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1655–1672-“De Aberratione”

Huygens’ practical optics and the aspirations of dioptrical theory
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Part of the Archimedes book series (ARIM, volume 9)

Keywords

Objective Lens Circular Motion Focal Distance Spherical Aberration Chromatic Aberration 
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References

  1. 1.
    Editor’s comment, OC15, 10. See also Anne van Helden, “Lens production”, 70.Google Scholar
  2. 3.
    OC15, 296–299.Google Scholar
  3. 4.
    Van Helden, “Huygens and the astronomers”, 150–154. Van Helden, “Divini vs Huygens”, 48–50.Google Scholar
  4. 5.
    OC15, 177; 230. Huygens employed Rhineland feet (0,3139 meters) and inches (0,026 meters).Google Scholar
  5. 6.
    It is reprinted in OC15, 403–437.Google Scholar
  6. 7.
    Van Helden, “Divini vs Huygens”, 36–40.Google Scholar
  7. 8.
    Van Helden, “Huygens and the astronomers” 148, 157–158.Google Scholar
  8. 9.
    Van Helden, Invention, 16–20.Google Scholar
  9. 10.
    Van Helden, Invention, 26; 47–48.Google Scholar
  10. 11.
    Descartes, Dioptrique, 2–3 (AT6, 82–83).Google Scholar
  11. 12.
    Shea, “Descartes and Ferrier”, 146–148.Google Scholar
  12. 13.
    AT1, 598–600. “Et il reussit parfaitement bien;⋯” It turned out that it was impossible to make a concave lens in the same way.Google Scholar
  13. 14.
    AT1, lts 8, 11, 12,13,22,21,27. Shea, “Descartes and Ferrier”. The letters not only reveal Ferrier’s mastery of the art but also his mathematical knowledge.Google Scholar
  14. 15.
    AT1, 33–35.Google Scholar
  15. 16.
    Descartes, Dioptrique, 141–150 (AT6, 215–224).Google Scholar
  16. 17.
    Ploeg, Constantijn Huygens, 34–38.Google Scholar
  17. 18.
    OC7, 111; 117; 487; 511–513. In 1654 Huygens described a mechanism to draw ellipses on the basis of a circle, apparently aimed at making elliptic lenses out of spherical ones; OC17, 287–292.Google Scholar
  18. 19.
    Next to numerous short entries, the main body is collected under the heading “Notes sur le rodage et le polisage des verres” in Beeckman, Journal, III, 371–431.Google Scholar
  19. 20.
    Beeckman, Journal, III, 69, 249, 308, 383.Google Scholar
  20. 21.
    Beeckman, Journal, III, 430.Google Scholar
  21. 22.
    OC1, 191. See also Anne van Helden, “Lens production”, 70–75.Google Scholar
  22. 23.
    OC1, 242. He distributed several telescopes of this design during the next decade. (OC1, 242; OC13, 264n3; OC4, 132–3; OC4, 224, 228–9)Google Scholar
  23. 24.
    OC17, 293–304.Google Scholar
  24. 25.
    OC17, 294. “altijdt redelijck nat gehouden om te beter de stof te bewaren. doch in’t eerst niet al te veel waters, want anders stoot het aen. altijdt dencken om gelijck te drucken, en dickwils de hand af gelicht en weer gelijck aen geset.’t is best alleen te sijn.⋯De andere sijde sleep ick eerst eens mis: daer de oorsaeck van was, of dat ick in’t eerst te veel water nam of dat ick niet op de goeije plaets en polijsten. ick verbeterdense eerst wat met op de rechte plaets noch eens te polijsten; daer nae met noch meer polijsten wierd het weer erger.”Google Scholar
  25. 26.
    The earliest lenses that remain—one in the Utrecht University Museum and two at Boerhaave Museum in Leiden—are not very good. Their fame as lens makers stems from the 1680s. Anne van Helden, “Lens production”, 75–78; Anne van Helden, Collection, IV; 22.Google Scholar
  26. 27.
    OC17, 299.Google Scholar
  27. 28.
    Beeckman, Journal, III, 232.Google Scholar
  28. 29.
    Bedini, “Makers”, 108–110; Bedini, “Lens making”, 688–691.Google Scholar
  29. 30.
    Bonelli, “Divini and Campani”, 21–25.Google Scholar
  30. 31.
    Van Helden, “Astronomical telescope”, 20–25. Compare Malet, “Kepler and the telescope”, 120.Google Scholar
  31. 32.
