally used in the traditional sense to refer to natural science in general, by the early nineteenth century ‘physics’ was being used in the modern and more specialised sense to denote the study of mechanics, electricity, and optics, employing a mathematical and experimental methodology. In the article entitled ‘Physical Sciences’ in the ninth edition of the Encyclopaedia Britannica in the 1870s, James Clerk Maxwell identified the scope of physics with the programme of mechanical explanation, first enunciated in the seventeenth-century ‘mechanisation of the world picture’, which sought to explain physical phenomena in terms of the structure and laws of motion of a mechanical system. In a critical exposition of current physical theory, The concepts and theories of modern physics (1881), Johann Bernhard Stallo gave an informative and more detailed definition of the theoretical structure of physics as conceived by contemporary theorists:

The science of physics, in addition to the general laws of dynamics and their application to the interaction of solid, liquid and gaseous bodies, embraces the theory of those agents which were formerly designated as imponderables – light, heat, electricity and magnetism, etc.; and all these are now treated as forms of motion, as different manifestations of the same fundamental energy.

In the nineteenth century the science of physics came to be defined in terms of the unifying role of the concept of energy and the programme of mechanical explanation.

The period circa 1800–1900 corresponds to a distinctive phase in the conceptual development of physics, bounded by the increasing dominance, from the late eighteenth century on, of quantification and the search for mathematical laws, together with the emergence of a unified physics based on the programme of mechanical explanation, and by the development in the early twentieth century of the quantum and relativity theories. I have aimed to provide a study of the development of physics in the nineteenth century in a form accessible to the reader without a specialised knowledge of physics and mathematics. The argument of the book is structured around the major conceptual problems of nineteenth-century physics: the emergence of energy physics and thermodynamics, the theory of the luminiferous and electromagnetic ether and the concept of the physical field, molecular physics and statistical thermodynamics, and the dominance of the programme of mechanical explanation. The book begins with an account of the transformation in the scope of the science of physics in the first half of the nineteenth century.

I am grateful to John Heilbron for reading a portion of the manuscript and to Crosbie Smith for reading the whole manuscript of this book, and for their helpful comments. I am also grateful to the Syndics of the Cambridge University Library for their kind permission to reproduce documents in their keeping, and to the Council of the Royal Society for the award of a grant for research undertaken in the preparation of this book.

The term ‘magnetic field’ was introduced by Faraday in 1845, and subsequently adopted by Thomson and Maxwell, whose usage clearly echoed Faraday's. Thomson first used the expression ‘field of feree’ in a letter to Faraday in 1849, following their discussion of the nature of magnetism; and Maxwell first referred to a ‘magnetic field’ in a letter to Thomson in 1854, in the context of a discussion of Faraday's ideas. Maxwell gave the term ‘field’ its first clear definition, in consonance with previous usage, in his paper ‘A dynamical theory of the electromagnetic field’ (1865); there he stated, ‘The theory I propose may therefore be called a theory of the Electromagnetic Field, because it has to do with the space in the neighbourhood of the electric or magnetic bodies’. The concept of a field was to be contrasted with an action-at-a-distance theory of electric action; that is, the mediation of forces by the agency of the contiguous elements of the field existing in the space between separated electrified bodies was to be distinguished from the action of forces operating directly between electrified bodies across finite distances of space.

The inclusive breadth of Maxwell's definition of the field makes it apparent that the physical status of the field was not defined uniquely. In a field theory the forces between bodies were mediated by some property of the ambient space or field.

In style and content, the physical theory of 1850 shows a marked contrast to that prevalent in 1800. By 1850 the limits and internal cohesion of the science of ‘physics’ were clearly articulated, and the subject had achieved a new and well-defined conceptual content and unity. By 1850 some of the main themes of nineteenth-century physics had been formulated: the unification of physical phenomena within a single explanatory framework, the primacy of mechanical explanation as an explanatory programme, the mathematisation of physical phenomena and the role of mathematical analogy as a guide to the formulation of physical theories, and the enunciation of the principle of energy conservation as a universal, unifying law. The emergence of these broad and unifying themes contrasts with the disunity in physical theory in 1800.

The general disjunction in eighteenth-century physical theory can be illustrated by a contrast between Newton's Philosophiae naturalis principia mathematica [Mathematical principles of natural philosophy] (1687) and his Opticks (1704). In the Principia Newton offered the paradigm of a mathematical science of ‘rational mechanics’, and though he expressed the hope that all physical phenomena could be subsumed under analogous mathematical methods (illustrating his intentions by a mathematical treatment of optical refraction), in the Opticks he based his treatment of the problems of optics and chemistry on an experimental methodology and a speculative theoretical structure, an atomistic physics that became bloated in later editions to include a variety of explanatory agents, forces, active principles, and the ether.