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The ‘Projet’ of 1672

The puzzle of strange refraction and causes in geometrical optics
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Part of the Archimedes book series (ARIM, volume 9)

Keywords

Mechanical Analogy Geometrical Optic Parallel Component Perpendicular Component Causal Account 
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References

  1. 1.
    Gabbey, “Huygens and mechanics”, 174–175; Andriesse, Titan, 235–243.Google Scholar
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  4. 4.
    OC13, 738–745. I date the sketch in 1672, instead of 1673 as the editors of Oeuvres Complètes have it. See page 92 above and page 140 below.Google Scholar
  5. 5.
    Hug2, 188r–188v.Google Scholar
  6. 6.
    OC13, 740. “mon principal dessein est de faire voir les raisons et les mesures des effects des lunettes ďapproche et des microscopes.”Google Scholar
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    OC13, 740. Huygens mentions Archimedes (things seen under water), Alhacen, Kepler and Galileo by name. He elaborated his historical account later during the 1680s.Google Scholar
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    OC13, 742. “difficultez contre des Cartes. ďoù viendrait ľacceleration. il fait la lumiere un conatus movendi, selon quoy il est malaisè ďentendre la refraction comme il ľexplique, a mon ais au moins.... lumiere s’estend circulairement et non dans ľinstant,...”Google Scholar
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  11. 11.
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    Kepler used ‘mensura’ (Kepler, KGW2, 78; Quoy qu’il suffise de poser ces loix pour principes de cette doctrine, comme estant tres certains par ľexperience, il ne sera pas hors de propos de rechercher plus profondement la cause de la refraction pour tascher de donner encore cette satisfaction a la curiositè de ľesprit qui aime a scavoir raison de toute chose. Et ďavoir au moins les causes possibles et vraysemblables que de demeurer dans une entiere ignorance.” see below). Descartes spoke of the laws of motion but of ‘mesurer les refractions’ (Descartes, AT6, 102). In his optical lectures of 1670 Newton used ‘regula’ and ‘mensura’ (Newton, Optical papers 1, I, 168–171 & 310–311). In Opticks Newton, like Huygens in Dioptrica, used ‘proportion’ or ‘ratio’ of sines (Newton, Opticks, 5–6 & 79’82).Google Scholar
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    This is equivalent with sini: tanr = constant. Lohne, “Kepler und Harriot”, 197. Compare Buchdahl, “Methodological aspects”, 283.Google Scholar
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  53. 57.
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  56. 60.
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    Descartes, AT6, 83. “imitant en cecy les Astronomes, qui, bien que leurs suppositions soyent presque toutes fausses ou incertaines, toutefois, a cause qu’elles se rapportent a diverses observations qu’ils ont faites, ne laissent pas ďen tirer plusieurs consequences tres vrayes & tres assurées.” (Translation based on Olscamp)Google Scholar
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    “Il est vray que ces loix de la refraction ne sont pas ľinvention de Mr. des Cartes selon toutes les apparences, car il est certain qu’il a vu le livre manuscrit de Snellius, que j’ay vu aussi;...” OC10, 405–6. See also OC13, 9 note 1.Google Scholar
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    Ziggelaar correctly points out that the problem of strange refraction was a reason Huygens did not directly elaborate ‘Projet’ (which he sees as a new plan for a treatise on dioptrics), but he does not discuss his first attempt to solve it beyond a single, and incorrect, characterization. Ziggelaar, “How”, 181–182. See also page 162.Google Scholar
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    disagree with the editors of the Oeuvres Complètes regarding the dating of the papers. I think this first study took place around the time of Pardies’ letter, much earlier than they presume. On 4 September 1672, hardly a month later, Huygens wrote to his brother Constantijn, saying he was not yet going to publish “what I have observed of the crystal or talc of Iceland” OC7, 219. “...ce que j’ay observè du Chrystal ou Talc ďIslande;...”. I think this remark refers to his discovery of another peculiar phenomenon displayed by Iceland crystal — polarization — recorded on the final pages of his investigation. The discovery is in OC19, 412–414. The editors date these between December 1672 and June 1673, but it is possible that they — or similar notes now lost — were written at the same, earlier date.Google Scholar
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    Hug2, 173v. One half of Hug2, 174r is torn away; the page contains a remark that seems of a later date.Google Scholar
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    Hug2, 173v; OC19, 407. “Perpendiculariter incidens refringitur Non facit duplicem reflexionem.” The editors combine this with a remark written on Hug2, 175v.Google Scholar
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    OC7, 193. “... il me semble qu’il n’est pas si malaisé que je m’estois imaginé, ďexpliquer cét effet. Je suis fort trompé si Ďon ne peut démonstrer que si Ďon taillait plusiers pieces de verre en rhomboide et qu’on les mit simplement Ďune sur Ďautre pour en faire un rhomboide total, il s’y feroit deux refractions.”Google Scholar
