Skip to main content

1655–1672-“De Aberratione”

Huygens’ practical optics and the aspirations of dioptrical theory

  • Chapter
Book cover Lenses and Waves

Part of the book series: Archimedes ((ARIM,volume 9))

  • 696 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Editor’s comment, OC15, 10. See also Anne van Helden, “Lens production”, 70.

    Google Scholar 

  2. OC15, 296–299.

    Google Scholar 

  3. Van Helden, “Huygens and the astronomers”, 150–154. Van Helden, “Divini vs Huygens”, 48–50.

    Google Scholar 

  4. OC15, 177; 230. Huygens employed Rhineland feet (0,3139 meters) and inches (0,026 meters).

    Google Scholar 

  5. It is reprinted in OC15, 403–437.

    Google Scholar 

  6. Van Helden, “Divini vs Huygens”, 36–40.

    Google Scholar 

  7. Van Helden, “Huygens and the astronomers” 148, 157–158.

    Google Scholar 

  8. Van Helden, Invention, 16–20.

    Google Scholar 

  9. Van Helden, Invention, 26; 47–48.

    Google Scholar 

  10. Descartes, Dioptrique, 2–3 (AT6, 82–83).

    Google Scholar 

  11. Shea, “Descartes and Ferrier”, 146–148.

    Google Scholar 

  12. 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. 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. AT1, 33–35.

    Google Scholar 

  15. Descartes, Dioptrique, 141–150 (AT6, 215–224).

    Google Scholar 

  16. Ploeg, Constantijn Huygens, 34–38.

    Google Scholar 

  17. 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. 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. Beeckman, Journal, III, 69, 249, 308, 383.

    Google Scholar 

  20. Beeckman, Journal, III, 430.

    Google Scholar 

  21. OC1, 191. See also Anne van Helden, “Lens production”, 70–75.

    Google Scholar 

  22. 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. OC17, 293–304.

    Google Scholar 

  24. 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. 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. OC17, 299.

    Google Scholar 

  27. Beeckman, Journal, III, 232.

    Google Scholar 

  28. Bedini, “Makers”, 108–110; Bedini, “Lens making”, 688–691.

    Google Scholar 

  29. Bonelli, “Divini and Campani”, 21–25.

    Google Scholar 

  30. Van Helden, “Astronomical telescope”, 20–25. Compare Malet, “Kepler and the telescope”, 120.

    Google Scholar 

  31. 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. Van Helden, “Compound eyepieces”, 34. The entire letter is reproduced on 34–35.

    Google Scholar 

  33. OC1, 308–311.

    Google Scholar 

  34. 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. 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. 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. Bedini & Bennet, “Treatise”.

    Google Scholar 

  38. Bedini & Bennet, “Treatise”, 120–121.

    Google Scholar 

  39. Bedini & Bennet, “Treatise”, 117.

    Google Scholar 

  40. 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. For example: Fontana’s Novae coelestium (1646) and Campani, Lettere di Giuseppe Campani intorne alľombre delle Stelle Medicee (1665).

    Google Scholar 

  42. OC21, 252–290.

    Google Scholar 

  43. Van Helden, “The telescope in the 17th century”, 44–49.

    Google Scholar 

  44. Bedini, “The tube of long vision”, 157–159.

    Google Scholar 

  45. OC15, 56.

    Google Scholar 

  46. OC13, 826. “N.B. me anno 1659 in Systemate Saturnio meo docuisse usum diaphragmatis quod vocant, in foco ocularis lentis ponendi, absque quo colorum vitio haec telescopia carere non poterant.” In 1694 he explicitly claimed that he was the first to use a diaphragm: OC13, 774.

    Google Scholar 

  47. McKeon, “Les débuts I”, 237.

    Google Scholar 

  48. OC15, 230–233.

    Google Scholar 

  49. Van Helden, “Compound eyepieces”, 33; Van Helden, “Huygens and the astronomers”, 158.

    Google Scholar 

  50. OC22, 568–576.

    Google Scholar 

  51. 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. Van Helden, “Compound eyepieces”, 33.

    Google Scholar 

  53. OC13, 252–259. The text in Oeuvres Complètes is probably from 1666. The notes contain some previous phrasing, probably from 1662. OC13, 252n1

    Google Scholar 

  54. 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. 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. 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. 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. OC13, 258–265. Discussed above, section 2.1.2.

