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‘My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments’.
Newton, Opticks (1704), p. 1.
In an advertisement to the reader to his Opticks, published at London in 1704, Newton explained that the work being published was not new but rather contained material which he had originally worked on in the 1670s and which had been sent to the Royal Society in 1675. Material from the 1680s was also included, as were the ‘Third Book and the last Proposition of the Second’. He explained his delay in publishing them as a desire to avoid ‘Dispute about these Matters’, a thinly veiled reference to his dispute with Robert Hooke in 1672 following Newton’s initial contact with the Royal Society. Guicciardini (2004) has pointed out that the effect of this dispute on Newton’s publishing had sometimes been exaggerated since Newton was apt, in the period between 1672 and 1687, when he committed himself in print in the Principia, to indulge in ‘scribal communication’, i.e. ‘publishing’ his treatises in manuscript form among his correspondence circle. Equally, Feingold (2004) has drawn attention to the fact that, though Newton had certainly written parts of the Opticks in the1670s, other parts were not written until the early eighteenth century.
Certainly if Newton was anxious to avoid dispute in 1704 his decision to append two mathematical treatises, both in Latin, seemed to contradict this aim. Newton explained the publication of his Tractatus de quadratura curvarum and the Enumeratio lineraum tertii ordinis in an English book on optics by stating that:
‘In a Letter written to Mr Leibnitz in the Year 1676 and published by Dr Wallis, I mentioned a Method by which I had found some general Theorems about squaring Curvilinear Figures, or comparing them with the Conic Sections, or other the simplest Figures with which they may be compared. And some Years I ago I lent out a Manuscript containing such Theorems, and having since met with some Things copied out of it, I have on this Occasion made it publick, prefixing to it an Introduction and subjoining a Scholium concerning the Method. And I have joined with it another small Tract concerning the Curvilinear Figures of the Second Kind, which was also written many Years ago, and made known to some Friends, who have solicited the making it publick.’
The addition of these two treatises, on a different subject and in a different language, at first sight seems strange. However, the inclusion of the Tractatus de quadratura curvarum as an appendix to the 1704 edition was a response to David Gregory’s claim that his uncle, James Gregory, had discovered the ‘prime theorem’ on quadratures. The Tractatus de quadratura curvarum was the first published work by Newton on his theory of fluxions, although he had clearly been working on fluxions in the late 1660s and early 1670s and had incorporated them into his Principia. The reference to the 1676 letter to Leibniz clearly refers to the famous priority dispute over who had discovered the calculus. If Newton wanted to avoid dispute he was certainly going the wrong way about it.
The decision to publish the Opticks in English invariably affected its reception on the continent and two years later a Latin edition was forthcoming. As Shapiro says (2006), reaction to the work varied: some, such as the Italian scientist Giovanni Poleni (1683-1761) taught it from 1707 onwards, others, such as Christian Wolff waited until Newton and Desaguliers had responded to his challenge in the Acta eruditorum to deal with Edmé Mariotte’s (ca. 1620-1684) 1681 failure to replicate his experiments (for further details on Desagulier’s experimental response see ‘Newton at the Royal Society’). This was undertaken in 1714 and published in the 1716 edition of Philosophical Transactions and was included by Wolff in the 1717 Acta eruditorum.
Bryan Robinson, in his preface to Richard Helsham’s A Course of Lectures in Natural Philosophy (Dublin, 1739), outlines Newton’s ‘Method of Philosophizing .. as laid down in his Opticks’ as follows:
‘As in mathematicks, so in natural philosophy, the investigation of difficult things by way of Analysis, ought ever to precede the method of composition. This Analysis consists in making experiments and observations, and in drawing general conclusions from them by induction, and admitting of no objections against the conclusions, but such as are taken from experiments or other certain truths. And although the arguing from experiments and observations by induction, be no demonstration of general conclusions; yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much the stronger, by how much the induction is more general. And if no exception occur from Phaenomena, the conclusion may be pronounced generally. But if at any time afterwards, any exceptions shall occur from experiments, it may then be pronounced with such exceptions as shall occur. 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 ends in the most general. This is the method of Analysis: And the Synthesis, consists in assuming the causes discovered, and established as principles, and by them, explaining the Phaenomena proceeding from them, and proving the Explanations.’