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    Lohne has published and translated an earlier draft of Experimenta, which shows that Bartholinus reordered the propositions for the final version and apparently rewrote the context of discovery. Lohne, “Nova experimenta”, 106–107.Google Scholar
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    Bartholinus, Experimenta, 19–20. The figure is erroneous, as Bartholinus pointed out too, for ED bisects the acute angle of the upper surface.Google Scholar
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    Bartholinus, Experimenta, 20–22. In the text the thirteenth experiment is also numbered XII.Google Scholar
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    In his fourteenth experiment, he explained how the mobile image might be rendered fixed — and viceversa — by considering alternative surfaces for observing the images. (Bartholinus, Experimenta, 22) It is questionable whether Bartholinus had actually made the observations he described here. Lohne has pointed out that, had it been carried out, it would have appeared to yield trivial or erroneous results. Lohne, “Nova Experimenta”, 135 note 29. Buchwald and Pedersen point out, however, that these observations are quite difficult to perform. Bartholinus, Experiments, 19–20 (Introduction).Google Scholar
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    Bartholinus, Experimenta, 29–30. Bartholinus attributed his discovery of strange refraction — that the duplicate image is caused by refraction instead of reflection — to this experiment, which however the earlier draft of his treatise does not include. Lohne, “Nova experimenta”, 106–107.Google Scholar
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    Bartholinus, Experimenta, 24. Translation by Archibald.Google Scholar
  130. 135.
    Bartholinus, Experimenta, 32. Translation by Archibald.Google Scholar
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    Bartholinus, Experimenta, 46–48. Modern notation: sin(i−17):sin(r−17)=5:3; Lohne, “Nova experimenta”, 142.Google Scholar
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    Bartholinus, Experimenta, 54. Translation by Archibald.Google Scholar
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    Bartholinus, Experiments, 18–19 (Introduction).Google Scholar
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    Hug2, 175v; OC19, 410 “Angulus FBC refractionis radii perpendicularis est paulo minor 7 grad. cum ad solis radios inquiritur.” The reference is to Figure 51.Google Scholar
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    Hug2, 175v; OC19, 410 “... introrsum versus perpendicularem refringuntur ut in LS, idque tanto magis quanto erunt ad KL radium obliquiores.”Google Scholar
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    Hug2, 176v; OC19, 412. “Adeo ut motus radij refracti intra crystallum sit veluti compositus ex motu quem regulariter haberet, et ex motu laterali cujus quantitas in toto descensu per crystallum est æqualis rectæ FC.”Google Scholar
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    Hag2, 177v; OC19, 412–413.Google Scholar
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    Hug2, 177r. Not reproduced in the Oeuvres Complètes.Google Scholar
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    Hug2, 178r; OC19, 413–414. “Pour rendre raison du phenomene de la page precedente, je me suis imaginè que dans ce crystal il y a deux matieres differentes, et qu’il y en a pareillement deux differentes en ľair ou ether dont le mouvement fait ce que nous appellons lumiere. Et que les deux mouvements ďundulation de ces deux matieres de ľether ont pouvoir ďemouvoir chacun sa matiere analogue des deux qui composent le crystal, et que reciproquement, ces matieres differentes du crystal estant esbranlees, ne sçavroient imprimer ce mouvement de lumiere qu’a leur matiere analogue de ľether.”Google Scholar
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    Hug2, 178r; OC19, 414. “Ce qui est tres difficile, car il faut pour cela, que ces rayons CE, DF quoyque non composez en frappant en certain sens la surface du crystal LN, puissent esbransler les 2 differentes matieres qui le composent, et en ďautres sens point.”Google Scholar
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    Hug2, 178v; OC19, 414–415. “Comment le rayon perpendiculaire peut il devenir oblique par la refraction, car il arrivera que les ondes ne seront pas a angles droits a la ligne de leur extension ou emanation, contre ce que demande notre hypothese de la lumiere.”Google Scholar
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    There is one reference to the nature of light in a planned introduction, of 1656, to his treatise on impact, which appears, however, to be in contradiction with his later views, as Huygens seems to adopt instantaneous propagation of light: “... if nature as a whole consists of certain corpuscules from the motion of which every diversity arises, and from the fastest impulse of which light is propagated in a moment of time and flows throughout the immense expanse of the sky,...” (OC16, 150; translation: Gabbey, “Huygens and mechanics”, 189)Google Scholar
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