    Google Scholar 

  59. 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. 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. 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. 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. Kepler, Paralipomena, 185–186 (KGW2, 168–169). Kepler repeated his insights in Dioptrice.

    Google Scholar 

  64. 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. OC13, LII (“Avertissement”), those later calculations are on pages 283–287.

    Google Scholar 

  66. OC13, 355–375.

    Google Scholar 

  67. OC13, 357.

    Google Scholar 

  68. OC13, 359.

    Google Scholar 

  69. OC13, 364. “DE spatium in axe intra quod radij omnes paralleli coguntur, quod spatium DE per regulam hanc definitur.”

    Google Scholar 

  70. OC13, 366–367. Modern methods yield the same result.

    Google Scholar 

  71. OC13, 375 and 370. In the latter case the solution yields a negative value for the radius of the posterior side.

    Google Scholar 

  72. OC13, 367. “Radius convexi objectivi ad radium convexi interioris in lente optima ut 1 ad 6. EUPHKA. 6 Aug. 1665.”

    Google Scholar 

  73. OC13, 280n2. “Quaenam lens sphaerica convexa melius radios parallelos coligat investigare.”

    Google Scholar 

  74. OC13, 280–281, “aberrationes radiorum quae ex figura superficierum sphaerica oriuntur”

    Google Scholar 

  75. 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. 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. OC1, 422. “propter accurationem”

    Google Scholar 

  78. OC1, 429.

    Google Scholar 

  79. Vermij and Atzema, “Specilla circularia”, 119.

    Google Scholar 

  80. 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. Vermij and Atzema, “Specilla circularia”, 117: “Unde constat, focum ipsum pro puncto mechanico tantum habendum esse.”

    Google Scholar 

  82. 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. OC13, 276–277.

    Google Scholar 

  84. OC13, 308–313.

    Google Scholar 

  85. OC13, 282–285. Each time he assumed an index of refraction 3: 2.

    Google Scholar 

  86. OC13, 284–285. “Exigua quidem differentiola, sed quae in illa lentium latitudine quae telescopiorum usibus idonea est, nullius sit momenti.”

    Google Scholar 

  87. OC13, 284–287.

    Google Scholar 

  88. OC13, 290–291. “Et haec quidem methodus ad exactam supputationem adhibenda esset. Invenimus autem et hic Regulam compendiosam...”

    Google Scholar 

  89. OC13, 290–291. “Quae regula... inventa est neglectis minimis, sed necessario cum delectu.”

    Google Scholar 

  90. OC13, 290–291& 302–303.

    Google Scholar 

  91. OC13, 302–303. “..., sed aliae minus perfectae, quarum nempe vitijs compensantur ac corrigentur vitia lentis convexae,...”

    Google Scholar 

  92. 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. OC13, 320–323.

    Google Scholar 

  94. 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. 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. OC13, 332–335.

    Google Scholar 

  97. OC13, 336–337. “sed diligenter expendendum quale incrementum exterioris lentis apertura perferre valeat”

    Google Scholar 

  98. OC13, 340–343.

    Google Scholar 

  99. OC13, 342–345.

    Google Scholar 

  100. OC13, 348–351.

    Google Scholar 

  101. OC13, 350–353.

    Google Scholar 

  102. OC13, 303n4; 331n4.

    Google Scholar 

  103. OC5, 375; OC6, 23.

    Google Scholar 

  104. OC6, 151; 205; 207.

    Google Scholar 

  105. OC6, 86–87; 151; 205.

    Google Scholar 

  106. OC6, 207.

    Google Scholar 

  107. OC6, 209.

    Google Scholar 

  108. OC6, 214–215.

    Google Scholar 

  109. 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. OC6, 218–220.

    Google Scholar 

  111. 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. OC17, 341. Huygens’ measurements, as well as the experiments Newton performed at the same time, are amply discussed in Westfall, “Rings”.

    Google Scholar 

  113. 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. 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 

  115. OC6, 266; 300.

    Google Scholar 

  116. OC6, 299–300.

    Google Scholar 

  117. OC6, 353. “Vous ne parlez plus des oculaires que vous m’avez promis.”

    Google Scholar 

  118. 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. 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 

  120. OC6, 348–351; particularly 350.

    Google Scholar 

  121. OC6, 363–367; particularly 364.

    Google Scholar 

  122. OC13, 408. “Lens composita hyperbolicae aemula. EUPHKA 1 Febr. 1669.”

    Google Scholar 

  123. 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. OC13, 413. “...[lens] compositae ex duabus VBC, KST, quae Hyperbolicae aut Ellipticae perfectionem aemulabitur.”

