Christiaan Huygens’ Galilean Mechanics

  • Christiane Vilain
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 239)


In 1646, Constantijn Huygens informed Marin Mersenne that his son Christiaan, who was only 16 years old, was studying the acceleration of falling bodies.1 We know that at that time, the young Huygens had not yet read Galileo’s Discorsi e dimostrazioni matematiche intorno a due nuove scienze (1638). His interest in the phenomenon of free fall had been kindled by the reading of the Sublimium ingeniorum crux by Juan Caramuel y Lobkowitz, a booklet published in 1644 and devoted to determining the exact law of natural acceleration.2 In this work, Caramuel first illustrated the rivalling laws of fall proposed by his contemporaries and the alleged empirical evidence in their favor and then presented his own mathematical and experimental analysis of this phenomenon.3 According to Caramuel, the acceleration of fall did not follow the Galilean law of the odd numbers, but rather the law of the natural numbers.


Seventeenth Century Free Fall Uniform Motion Successive Interval Inertial Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    On 12 September, 1646, Constantijn Huygens sr. sent to Mersenne a copy of a letter that his son Christiaan had sent to his elder brother Constantijn, announcing among other things, that he had managed to demonstrate that the spaces traversed in equal and successive intervals of time by a body falling from rest grow according to series of the odd numbers. See Christiaan Huygens to Constantijn Huygens jr., 3 September, 1646, Huygens, Oeuvres, I, pp. 18–19; Constantijn Huygens sr. to M. Mersenne, 12 September, 1646, Huygens, Oeuvres, II, pp. 547–550.Google Scholar
  2. 2.
    See Huygens, De motu naturaliter accelerato in Huygens, Oeuvres, xI, pp. 68–75.Google Scholar
  3. 3.
    Caramuel y Lobkowitz, Sublimium ingeniorum crux. Google Scholar
  4. 4.
    Huygens, Oeuvres, I, pp. 558–559.Google Scholar
  5. 5.
    See Huygens’ letter to Mersenne of 28 October 1646, Huygens, Oeuvres, I, pp. 24–27. Huygens’ proof has been analyzed in detail in Nardi, “Spazi del moto,” pp. 336–337; Costabel, “Huygens et la mécanique,” pp. 140–141, and Palmerino, “Infinite Degrees of Speed,’ pp. 323–324. It should be mentioned that in Caramuel’s work there was no talk of scale invariance and that in his Sublimium ingeniorum crux, he tacitly assumed that all alternative laws of fall were valid irrespective of the interval of time that was chosen as the unit of measure. This was however, only true for the Galilean law.Google Scholar
  6. 6.
    Galilei, Le Opere [Favaro], vIII, p. 211.Google Scholar
  7. 7.
    Horologium oscillatorium, Pars secunda, Huygens, Oeuvres, xvIII, pp. 125–133.Google Scholar
  8. 8.
    I have investigated this question in Vilain, La Mécanique. A good analysis of Huygens’ writings on the relativity of motion is found in Mormino, Penetralia Motus. Google Scholar
  9. 9.
    In his Dialogo, Galileo had maintained that an iron ball of loo pounds needed 5 seconds to traverse 1oo braccia. In the Harmonie universelle, Mersenne declared that upon repeating this experiment many times and in the presence of witnesses, he had found that, in 5 seconds, a falling body traversed not Ioo, but 180 braccia. See Mersenne, Harmonie universelle, I, pp. 85–92. Such measurements were usual before 1644, as testified by Caramuel’s work.Google Scholar
  10. 10.
    See Dear, Discipline, ch. 5; Dear, “Mersenne;’ and Dear, Revolutionizing the Sciences, ch.7, for a more synthetic approach to the role of experience in seventeenth century science.Google Scholar
  11. 11.
    This procedure is well described in Costabel, “Isochronisme et accélération., Costabel’s paper is the ideal follow-up of Koyré, “Une expérience.,Google Scholar