The following plate, with its accompanying text of Newton’s Proposition IV Problem 1, shows us Newton in action.
Proposition IV Problem 1: ‘To separate from one another the Heterogeneous Rays of Compound Light’.
‘The Heterogeneous Rays are in some measure separated from one another by the Refraction of the Prism in the third Experiment, and in the fifth Experiment by taking away the Penumbra from the Rectilinear sides of the Coloured Image, that separation in those very Rectilinear sides or straight edges of the Image becomes perfect. But in all places between those rectilinear edges, those innumerable Circles there described, which are severally illuminated by Homogeneral Rays, by interfering with one another, and being every where commixt, do render the Light sufficiently Compound. But if these Circles, whilst their Centers keep their distances and positions, could be made less in Diameter, their interfering one with another and by consequence the mixture of the Heterogeneous Rays would be proportionally diminished. In the 23th Figure let AG, BH, CJ, DK, EL, FM be the Circles which so many sorts of Rays flowing from the same Disque of the Sun, do in the third Experiment illuminate; of all which and innumerable other intermediate ones lying in a continual Series between the two Rectilinear and Parallel edges of the Sun’s oblong Image PT, that Image is composed as was explained in the fifth Experiment. And let a g, b h, c i, d k, e l, f m be so many less Circles lying in a like continual Series between two Parallel right Lines a f and g m with the same sorts of Rays, that is the Circle a g with the same sort by which the corresponding Circle A G was illuminated, and the Circle b h with the same sort by which the corresponding Circle B H was illuminated, and the rest of the Circles c I, d k, e l, f m respectively, with the same sorts of Rays by which the several corresponding Circles C J, D K, E L, F M were illuminated. In the Figure P T composed of the greater Circles, three of those Circles AG, B H, C J, are so expanded into one another, that the three sorts of Rays by which those Circles are illuminated, together with other innumerable sorts of intermediate Rays, are mixed at Q R in the middle of the Circle B H. And the like mixture happens throughout almost the whole length of the Figure P T. But in the Figure p t composed of the less Circles, the three less Circles a g, b h, c I, which answer to those three greater, do not extend into one another; not are there any where mingled so much as any two of the three sorts of Rays by which those Circles are illuminated, and which in the Figure P T are all of them intermingled at B H.
Now he that shall thus consider it, will easily understand that the mixture is diminished in the same Proportion with the Diameters of the Circles. If the Diameters of the Circles whilst their Centers remain the same, be made three times less than before, the mixture will be also three times less; if ten times less, the mixture will be also ten times less, and so of other Proportions. That is, the mixture of the Rays in the greater Figure P T will be to their mixture in the less p t, as the Latitude of the greater Figure is to the Latitude of the less. For the Latitudes of these Figures are equal to the Diameters of their Circles. And hence it easily follows, that the mixture of the Rays in the refracted Spectrum p t is to the mixture of the Rays in the direct and immediate Light of the Sun, as the breadth of that Spectrum is to the difference between the length and breadth of the same Spectrum.
So then, if we would diminish the mixture of the Rays, we are to diminish the Diameters of the Circles. Now these would be diminished if the Sun’s Diameter to which they answer could be made less than it is, or (which come to the same purpose) if without Doors, at a great distance from the Prism towards the Sun, some opake body were placed, with a round hole in the middle of it, to intercept all the Sun’s Ligt, excepting so much as coming from the middle of his Body could pass through that hole to the Prism. For so the Circles A G, B H and the rest, would not any longer answer to the whole Disque of the Sun, but only to that part of it which could be seen from the Prism through that hole, that is to the apparent magnitude of that hole viewed from the Prism. But that these Circles may answer more distinctly to that hole a Lens is to be placed by the Prism to cast the Image of the hole, (that is, every one of the Circles A G, B H &c) distinctly upon the Paper within the Room, and the Rectilinear Sides of the oblong solar Image in the fifth Experiment became distinct without any Penumbra. If this be done it will not be necessary to place that hole very far off, no not beyond the Window. And therefore instead of that hole, I used the hole in the Window-shut as follows.