    Van Helden, “Compound”, 27–29; Keil, “Technology transfer”, 272–273. They are first mentioned in Rheita’s Oculus Enoch et Eliae (1645), who referred his readers to Wiesel. For the relationship between Rheita and Wiesel see Keill, Augustanus Opticus, 66–77.Google Scholar
  32. 33.
    Van Helden, “Compound eyepieces”, 34. The entire letter is reproduced on 34–35.Google Scholar
  33. 34.
    OC1, 308–311.Google Scholar
  34. 35.
    See for example the recent, formidable study on Wiesel by Inge Keill which may serve as a guide to themes and literature: Keil, Augustanus Opticus.Google Scholar
  35. 36.
    Daza, Uso de los antojos, 137–140. It appears that this classification in terms of ‘degrees’ was, at that time, replacing an older one in terms of the common age of someone bearing spectacles of a particular strength. The ‘grados’ Daza employs seem to be identical with the ‘punti’ Garzoni mentions in his discussion of the craft in La piazza universale (1585). See also: Pflugk, “Beitrâge”, 50–55.Google Scholar
  36. 37.
    Daza did not explain how the scale on the paper was established. Von Rohr has given an alluring suggestion as to how such a scale might be construed. Spectacle makers knew that multiple lenses of a given strength could be substituted by a stronger one to reach the same effect. Thus the first position on the scale was determined by a weak lens and the other positions determined by the amount of equal lenses which had to be put in those positions. Von Rohr, “Versuch”, 4.Google Scholar
  37. 38.
    Bedini & Bennet, “Treatise”.Google Scholar
  38. 39.
    Bedini & Bennet, “Treatise”, 120–121.Google Scholar
  39. 40.
    Bedini & Bennet, “Treatise”, 117.Google Scholar
  40. 41.
    Willach discusses dioptrical theory emerging from the correspondence of Rheita en Wiesel which suggests similar lines. Willach, “Development of telescope optics”, 390–394.Google Scholar
  41. 42.
    For example: Fontana’s Novae coelestium (1646) and Campani, Lettere di Giuseppe Campani intorne alľombre delle Stelle Medicee (1665).Google Scholar
  42. 43.
    OC21, 252–290.Google Scholar
  43. 44.
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  46. 47.
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  47. 48.
    McKeon, “Les débuts I”, 237.Google Scholar
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    OC15, 230–233.Google Scholar
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    Van Helden, “Compound eyepieces”, 33; Van Helden, “Huygens and the astronomers”, 158.Google Scholar
  50. 51.
    OC22, 568–576.Google Scholar
  51. 52.
    OC4, 242–3: “car pour les oculaires vous voyez bien que j’y ay trouvè quelque chose de nouveau, qui cause cette nettetè dans les lunettes du jour, et de mesme dans les plus longues, leur donnant en mesme temps une grande ouverture.”Google Scholar
  52. 53.
    Van Helden, “Compound eyepieces”, 33.Google Scholar
  53. 54.
    OC13, 252–259. The text in Oeuvres Complètes is probably from 1666. The notes contain some previous phrasing, probably from 1662. OC13, 252n1Google Scholar
  54. 55.
    OC13, 252–253. “Quanquam lentes non frustra sint multiplicandae, quod et vitri crassitudine et iteratis reflexionibus non parum lucis depereat; hic tamen utiliter id fieri experientia docuit.”Google Scholar
  55. 56.
    OC13, 256–257. “Atque ex hac oculi propinquitate sit primum ut naevi, seu bullulae minutissimae, quibus vitri materia nunquam caret, in lente EF percipi non possint. Sed neque in lente CD; quoniam oculus confuse cernit quae hic objiciuntur, distincte vero quae ad H.”Google Scholar
  56. 57.
    He developed a systematic theory of the field of view of a telescope much later, after 1685: OC13, 450–461, 468–73.Google Scholar
  57. 58.
    OC13, 252–253. “Dabimus autem in his, etsi non omnium optimam lentium compositionem, quam investigare longum esset ac forsan impossibile, at ejusmodi quam nobis experientia utilem esse ostendit.”Google Scholar
  58. 59.
    OC13, 258–265. Discussed above, section 2.1.2.Google Scholar
  59. 60.
    OC13, 262–263. “... res visas, atque etiam distinctiores efficere, nullisque colorum pigmentis infectas quod in hic lentium trium compositione aegre vitari potest.”Google Scholar
  60. 61.