  12. 12.
    See the Appendix I of the De motu corporum ex percussione, Huygens, Oeuvres, xvI, p. 92.Google Scholar
  13. 13.
    Huygens to René de Sluse, 13 January, 1658: “Experientias me sectari ne existimes, scio enim lubricas esse,” Huygens, Oeuvres, II, p. 115. See also Huygens, Oeuvres, xvI, p. 172. Huygens’ sentence is however too isolated to be taken as a personal methodological declaration.Google Scholar
  14. 14.
    See Galilei, Two New Sciences [Drake], p. 76.Google Scholar
  15. 15.
    The case is different for the experiments on void performed by Blaise Pascal and others.Google Scholar
  16. 16.
    I have tried to summarize this demonstration in Vilain, “Figures et écritures:’ However, the best account is still found in Huygens, Oeuvres, xvI, pp. 254–301Google Scholar
  17. 17.
    See for instance the drawing that appears in Huygens’ letter to Pierre Petit dated 1 November,1658, Huygens, Oeuvres, II, p. 271.Google Scholar
  18. 18.
    Such an intuitive approach is even more evident in a further demonstration found in Pardies, La Statique. Google Scholar
  19. 19.
    For a more detailed explanation of how Huygens and Newton used the Galilean law of fall as a sort of ”algorithm” for integration, see Vilain, “La loi galiléenne:’Google Scholar
  20. 20.
    For an exhaustive and clever presentation of Huygens’ mathematical physics, see Yoder, Unrolling Time. Google Scholar
  21. 21.
    As is well known, Galileo’s new science of motion relied on Cavalieri’s geometry of indivisibles rather than on the Archimedean method.Google Scholar
  22. 22.
    Huygens, Oeuvres, xvI, p. 398. This draft is part of a very important manuscript concerning the discovery of the tautochronism of the cycloid and has been duly commented by the editors of Huygens’ works (ibid., pp. 392–413). Google Scholar
  23. 23.
    On the role of principles in Huygens’ mechanics, see Gabbey, “Huygens and Mechanics:’Google Scholar
  24. 24.
    De motu corporum ex percussione, Huygens, Oeuvres, xvI, pp. 30–91. This work, which was written by Huygens in 1656, was not published during his lifetime. It appeared for the first time in the posthumous edition by de Volder and Fullenius of 1703. Though Huygens did not publish the treatise, he must have attached great importance to it because he tried to improve it until the end of his life.Google Scholar
  25. 25.
    We recall that the first of Descartes’ rules of impact states that if two bodies of equal size that move with the same speed in a straight line towards one another collide they both rebound, returning in the direction from which they have come without losing any speed.Google Scholar
  26. 26.
    See La Cena de le Ceneri (London, 1584) in Bruno, Dialoghi italiani [Gentile e.a.], pp. 116–117.Google Scholar
  27. 27.
    Descartes, Oeuvres [Adam e.a.], IX-2, p. 88.Google Scholar
  28. 28.
    I have discussed this important problem in ch.5 of Vilain, La Mécanique. Google Scholar
  29. 29.
    See Huygens, Oeuvres, xvI, pp. 32–33.Google Scholar
  30. 30.
    “Ex nostro principio [ ... ] motum non esse nisi respectum [ ... ] ;’ Huygens writes in the manuscript L, folio 6R.Google Scholar
  31. 31.
    “Non est mathematicè difficilis materia, sed physicè aut hyperphysicè;’ Huygens, Oeuvres, xvI, p. 213.Google Scholar
  32. 32.
    ”Ex hoc vero motu ad corpora inter se quiescentia relato, intelligi ac definiri demum potest quid sit in linea recta libere at aequabiliter moveri adeo ut nec cursus rectus et aequabilis navigij, [ ...1 alia ratione talis censeri queat, quam partium terrae inter se quiescentium respectu;’ Huygens, Oeuvres, xvI, pp. 218–219.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Christiane Vilain

There are no affiliations available

Personalised recommendations