Exper. 11. In the Sun’s Light let into my darkned Chamber through a small round hole in my Windowshut, at about 10 or 12 Feet from the Window, I placed a Lens, by which the Image of the hole might be distinctly cast upon a sheet of white Paper, placed at the distance of six, eight, ten or twelve Feet from the Lens. For according to the difference of the Lenses I used various distances, which I think not worth the while to describe. Then immediately after the Lens I place a Prism, by which the trajected Light might be refracted either upwards or sideways, and thereby the round Image which the Lens alone did cast upon the Paper might be drawn out into a long one with Parallel Sides, as in the third Experiment. This oblong Image I let fall upon another Paper at about the same distance from the Prism as before, moving the Paper either towards the Prism or from it, until I found the just distance where the Rectilinear Side of the Image became most distinct. For in this case the circular Images of the hole which compose that Image after the same manner that the Circles a g, b h, c I, &c do the Figure p t, were terminated most distinctly without any Penumbra, and therefore extended into one another the least that they could, and by consequence the mixture of the Heterogeneous Rays was now the least of all. By this means I used to form an oblong Image (such as is p t) of circular Images of the hole ( such as are a g, b h, c I, &c) and by using a greater or less hole in the Window-shut, I made the circular Images a g, b h, c I, &c of which it was formed, to become greater or less at pleasure, and thereby the mixture of the Rays in the Image p t to be as much or as littler as I desired.
Illustration. In the 24th Figure, F represents the circular hole in the Window-shut, M N the Lens whereby the Image or Species of that hole is cast distinctly upon a Paper at J, A B C the Prism whereby the Rays are at their emerging out of the Lens refracted from J towards another Paper at p t, and the round Image at J is turned into an oblong Image p t falling on that other Paper. This Image p t consists of Circles placed one after another in a Rectilinear order, as was sufficiently explained in the fifth Experiment; and these Circles are equal to the Circle I, and consequently answer in Magnitude to the hole F; and therefore by diminishing that hole they may be at pleasure diminished, whil’st their Centers remain in their places. But this means I made the breadth of the Image p t to be forty times, and sometimes sixty or seventy times less than its length. As for instance, if the breadth of the hole F be 1/10 of an Inch, and M F the distance of the Lens from the hole be 12 Feet; and if p B or p M the distance of the Image p t from the Prism or Lens be 10 Feet, and the refracting Angle of the Prism be 62 degrees, the breadth of the Image p t will be 1/12 of an Inch and the length about six Inches, and therefore the length to the breadth as 72 to 1, and by consequence the Light of this Image 71 times less compound than the Sun’s direct Light. And Light thus far Simple and Homogeneal, is sufficient for trying all the Experiments in this Book about simple Light. For the composition of Heterogeneal Rays is in this Light so little that it is scarce to be discovered and perceived by sense, except perhaps in the Indigo and Violet; for these being dark Colours, do easily suffer a sensible allay by that little scattering Light which uses to be refracted irregularly by the inequalities of the Prism.
Yet instead of the circular hole F, ‘tis better to substitute an oblong hole shaped like a long Parallelogram with its length Parallel to the Prism A B C. For if this hole be an Inch or two long, and but a tenth or twentieth part of an Inch broad or narrower: the Light of the Image p t will be as Simple as before or simpler, and the Image will become much broader, and therefore more fit to have Experiments tried in its Light than before.