    OC13, 264–265. “Alij vero aliter lentes oculares in his inter se consociant, sola experientia duce quid optimum sit quaerentes. nec sane facile foret certa ratione aliquid circa haec praecipere, quum colorum consideratio ad geometriae leges revocari nequeat,...”Google Scholar
  61. 62.
    A way to reduce colors that was more commonly employed, was to make objective lenses with large focal distances. These, however, had the drawback that telescopes became very long and tubes too heavy to remain straight. In 1662, it occurred to Huygens that this could be circumvented by making a tubeless telescope. He realized it much later and published a little tract on it, Astroscopia Compendiaria (1684). OC21, 201–231.Google Scholar
  62. 63.
    OC13, 318–319. “creditum est hactenus ⋯ sphaericae superficies minus aptae essent his usibus, nemine suspicante vitium convexarum lentium lentibus cavis tolli posse.”Google Scholar
  63. 64.
    Kepler, Paralipomena, 185–186 (KGW2, 168–169). Kepler repeated his insights in Dioptrice.Google Scholar
  64. 65.
    OC13, 82–83. “..., accuratius aliquanto eos propiusque ad unum punctum convenire ï, cum superficies convexa venientibus opposita est radijs, quam si plana ad illos convertatur.” Huygens had also written this to Gutschoven in his letter of 6 March 1653: OC1, 225. As we have seen above, Flamsteed carried out a numerical calculation and came to the same conclusion, which returned in Molyneux’ Dioptrica nova. Flamsteed, Gresham Lectures, 120–127. Molyneux, Dioptrica nova, 23–25.Google Scholar
  65. 66.
    OC13, LII (“Avertissement”), those later calculations are on pages 283–287.Google Scholar
  66. 67.
    OC13, 355–375.Google Scholar
  67. 68.
    OC13, 357.Google Scholar
  68. 69.
    OC13, 359.Google Scholar
  69. 70.
    OC13, 364. “DE spatium in axe intra quod radij omnes paralleli coguntur, quod spatium DE per regulam hanc definitur.”Google Scholar
  70. 71.
    OC13, 366–367. Modern methods yield the same result.Google Scholar
  71. 72.
    OC13, 375 and 370. In the latter case the solution yields a negative value for the radius of the posterior side.Google Scholar
  72. 73.
    OC13, 367. “Radius convexi objectivi ad radium convexi interioris in lente optima ut 1 ad 6. EUPHKA. 6 Aug. 1665.”Google Scholar
  73. 74.
    OC13, 280n2. “Quaenam lens sphaerica convexa melius radios parallelos coligat investigare.”Google Scholar
  74. 75.
    OC13, 280–281, “aberrationes radiorum quae ex figura superficierum sphaerica oriuntur”Google Scholar
  75. 76.
    The original tract is lost, but has been identified by Vermij with two manuscript copies discovered in London and Hannover. Both are dated 25 April 1656 and one gives the name of the author: “Huddenius consul Amstelodamensis”, which suggests the copy itself was made in or after 1672. Vermij, “Bijdrage”, 27; Vermij and Atzema, “Specilla circularia”, 104–107.Google Scholar
  76. 77.
    Spinoza, “Briefwisseling”, 251. Spinoza’s letters contain calculations that are similar to those in Specilla circularia. The letter can also be found in OC6, 36–39, where it is assumed to be addressed to Huygens.Google Scholar
  77. 78.
    OC1, 422. “propter accurationem”Google Scholar
  78. 79.
  79. 80.
    Vermij and Atzema, “Specilla circularia”, 119.Google Scholar
  80. 81.
    Vermij and Atzema, “Specilla circularia”, 116: “Ex quibus patet, quanto x sive BF minor est, tanto etiam punctum I longius distare ab N;”Google Scholar
  81. 82.
    Vermij and Atzema, “Specilla circularia”, 117: “Unde constat, focum ipsum pro puncto mechanico tantum habendum esse.”Google Scholar
  82. 83.
    Vermij and Atzema, “Specilla circularia”, 114: “Punctum autem mechanicum appello, quod in mechanicis aut divisible non est, aut cujus partes hic non sunt considerata digna.”Google Scholar
  83. 84.
    OC13, 276–277.Google Scholar
  84. 85.
    OC13, 308–313.Google Scholar
  85. 86.
    OC13, 282–285. Each time he assumed an index of refraction 3: 2.Google Scholar
  86. 87.
    OC13, 284–285. “Exigua quidem differentiola, sed quae in illa lentium latitudine quae telescopiorum usibus idonea est, nullius sit momenti.”Google Scholar
  87. 88.
