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.