Instead of this Parallelogram-hole may be substituted a Triangular one of equal Sides, whose Base for instance is about the tenth part of an Inch, and its height an Inch or more. For by this means, if the Axis of the Prism be Parallel to the Perpendicular of the Triangle, the Image p t will now be formed of Equierural Triangles a g, b h, c i, d k, e l, f m, &c and innumerable other intermediate ones answering to the Triangular hole in shape and bigness, and lying one after another in a continual Series between two Parallel lines a f and g m. These Triangles are a little intermingled at their Bases but not at their Vertices, and therefore the Light on the brighter side a f of the Image where the Bases of the Triangles are is a little compounded, but on the darker side g m is altogether uncompounded, and in all places between the side of the Composition is Proportional to the distances of the places from that obscurer side g m. And having a Spectrum p t of such a Composition, we may try Experiments either in its stronger and less simple Light near the side a f, or in its weaker and simpler Light near the othe side l m, as it shall seem most convenient.
But in making Experiments of this kind the Chamber ought to be made as dark as can be, least any foreign Light mingle it self with the Light of the Spectrum p t, and render it compound; especially if we would try Experiments in the more simple Light next the side g m of the Spectrum; which being fainter, will have a less Proporition to the foreign Light, and so by the mixture of that Light be more troubled and made more compound. The Lens also ought to be good, such as may serve for Optical Uses, and the Prism ought to have a large Angle, suppose of 70 degrees, and to be well wrought, being made of Glass free from Bubbles and Veins, with its side not at little Convex or Concave as usually happens but truly Plane, and its polish elaborate, as in working Optick-glasses, and not such as is usually wrought with Putty, whereby the edges of the Sand-holes being worn away, there are left all over the Glass a numberless company of very little Convex polite risings like Waves. The edges also of the Prism and Lens so far as they may make any irregular Refraction, must be covered with a black Paper glewed on. And all the Light of the Sun’s beam let into the Chamber which is useless and unprofitable to the Experiment, ought to be intercepted with black Paper or other black Obstacles. For otherwise the useless Light being reflected every way in the Chamber, will mix with the oblong Spectrum and help to disturb it. In trying these things so much Diligence is not altogether necessary, but it will promote the success of the Experiments, and by a very scrupulous Examiner of things deserves to be applied. It’s difficult to get glass Prisms fit for this purpose, and therefore I used sometimes Prismatick Vessels made with pieces of broken Looking-glasses, and filled with rain Water. And to increase the Refraction, I sometimes impregnated the Water strongly with Saccharum Saturni.’
At the end of the plate is a depiction of Newton’s reflecting telescope. The range of experiments outlined in the Opticks ensured that it became a staple for the experimental lecturing at London in the early eighteenth century. Desaguliers’s experiments both at the Royal Society and in his own lecturing course at London invariably focused on the Opticks as his principle source material. As Friesen (2003) suggests, the experimental Newtonianism evident after the 1704 publication of the Opticks was of a different character to the Newtonianism which had preceded its publication.
Feingold, Mordechai (2004), The Newtonian Moment. Isaac Newton and the Making of Modern Culture (New York and Oxford).
Friesen, John (2003), ‘Archibald Pitcairne, David Gregory and the Scottish origins of English Tory Newtonianism’, History of Science xli, pp. 163-191.
Guicciardini, Niccolò (1989), The Development of Newtonian Calculus in Britain 1700-1800 (Cambridge).
Guicciardini, Niccolò (2004), ‘Isaac Newton and the publication of his mathematical manuscripts’, Studies in the History and philosophy of Science 35, pp. 455-470.
Guicciardini, Niccolò (2004), ‘Dot-Age: Newton’s Mathematical Legacy in the Eighteenth Century’ Early Science and Medicine 9, no. 3, Newtonianism: Mathematical and ‘Experimental’, pp 218-256.
Hall, A. Rupert (1999), Isaac Newton. Eighteenth-Century Perspectives (Oxford).
Shapiro, A. E. (2006), ‘The Reception of Newton’s Theory of Light and Colour’, Mini-Worshop: On the Reception of Isaac Newton in Europe, Mathematisches Forschungsinstitut Oberwolfach Report no. 10. Available online at: http://www.ruhr-uni-bochum.de/wtundwg/Forschung/tagungen/OWR_2006_10.pdf