    OC13, 284–287.Google Scholar
  88. 89.
    OC13, 290–291. “Et haec quidem methodus ad exactam supputationem adhibenda esset. Invenimus autem et hic Regulam compendiosam...”Google Scholar
  89. 90.
    OC13, 290–291. “Quae regula... inventa est neglectis minimis, sed necessario cum delectu.”Google Scholar
  90. 91.
    OC13, 290–291& 302–303.Google Scholar
  91. 92.
    OC13, 302–303. “..., sed aliae minus perfectae, quarum nempe vitijs compensantur ac corrigentur vitia lentis convexae,...”Google Scholar
  92. 93.
    OC13, 318–319. “Ex lentibus sphæricis cavis et convexis telesopia componere hactenus cognitis ejus generis meliora, perfectionemque eorum quæ ellipticis hyperbolicisve lentibus constant æmulantia.”Google Scholar
  93. 94.
    OC13, 320–323.Google Scholar
  94. 95.
    OC13, 324–327. For the rays KK and LM — that are not extreme rays — Huygens used the proposition on the linear proportion between aberration of a ray and the square of its distance to the axis. OC13, 308–313.Google Scholar
  95. 96.
    OC13, 318–319. “Sed certum est in convexis inter se compositis emendationem illam mutuam non reperiri. Imo contra, vitium exterioris lentis a lente ocularis augetur semper nonnihil neque id ulla ratione impediri potest.”Google Scholar
  96. 97.
    OC13, 332–335.Google Scholar
  97. 98.
    OC13, 336–337. “sed diligenter expendendum quale incrementum exterioris lentis apertura perferre valeat”Google Scholar
  98. 99.
    OC13, 340–343.Google Scholar
  99. 100.
    OC13, 342–345.Google Scholar
  100. 101.
    OC13, 348–351.Google Scholar
  101. 102.
    OC13, 350–353.Google Scholar
  102. 103.
    OC13, 303n4; 331n4.Google Scholar
  103. 104.
    OC5, 375; OC6, 23.Google Scholar
  104. 105.
    OC6, 151; 205; 207.Google Scholar
  105. 106.
    OC6, 86–87; 151; 205.Google Scholar
  106. 107.
  107. 108.
  108. 109.
    OC6, 214–215.Google Scholar
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    OC6, 214. “Ce composè,..., doibt faire autant que les verres hyperboliques, parce que le concave corrige les defauts de ľobjectif qui vienent de la figure spherique. c’est pourquoy je ne puis pas determiner ľouverture de ľobjectif qui peut etre pourra estre 3 ou 4 fois plus grande qu’a ľordinaire, mais si nous la pouvons seulement faire double ce sera beaucoup gaignè et la clartè sera assez grande pour la multiplication de 30.”Google Scholar
  110. 111.
    OC6, 218–220.Google Scholar
  111. 112.
    OC6, 220–221. “mais en decouvrant tout le verre je vois un peu de couleurs ce qui me fait croire qu’il y a un inconvenient de costè la, qui provient de ľangle que font les 2 surfaces de ľobjectif vers les bords. qui cause necessairement des couleurs, de sorte qu’en faisant des verres hyperboliques ľon trouueroit la mesme chose en les faisant fort grands.”Google Scholar
  112. 113.
    OC17, 341. Huygens’ measurements, as well as the experiments Newton performed at the same time, are amply discussed in Westfall, “Rings”.Google Scholar
  113. 114.
    OC6, 221. “mais devant que de ľassurer je serois bien aise de faire ľessay avec un verre entier, que je vous ay priè de me vouloir faire.”Google Scholar
  114. 115.
    OC6, 236; 266. He did not show consideration for the fact that Constantijn was getting ready for his marriage on 28 August 1668.Google Scholar
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    OC6, 266; 300.Google Scholar
  116. 117.
    OC6, 299–300.Google Scholar
  117. 118.
    OC6, 353. “Vous ne parlez plus des oculaires que vous m’avez promis.”Google Scholar
  118. 119.
    Little is known about him. He published an anti-Cartesian treatise Elementa physica in 1669 in which he included an extract of a letter written by Christiaan (OC6, 420–421). He first appears in a letter to Huygens of 20 December 1668, which suggests that they had met, probably in Paris. OC6, 304–305.Google Scholar
  119. 120.
