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The Optics
The Mathematical Principles of Natural Philosophy
EXPLANATORY INDEX
OPTICS
The first edition of Newton’s Optics was published, in English, in 1704 (London: Smith & Walford). Included with it was a Latin treatise on The Enumeration of Lines of the Third Order. As the Preface makes clear, Newton’s motive was to establish his case that he had discovered the differential calculus before Leibniz, and that Leibniz had stolen his main ideas. It may be that Newton wrote some parts of the Optics with Leibniz specifically in mind — whether as a defence of his own views, or as an attack on Leibniz’s.
The work is in three Books, of which the third has only Part I. Despite its going through three further editions, no Part II was ever written. The first two Books are written in the geometrical style, with definitions, axioms, propositions, etc. Book III is much more loosely written, and consists of 11 ‘Observations’, followed by a series of ‘Queries’ or ‘Questions’. In the first edition, there were 16 questions, and the work ends very abruptly with a discussion of the sensation of colour being due to vibrations in the eye.
Almost immediately, Newton’s young friend and disciple, Samuel Clarke (1675–1729), started translating it into Latin, so that it would reach an international readership. Clarke’s translation was published by Smith and Walford in 1706. There are two striking things about this translation.
The first is that Clarke adds some new questions at the end (17–24). It is clear that they were written by Newton himself, since he included them in the next English edition. I suspect he may have written them in Latin, and only later translated them into English, since, when Clarke gave an English version of a couple of passages before the second English edition was published, the wording is different. Both the passages I have selected are from these new questions, and they are significant for their philosophical and theological content. They are from questions 20 and 24, the latter of which serves as a peroration to the work, rounding it off nicely with an argument that the study of science leads to a knowledge of God and morality.
The second striking thing is that, while the work was in press, Newton and/or Clarke had cold feet about one particular passage (which I have included in my selection). The original version states baldly that space is God’s ‘sensory’, or perceptual space. The thesis is that real things are situated in God’s sensory, in the same way as images of things are situated in our individual sensories. The heretical implication is that the whole universe is nothing other than a set of images in God’s mind. I personally have no doubt that Newton meant what he said, but it is hardly surprising that he was worried about its appearing in print.
Consequently, he rewrote a couple of sentences, and instead of saying that space was God’s sensory, he said it was as if it was God’s sensory. Before the copies were bound, the offending page was cut out, and a new page (with the same beginning and end) was inserted. The substitution is perfectly easy to detect, since in order to stitch the new page in (and the page opposite the one cut out), there had to be an overlap of about half an inch.
Unfortunately for Newton and Clarke, a few copies got out before the substitution was made. One of these copies was the one which ended up in Leibniz’s hands, and many years later, in his correspondence with Clarke (1715–16), Leibniz went to town on the sentence without the as if, or tanquam in Latin. To his shame, Clarke never admitted what had happened, and he accused Leibniz of lying about what was written in the text.
This incident is discussed in some detail in A. Koyré and I.B. Cohen, ‘The Case of the Missing Tanquam: Leibniz, Newton & Clarke,’ Isis 52, 1961, 555–566 [EBL 10 Hist. of Sci. A–0.01 ISI].
The second English edition was published in 1718. It adds yet more questions before the Latin material (17–23), and the amended versions of the new Latin questions are renumbered as 24–31.
There were further, less significant changes in the third edition (1721), and the fourth edition, which was published posthumously in 1730, but with Newton’s own corrections.
The most readily available edition is I. Bernard Cohen et al. (eds.), Sir Isaac Newton, Opticks (New York: Dover, 1952, 1979), originally published by Bell (London, 1931). Unfortunately it is a straight reprint of the fourth edition, and it has no apparatus criticus showing the variations from one edition to the next.
I have translated from the Latin text of 1706, of which there is a copy in the Brotherton Collection. This copy has the amended page (known as a ‘cancel’), and for the original text I have used the photocopy in Koyré and Cohen. Page numbers in square brackets refer to page numbers in the Latin text.
Both extracts are from the questions at the end of Book 3, Part 1, which appeared for the first time in the Latin.
