¹ See Cohen, I. Bernard, “Hypotheses in Newton's Philosophy”, Physis, xviii (1966), 165–184Google Scholar; Kubrin, David, “Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy”, Journal of the History of Ideas, xxvii (1967), 325–346CrossRefGoogle Scholar; McGuire, J. E., “Body and Void and Newton's ‘De Mundi Systemate’: Some New Sources”, Archives for History of Exact Sciences, iii (1966), 206–248CrossRefGoogle Scholar; McGuire, J. E., “Transmutation and Immutability: Newton's Doctrine of Physical Qualities”, Ambix, xiv (1967), 69–95CrossRefGoogle Scholar; McGuire, J. E., “The Origin of Newton's Doctrine of Essential Qualities”, Centauras, xii (1968), 233–260CrossRefGoogle Scholar; McGuire, J. E. and Rattansi, P. M., “Newton and the ‘Pipes of Pan’”, Notes and Records of the Royal Society of London, xxi (1966), 108–143.CrossRefGoogle Scholar

² This is interestingly discussed in a recent study by Axtell, James, “John Locke and the Two Cultures” in John Locke: Problems and Perspectives (Cambridge, 1969).Google Scholar

³ The Correspondence of Isaac Newton, iii (Cambridge, 1961), 338–339.Google Scholar

⁴ Op. cit. (1). See especially McGuire, J. E., “Transmutation and Immutability” and “The Origin of Newton's Doctrine of Essential Qualities”.Google Scholar

⁵ U.L.C. Add. 3970.3, folio 479^r-v and 480^v respectively. The manuscript sequence comprises folios 477^r to 480^v.

⁶ I am grateful to Dr. Derek T. Whiteside for pointing this out to me in a private communication. The calculations are found on folio 480^r. Optically the diagrams differ, but geometrically they are the same.

⁷ Newton, Isaac, Opticks, or a Treatise of the Reflections, Refractions, Inflections and Colours of Light (4th edn., London, 1704; reprint: New York, Dover, 1952).Google Scholar

⁸ Hall, A. R. and Hall, Marie Boas, Unpublished Scientific Papers of Isaac Newton (Cambridge, 1962), 370.Google Scholar

⁹ Boyle, Robert, Works of the Honourable Robert Boyle, ed. Birch, T. (London, 1772), i. 301–302.Google Scholar

¹⁰ Locke, John, An Essay Concerning Human Understanding (London, 1690)CrossRefGoogle Scholar. Book IV, chap. XII, 328.

¹¹ Edleston, Joseph, Correspondence of Sir Isaac Newton and Professor Cotes (London, 1850), 155.Google Scholar

¹² Locke, John, op. cit., Book IV, chapters VI, VII and VIII, 292–311.Google Scholar

¹³ Opticks, ed. cit. (7), 404.Google Scholar

¹⁴ Ibid., 404.

¹⁵ Hall, A. Rupert and Hall, Marie Boas, Unpublished Scientific Papers of Isaac Newton (Cambridge, 1962), 305–308, 333–337.Google Scholar

¹⁶ Locke, John, op. cit., Book IV.Google Scholar

¹⁷ The square brackets in the text are Newton's, the parentheses indicate cancellations and interpolations.

¹⁸ Newton probably has in mind Descartes, the Cartesians and Charleton, all of whom tended to relate, in a direct way, the qualities of internal “explanatory mechanisms” to the observable properties of phenomena.

¹⁹ Newton makes similar observations in the Opticks, ed. cit. (7), 369–370, 402–403.Google Scholar

²⁰ Newton's examples show that he is concerned to argue for design as well as from design. Notice, also, that he thinks of God as having possession of “scientific” knowledge. The argument for design in terms of such knowledge is more pronounced in Newton than in his predecessors.

²¹ Here in English is a clear expression of Newton's full doctrine of gravitation. It is perhaps the earliest non-mathematical statement in his own words.

²² The examples of the porosity of matter are the same as in the Opticks itself. In this draft Newton gives a clear statement of the basic principle of his theory of colours.

²³ In Query 31 of the Opticks, Newton uses the term “analysis” for resolution, ed. cit. (7), 404.

²⁴ Now speaking of alternating between “experiments” and “conclusions” in Query 31 of the Opticks Newton is less explicit: “By this way of Analysis we may proceed from Compounds to Ingredients, and from Motions to the Forces producing them; and in general, from Effects to their Causes, and from particular Causes to more general ones, till the Argument end in the most general” (p. 404).

As has been discussed by Stewart, Dugald, Elements of the Philosophy of the Human Mind, in Works, II (Cambridge, 1829)Google Scholar and by Henry, Brougham, Lord, Natural Theology (London, 1856)Google Scholar, Newton and many of his predecessors make a false analogy between the mathematical use of the techniques of analysis and synthesis, and their use in natural philosophy. See Stewart's perceptive analysis (Works, II, 252–272), and Brougham (op. cit., pp. 109–110). Both Stewart and Brougham point out that in mathematics the two operations, of necessity, use the same steps “the one being the steps of the other taken in reverse order” (p. 110). Brougham continues: “In physics, to make the operation similar to these, the same facts should be the ground or component parts of both. In analysis, we should ascend not only from particulars to generals, but from the same particulars, and then the synthesis would be a descent through the same steps to the particular phenomena from the general fact. But it is a spurious synthesis unlike the mathematical, and not warranted by induction, to prove the proposition by one set of facts, and by that proposition to explain—that is, classify—another set, without explaining it by itself”. Though neither writer thinks that the method thus understood has no application in science—they mention that it has in astronomy and chemistry—they hold that Newton's conception of the method leads to an unclear view of the role of induction in science. Both Stewart and Brougham recognized that Hooke used the terms by analogy with Greek geometry. Stewart quotes with commendation from Hooke's Posthumous Works to show that the latter used the terms “precisely in the contrary acceptions to those assigned them in the definition of Sir Isaac Newton (op. cit., II, p. 265). Thus Hooke attempted to use the method by strict analogy with the sense of the ancients in setting out his method of investigation in science. For a recent discussion of Hooke's methodology see Hesse, Mary M., “Hooke's Philosophical Algebra”, Isis, xlvii (1966), 69–83.Google Scholar

²⁵ Notice that Newton uses the expression “Feign Hypotheses” in the sense of constructing plausible a priori suppositions. It was this practice that he had earlier denigrated in the optical work of Hooke, Pardies and Huyghens.