    OC6, 353, “Le Seigneur Baron de Nulandt commence a parler en grand docteur, et me mande froidement, ďavoir trouvè les mesmes proportions de verres, pour imiter ľHyperbole, dont je lui avois parlè dans ma lettre, quoique je sasche bien que cela passe infiniment sa capacitè. Les calcus qu’il m’envoye sont trop eloignez de la veritè, et je ne manqueray pas de le lui remontrer.”Google Scholar
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    OC6, 348–351; particularly 350.Google Scholar
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    OC6, 363–367; particularly 364.Google Scholar
  122. 123.
    OC13, 408. “Lens composita hyperbolicae aemula. EUPHKA 1 Febr. 1669.”Google Scholar
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    OC6, 377. “Vous pourrez luy dire que je le quite pour ce qui est du petit oculaire que je luy avois demandè, ayant trouvè quelque chose meilleur et de plus considerable en cette matiere, dont j’ay envie de faire moy mesme ľessay.”Google Scholar
  124. 125.
    OC13, 413. “...[lens] compositae ex duabus VBC, KST, quae Hyperbolicae aut Ellipticae perfectionem aemulabitur.”Google Scholar
  125. 126.
    OC13, 411–413.Google Scholar
  126. 127.
    OC13, 417n2. “Lens e duabus composita hyperbolicam aemulatur, altera planoconvexa altera cava utrimque. Semidiametri superficierum sunt proximè duo, quinque, decem.”Google Scholar
  127. 128.
    OC4, 354–355 and OC13, 417. The solution of the anagram is: “Lens e duabus composita hyperbolicam aemulatur”.Google Scholar
  128. 129.
    Huygens may have tested the idea to combine two lenses into an objective earlier, at the time of the invention of 1665. Hug29, 76v and 77r contain sketches reminiscent of the earlier invention as well as ones reminiscent of the 1669 invetion. The folios can date from any time between the two inventions, but appear to reflect some intermediate stage in his thinking.Google Scholar
  129. 130.
    OC6, 460. In November the Royal Society decided to send Huygens a piece of the excellent glass made in England. OC6, 533 and note 5.Google Scholar
  130. 131.
    OC6, 389. “Monsieur permettez moy de vous presser de vouloir acheuer vostre Dioptrique de peur que vous n’y soyez prevenu de quelque autre.” He warned him again on April 8. OC6, 416.Google Scholar
  131. 132.
  132. 133.
    Rigaud, Correspondence II, 70.Google Scholar
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    OC7, 2–3. “...vous verrez quelque jour que ce que j’en ey escrit est encore tout different.”Google Scholar
  134. 135.
    OC7, 7–13; especially 10–11.Google Scholar
  135. 136.
    Discussed in: Bruins, “Problema Alhaseni”.Google Scholar
  136. 137.
    Hug2, 72r and Hug29, 87r respectively.Google Scholar
  137. 138.
    OC13, 409n2. “Hoc inutile est inventum propter Abberationem Niutoniana quae colores inducit.”Google Scholar
  138. 139.
    OC13, 314n1.Google Scholar
  139. 142.
    OC7, 124–125. “... qui envoye ľobject à ľoeil, et ľy represente sans aucune couleur et fort distinctement en toutes ses parties.”Google Scholar
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    OC7, 129–131.Google Scholar
  141. 144.
    OC7, 131 Huygens’ note a; 140–143. 145OC7, 134–136.Google Scholar
  142. 146.
    OC7, 134–136 (to Gallois); 140–141 (to Oldenburg). In a note added to the description of Newton’s reflector, Huygens calculated the difference of spherical aberration produced by a spherical lens and a spherical mirror. The aberrations produced by a lens and a mirror with the same focal distance and aperture are 28 to 3. Therefore, he concluded, the aperture of a mirror can be three times as large. OC7, 132.Google Scholar
  143. 147.
    OC7, 134 (to Gallois); 141 (to Oldenburg). Oldenburg had pointed this out to Huygens in the letter accompanying the description of Newton’s reflector: OC7, 128.Google Scholar
  144. 148.
    Oldenburg’s translation of OC7, 140 in: OldCor8, 520.Google Scholar
  145. 149.
    OC7, 156. “Dans cet imprimé vous trouverez une theorie nouvelle de Monsieur Newton, (...) touchant la lumiere et les couleurs: ou il maintient, que la lumiere n’est pas une chose similaire, mais un meslange de rayons refrangibles differemment...” The paper was therefore published in the issue preceding the one containing the description of his reflector.Google Scholar
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    Newton, Correspondence I, 95.Google Scholar
  147. 151.
    Newton, Correspondence I, 96–100.Google Scholar
  148. 152.