The first extract is from Question 20 (pp.312–315), which becomes Query 28 in the fourth edition (Dover edition, pp.367–370). The extract starts with Newton’s arguments for atoms and the void, as against the theory of Hobbes, Descartes, Spinoza, Huyghens, Leibniz and others, that light consists of a wave motion in an all-pervasive, material ether. He then suggests that the phenomena point to the existence of God, and it is here that he introduces the notorious suggestion that space might be (or might as it were be) the sensory of God.
The second extract is from the lasts question, Question 24 (pp.344–348), which becomes Query 31 in the fourth edition (Dover edition, pp.401–406). Here, Newton is mainly concerned to argue that gravity is not an ‘occult quality’, but an actual principle of Nature which is deducible from the phenomena, even if we don’t know its cause. In passing, he makes a number of other points:
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PRINCIPLES
Newton’s Mathematical Principles of Natural Philosophy was written in Latin, and first published in 1687. A second edition appeared in 1713, and a third in 1727. In addition to the printed texts, we have Newton’s own original manuscript, and his hand-written amendments to his personal copies.
There is a magnificent modern edition, which is based on a photographic reprint of the third edition, and which lists all the variations from earlier printed and manuscript versions: Isaac Newton’s Principia, edited by Alexandre Koyré and I. Bernard Cohen, 2 vols (Cambridge, 1972). This is the edition I have used for my translations, and page numbers in square brackets refer to the page numbers of the third edition.
As far as I am aware, the only English translation is that by Andrew Motte (London: Benjamin Motte, 1729). It has been reprinted a number of times. For example, the often reprinted Florian Cajori (Ed.), Sir Isaac Newton's Mathematical Principles of Natural Philosophy and his System of the World, 2 vols (University of California, 1934) [EBL10, Hist. of Sci. C–9 NEW].
The Principles contains very little philosophical reflection, and I have extracted the two most important passages. Both are from the last Book, which is Book III.
The Rules
In the short Preface to Book III, Newton explains that the first two Books were purely mathematical, and that it is only now that he applies the mathematics to the phenomena of Nature — in particular, how the solar system is governed by the law of universal gravitation.
He starts with a brief disquisition on scientific method. In the first edition, this takes the form of three ‘Hypotheses’, but in the second edition they become three ‘Rules of Philosophising’ (a fourth Rule was added in the third edition).
There are substantial differences from the version in the first edition, and I have chosen to translate from the second edition, since it reflects Newton’s thinking during the period when he was in dispute with Leibniz (Latin Optics: 1706; Principles 2nd edition: 1713; Leibniz-Clarke correspondence: 1715–1716). Leibniz had copies of each edition as they appeared.
The most important rule is Rule 3, in which Newton argues that we can establish the universal qualities of bodies, not by reason, but by induction from sense experience (though he doesn’t actually use the word ‘induction’ here).
The General Scholium
At the end of Book III, Newton adds an entirely new ‘General Scholium,’ which wasn’t in the first edition at all. He starts with an attack on the Cartesian theory that the planets are carried round by vortices in the ether. He then moves to the argument that the system of the universe can only have been created by a single supreme Being. Having established the existence of God, he speculates about his nature and his relation to the world. Among other things, although he doesn’t use the word ‘sensory’, he comes very close to the doctrine of the Optics, when he says that God ‘constitutes’ space and time, and senses everything through his omnipresence. Like Leibniz, he stresses the special relationship between God and human beings, of whom he is the ‘Lord’ or ‘Master’.
He then comes back to the question of gravity. He denies the Leibnizian accusation that it is an ‘occult quality’, and says that we know it exists, even if we cannot explain its cause. And it is not the job of the scientist to speculate about what is not known through experience (his famous hypotheses non fingo — ‘I do not invent hypotheses’).
Finally, he admits that there must be an ubiquitous, very tenuous (and hence presumably material) spirit, to account for the cohesion of bodies, magnetism, certain phenomena of light, and sensation in animals — but we have too little observational evidence about it to be able to say any more. Nor does he explain how this is consistent with his repeated assertion that most of space is empty of matter.
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