During the course of the eighteenth century important changes occurred in the conception of matter held by British natural philosophers. Historians of science have described these changes in different ways, but certain common features can be abstracted from the more recent accounts. First, there was a movement away from Newtonian matter theory, which saw all matter as the various organizations of homogeneous particles and the forces of attraction and repulsion acting between them. In place of this theory increasing favour was shown towards a more empirical or ‘chemical’ approach to matter which assumed the existence of several essentially distinct types of matter each endowed with different specific qualities or properties. Second, there was an increasing tendency to accept activity as a property of matter itself rather than to ascribe it to immaterial forces.

In this paper I want to examine in some detail one eighteenth-century attempt to restructure the foundations of mechanics, that of Leonhard Euler. It is now generally recognized that the idea, due to Mach, that all that happened in the eighteenth century was the elaboration of a deductive and mathematical mechanics on the basis of Newton's Laws is misleading at best. Newton's Principia needed much more than a reformulation in analytic terms if it was to provide the basis for the comprehensive mechanics that was developed in the eighteenth century. Book II of the Principia, in particular, where the problem of the resistance offered to the motion of a finite body by a fluid medium was raised, was generally (and rightly) thought to be in large part mistaken and confused. There were also a number of areas crucial to the unification of mechanics which Newton did not deal with at all in the Principia: particularly the dynamics of rigid, flexible and elastic bodies, and the dynamics of several bodies with mutual interactions. Although a start had been made on some of these topics in the seventeenth century (notably by Galileo, Beeckman, Mersenne, Huygens, Pardies, Hooke, and Leibniz), it was only in the eighteenth century that they were subjected to detailed examination, and Euler's contribution to the development of these topics, and hence to the unification of mechanics, was immense.

In 1859 Charles Darwin in chapter nine of the Origin of Species showed how he had calculated that the age of the Weald was three hundred million years and that consequently the age of the earth was considerably greater than that. Darwin of course needed such a long period of time for the process of evolution by natural selection to occur. Arguments which showed that the earth could not be that old would therefore cast serious doubt on his theory. Such views were advanced in 1862 by William Thomson, later Lord Kelvin, professor of Natural Philosophy at Glasgow. He specifically challenged the result of Darwin's calculation of the age of the Weald by arguing that the sun could not have emitted its heat and light for that length of time. The consequences of this assertion for the biological and geological sciences for the remainder of the nineteenth century have already been delineated by Burchfield. What I wish to do in this paper is to show that the theoretical basis of Thomson's 1862 assertion had not been specifically developed as a response to Darwin, but that it was a consequence of the formulation of the first two laws of thermodynamics. I shall also show that Thomson's work was not done in isolation but that the question of the maintenance of solar energy was a serious concern of a number of physicists who had formulated the laws of thermodynamics.