    Google Scholar 

  125. OC13, 411–413.

    Google Scholar 

  126. OC13, 417n2. “Lens e duabus composita hyperbolicam aemulatur, altera planoconvexa altera cava utrimque. Semidiametri superficierum sunt proximè duo, quinque, decem.”

    Google Scholar 

  127. OC4, 354–355 and OC13, 417. The solution of the anagram is: “Lens e duabus composita hyperbolicam aemulatur”.

    Google Scholar 

  128. 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. 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. 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. OC6, 534.

    Google Scholar 

  132. Rigaud, Correspondence II, 70.

    Google Scholar 

  133. OC7, 2–3. “...vous verrez quelque jour que ce que j’en ey escrit est encore tout different.”

    Google Scholar 

  134. OC7, 7–13; especially 10–11.

    Google Scholar 

  135. Discussed in: Bruins, “Problema Alhaseni”.

    Google Scholar 

  136. Hug2, 72r and Hug29, 87r respectively.

    Google Scholar 

  137. OC13, 409n2. “Hoc inutile est inventum propter Abberationem Niutoniana quae colores inducit.”

    Google Scholar 

  138. OC13, 314n1.

    Google Scholar 

  139. OC7, 124–125. “... qui envoye ľobject à ľoeil, et ľy represente sans aucune couleur et fort distinctement en toutes ses parties.”

    Google Scholar 

  140. OC7, 129–131.

    Google Scholar 

  141. OC7, 131 Huygens’ note a; 140–143. 145OC7, 134–136.

    Google Scholar 

  142. 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. 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. Oldenburg’s translation of OC7, 140 in: OldCor8, 520.

    Google Scholar 

  145. 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 

  146. Newton, Correspondence I, 95.

    Google Scholar 

  147. Newton, Correspondence I, 96–100.

    Google Scholar 

  148. 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. See also: Sabra, Theories of Light, 268–267.

    Google Scholar 

  150. 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 

  151. Newton, Correspondence I, 137.

    Google Scholar 

  152. Newton, Correspondence I, 212–213; OC7, 207–208.

    Google Scholar 

  153. OC7, 207–208.

    Google Scholar 

  154. OC7, 215.

    Google Scholar 

  155. Newton, Correspondence 1, 131–132.

    Google Scholar 

  156. Newton, Correspondence 1, 157.

    Google Scholar 

  157. 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. Sabra, Theories of Light, 270.

    Google Scholar 

  159. 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 

  160. OC7, 242–244.

    Google Scholar 

  161. 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 

  162. 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. 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 

  164. Newton, Correspondence I, 173.

    Google Scholar 

  165. Shapiro, “Evolving structure”, 224–225.

    Google Scholar 

  166. OC7, 265–266 and Newton, Correspondence I, 264–265.

    Google Scholar 

  167. 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 

  168. 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 

  169. OC7, 302. “..., mais voyant qu’il soustient son opinion avec tant de chaleur cela m’oste ľenvie de disputer.”

    Google Scholar 

  170. OC7, 315.

    Google Scholar 

  171. OC7, 328–333 and Newton, Correspondence I, 291–295. See also Shapiro, “Evolving structure”, 225–228.

    Google Scholar 

  172. For example Sabra, Theories of Light, 268–272.

    Google Scholar 

  173. Shapiro, “Gradual acceptance”, 78–80.

    Google Scholar 

  174. With connected reproduced in OC17, 364–516. On the dating see OC17, 359.

    Google Scholar 

  175. OC17, 373. “Doch de reden van dese couleuren verder te ondersoecken, te weten waerom die in een prisma gegenereert worden, wil ick geensins ondernemen, emo fateor rationem eorum me prorsus ignorare, neque facile quemquam ipsas perspecturum arbitror quandiu naturalium rerum scientiae major aliqua lux non affulserit.”

