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different force laws in Books I and II, then treats physics, chiefly the application of the inverse square law to the solar system and other phenomena, in Book III. Philosophy should then give a more ultimate explanation through causes and the ultimate constituents of matter. (His Third Rule of Reasoning in Philosophy and General Scholion)Opticks. It differed from Boyle's atomism chiefly in substituting a hierarchy of forces for contact action.8

An explanation of the properties of the material universe in terms of its ultimate constituents has remained the Holy Grail of physics. Its foundational role in mechanics, however, proved evanescent.  Its explicit rejection occurred in Euler's 1755 paper on hydrodynamics, where he declared that the atomic hypothesis may be true but is absolutely sterile. (Euler, series II, vol. 12, p. 3). He replaced Newton's molecular model of fluids with a model of continuous homogeneous material. As Truesdell, the editor of Euler's collected works, summarizes it: "Henceforth the principles of mechanics are applied directly to the bodies of physical experience. Atoms are replaced by the fiction of point masses while the continuum model of matter supplies a basis for a formulation of mechanics in terms of differential equations" (Euler, series II, Vol. 12, pp.ix-cxxv). In his later, immensely popular, Letters to a German Princess9 he refuted the standard arguments for ultimate simples and presented extension, mobility, and impenetrability as the essential characteristics of bodies. This reinterpretation of mechanics reached its culmination in Lagrange's Mécanique analytique, where mechanics is presented as a branch of analysis.

Euler's criticism of atomism was part of his larger campaign against materialism. The atomic hypothesis was not generally abandoned, but it no longer supplied even a hypothetical foundation for mechanics. Mechanics was based on the properties of gross matter that admitted of quantitative measurement.  At about the same time, Berkeley and especially Hume reinterpreted the distinction between primary and secondary qualities as an epistemological, rather than an ontological distinction, something based on an analysis of how we come to know matter, rather than on how it exists objectively. The net result was that the categorial system of  physics dropped the Aristotelian emphasis on substantial units, or relegated it to biology and psychology, and treated quantifiable qualities as the basic properties of objects. The prototypical quantities were quantities of gross matter, not ultimate corpuscles.

1.3  The Second Scientific Revolution

The second scientific revolution centers on the attempts, led by Laplace, to incorporate the Baconian sciences into  mechanical account of physical reality. Though it did not achieve the foundational goals intended, nevertheless it had an effect that was not anticipated. It supplied a unified language with a mechanical core that interrelated the different branches of physics. Our primary concern is with this linguistic residue of a failed ontology.

8 The role of Newton's atomism is treated in A. R. Hall and M. B. Hall, 1970;  McGuire, 1970; McMullin, 1978;  and Westfall, 1971, and  1980.

9 Euler, series III, vol. 2. The basic properties of matter are explained on pages 149-152, while the rejection of atomism is on pages 297-301. These two volumes of popular science were reprinted in twelve French, ten English, six German, four Russian, two Dutch, two Swedish, one Italian, one Danish, and one Spanish edition. This and the French Encyclopédie communicated to the reading public of the Enlightenment era the significance of the new science.

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