    OC7, 165. “... je vois qu’il a remarquè comme moy le defaut de la refraction des verres convexes objectifs a cause de ľinclination de leurs surfaces. Pour ce qui est de sa nouvelle Theorie des couleurs, elle me paroit fort ingenieuse, mais il faudra veoir si elle est compatible avec toutes les experiences.”Google Scholar
  149. 153.
    See also: Sabra, Theories of Light, 268–267.Google Scholar
  150. 154.
    OC7, 186. “Pour ce qui est de sa nouvelle hypothese des couleurs dont vous souhaittez scavoir mon sentiment, j’avoue que jusqu’icy elle me paroist tres vraysemblable, et ľexperimentum crucis (si j’entens bien, car il est ecrit un peu obscurement) la confirme beaucoup. Mais sur ce qu’il dit de ľabberration des rayons a travers des verres convexes je ne suis pas de son avis. Car je trouvay en lisant son ecrit que cette aberration suivant son principe devroit estre double de ce qu’il la fait, scavoir 1/25 de ľouverture du verre, a quoy pourtant ľexperience semble repugner. de sorte que peut estre cette aberration n’est pas tousjours proportionelle aux angles ďinclinaison des rayons.”Google Scholar
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    Newton, Correspondence I, 137.Google Scholar
  152. 156.
    Newton, Correspondence I, 212–213; OC7, 207–208.Google Scholar
  153. 157.
    OC7, 207–208.Google Scholar
  154. 158.
  155. 159.
    Newton, Correspondence 1, 131–132.Google Scholar
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    Newton, Correspondence 1, 157.Google Scholar
  157. 161.
    Newton, Correspondence 1, 205. “Je suis tres satisfait de la derniere réponse que M. Newton a bien voulu faire à mes instances.”Google Scholar
  158. 162.
    Sabra, Theories of Light, 270.Google Scholar
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    OC7, 228–229. “De plus quand il seroyt vray que les rayons de lumiere, des leur origine, fussent les uns rouges, les autres bleus &c. il resteroit encor la grande difficultè ďexpliquer par la physique, mechanique en quoy consiste cette diversitè de couleurs.”Google Scholar
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    OC7, 243. “Je ne vois pas aussi pourquoy Monsieur Newton ne se contente pas des 2 couleurs jaune et bleu, car il sera bien plus aisè de trouver quelque hypothese par le mouvement qui explique ces deux differences que non pas pour tant de diversitez quîl y a ďautres couleurs. Et jusqu’a ce qu’il ait trouvè cette hypothese il ne nous aura pas appris en quoy consiste la nature et difference des couleurs mais seulement cet accident (qui assurement est fort considerable) de leur differente refrangibilitè.”Google Scholar
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    OC7, 243–244. “Au reste pour ce qui est de ľeffect des differentes refractions des rayons dans les verres de lunettes, il est certaine que ľexperience ne s’accorde pas avec ce que trouve Monsieur Newton, car a considerer seulement la peinture distincte que fait un objectif de 12 pieds dans une chambre obscure, ľon voit qu’elle est trop distincte et trop bien terminée pour pouvoir estre produite par des rayons qui s’escarteroient de la 50me partie de ľouverture de sorte que, comme je vous crois avoir mandè desia cy devant la difference de la refrangibilité ne suit pas peut estre tousjours de la mesme proportion dans les grandes et petites inclinations des rayons sur les surfaces du verre.”Google Scholar
  163. 167.
    Because he was a ‘devoted water-color painter’, Shapiro is puzzled about Huygens’ assertion that yellow and blue may produce white, “... because this is contrary to all beliefs about color mixing held in the seventeenth century.” Shapiro, “Evolving structure”, 223–224. We should bear in mind that Huygens was also an experienced employer of magic lanterns.Google Scholar
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    Newton, Correspondence I, 173.Google Scholar
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    OC7, 265–266 and Newton, Correspondence I, 264–265.Google Scholar
  167. 171.
    OC7, 267 and Newton, Correspondence I, 266. In Opticks, he elaborated this argument a bit further and mathematically, and reduced chromatic aberration to 1/250 of the aperture as contrasted to the original 1/50. Newton, Optical lectures, 429n15.Google Scholar
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    OC7, 302–303. “...mais aussi doit il avouer que cette abstraction des rayons ne nuit donc pas tant aux verres qu’il semble avoir voulu faire accroire, lors qu’il a proposè les mirroirs concaves comme la seule esperance de perfectionner les telescopes.”Google Scholar
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© Springer Science + Business Media, Inc. 2005

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