    Google Scholar 

  176. Newton, Certain philosophical questions, 467.

    Google Scholar 

  177. Westfall, Never at rest, 163–164.

    Google Scholar 

  178. Newton, Optical papers 1, 47 & 281.

    Google Scholar 

  179. Newton, Optical papers 1, 49 & 283.

    Google Scholar 

  180. Newton, Correspondence 1, 96.

    Google Scholar 

  181. Traité, 1. “... toutes les sciences où la Geometrie est appliquée à la matiere,...”

    Google Scholar 

  182. Yoder, Unrolling time, 16–17.

    Google Scholar 

  183. Yoder, Unrolling time, 33–34.

    Google Scholar 

  184. Yoder, Unrolling time, 19–23. This expression for centrifugal tendency amounts to the modern formula: F=mv2/r.

    Google Scholar 

  185. Yoder, Unrolling time, 27–32.

    Google Scholar 

  186. Yoder, Unrolling time, 48–59.

    Google Scholar 

  187. The first draft of De vi centrifuga opened with a quotation of Horace: “Freely I stepped into the void, the first”, above his discovery of the isochronicity of the cycloid he wrote: “Great matters not investigated by the men of genius among our forefathers; Yoder, Unrolling time, 42 and 61.

    Google Scholar 

  188. Yoder, Unrolling time, 62–64.

    Google Scholar 

  189. Westfall, Force, 160–165.

    Google Scholar 

  190. Yoder, Unrolling time, 171–173.

    Google Scholar 

  191. Yoder, Unrolling time, 31–32.

    Google Scholar 

  192. Yoder, Unrolling time, 170–171.

    Google Scholar 

  193. Cohen, Quantifying music, 209–230 and Cohen, “Huygens and consonance”, 271–301.

    Google Scholar 

  194. OC20, 37. Translation: Cohen, Quantifying music, 214.

    Google Scholar 

  195. Most of Huygens’ musical studies is reproduced in OC20, 1–173. The French and Latin versions of the letter have been reprinted with Dutch and English translations by Rasch in: Huygens, Le cycle harmonique.

    Google Scholar 

  196. Cohen, Quantifying music, 225–226.

    Google Scholar 

  197. Cohen, Quantifying music, 209. It should be noted that, unlike his predecessors, Huygens possessed logarithms and was therefore readily able to calculate, for example, \( a\sqrt[4]{{\tfrac{1} {5}}}\).

    Google Scholar 

  198. Cohen, “Huygens and consonance”, 293–294.

    Google Scholar 

  199. Yoder, Unrolling time, 71–73.

    Google Scholar 

  200. Westfall, Force, 165–167.

    Google Scholar 

  201. Cohen, Quantifying music, 224.

    Google Scholar 

  202. In his lectures Newton derived a formula for spherical aberration. Newton, Optical papers 1, 405–411.

    Google Scholar 

  203. His discovery of dispersion led him to conclude that no lens could ever prevent the disturbing effects of aberration and made him design his reflector. Shortly after he published his theory, he did consider the possibility that chromatic aberration could be prevented in lenses. In a letter to Hooke (Newton, Correspondence I, 172), he alluded to the possibility of constructing a compound lens that canceled out chromatic aberration. Pursuing an idea of Hooke’s, he considered the possibility of using a lens compounded of different refracting media in which chromatic aberration was cancelled in the course of consecutive refractions. (Newton, Mathematical Papers I, 575–576). In Opticks he ruled out this possibility, probably because it was at odds with the dispersion law he put forward in it. Shapiro, “Dispersion law”, 102–113; Bechler, “Disagreeable”, 107–119.

    Google Scholar 

  204. OC13, 435. “Sed hoc tam longe abest, ut fortuito reperti artificij rationem non adhuc satis explicare potuerint viri doctissimi.”

    Google Scholar 

  205. Van Helden, “Huygens and the astronomers”, 148 & 158–159.

    Google Scholar 

  206. Boas, “Oldenburg, the ‘Philosophical transactions’, and technology”, 27–35; Ochs, “Royal society”

    Google Scholar 

  207. Another example is Castelli’s attempt to engineer river hydraulics, discussed in Maffioli, Out of Galileo.

    Google Scholar 

  208. OC4, 325–329.

    Google Scholar 

  209. Westfall, “Science and technology”, 72.

    Google Scholar 

  210. OC13, 439. “Quae magna et praeclara esse quis nisi plane stupidus non agnoscit?”

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science + Business Media, Inc.

About this chapter

Cite this chapter

(2005). 1655–1672-“De Aberratione”. In: Lenses and Waves. Archimedes, vol 9. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2698-8_3

Download citation

Publish with us

Policies and ethics