By the time of the Leibniz-Clarke correspondence of 1716 the Newtonian and Leibnizian systems of natural philosophy had reached maturity. Each system consisted of different physical as well as metaphysical principles which, taken together, formed a world view. At the time of their famous debates, Leibniz at 70 and Newton at 74, the founders of two highly developed scientific philosophies, were struggling to establish and defend the ontological and mechanical bases of differing bodies of organized knowledge.

The catalogues of mid-eighteenth-century mathematical instrument makers included not only instruments in the sense ‘tools of science’ but also devices intended primarily for educational use. Among the latter would be found mechanical models of the solar system, in varying degrees of complexity and under various names; for convenience such models may be, and often were, loosely called orreries.

Two imposing related problems confronted the chemical spectroscopist of the late nineteenth century. First, he lacked a criterion for judging the validity of claims for elemental discoveries; indeed, he possessed no satisfactory operational definition of the chemical element. Secondly, he felt the need for correlating the spectra of the elements to a conception of their ultimate constitution.