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Horologium Oscillatorium

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Horologium Oscillatorium: Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (The Pendulum Clock: or Geometrical Demonstrations

Horologium Oscillatorium
AuthorChristiaan Huygens
LanguageLatin
GenrePhysics, Horology
Publication date
1673

Concerning the Motion of Pendula as Applied to Clocks)[1] is a book published by Christiaan Huygens in 1673 on pendulums and horology.[2] It is regarded as one of the three most important works on mechanics in the 17th century, the other two being Galileo’s Discorsi e dimostrazioni matematiche intorno a due nuove scienze (1638) and Newton’s Philosophiæ Naturalis Principia Mathematica (1687).[3][4]

Much more than a mere description of clocks, Huygens' Horologium Oscillatorium is the first modern treatise in which a physical problem (the accelerated motion of a falling body) is idealized by a set of parameters then analyzed mathematically, and constitutes one of the seminal works of applied mathematics. The book is also known for its strangely worded dedication to Louis XIV.[5] The appearance of the book in 1673 was a political issue, since at that time the Netherlands was at war with France; Huygens was anxious to show his allegiance to his patron, which can be seen in the obsequious dedication to Louis XIV.[6]

Overview

Illustration of Huygens' 1673 experimental pendulum clock from Horologium Oscillatorium. Huygens placed cycloidal-shaped metal "cheeks" on either side of the pendulum string, to force the pendulum to move in a cycloidal path, to increase accuracy.

In the winter of 1656-1657, Huygens developed the idea of using a pendulum as a regulator for clockworks. Pendulums were used in astronomical observations, sometimes connected to counting mechanisms. In cogwheel clocks, on the other hand, the movement was regulated by balances, the periods of which were strongly dependent on the sources of motive power of the clock and hence unreliable. The necessity for accurate measurement of time was felt especially in navigation, since good clocks were necessary to find longitude at sea. In a seafaring country like the Dutch Republic, this problem was of paramount importance.

Huygens designed his clock with the application of a freely suspended pendulum, whose motion is transmitted to the clockwork by a handle and fork. The first such clock dates from 1657, and was patented in the same year. Huygens’ invention was a rather obvious combination of existing elements, but it was a great success; many pendulum clocks were built and by 1658 pendulums had been applied to the tower clocks of Scheveningen and Utrecht.

Huygens continued his theoretical studies of the pendulum clock after 1658. The problem central to such mechanisms is that the usual simple pendulum is not exactly tautochronous. Its period depends on the amplitude, although when the amplitudes are small this dependence may be neglected. The best solution was to design the pendulum so that its bob moves in such a path that the dependence of period on amplitude is entirely eliminated. In 1659, Huygens discovered that complete independence of amplitude (and thus the ability to keep perfect time) can be achieved if the path of the pendulum bob is a cycloid. The next problem was what form to give the cheeks in order to lead the bob in a cycloidal path. This question led Huygens to the theory of evolutes of curves. His famous and surprising solution was that the cheeks must also have the form of a cycloid, on a scale determined by the length of the pendulum.

Huygens also studied the relation between period and length of the pendulum and developed the theory of the center of oscillation. By this theory the notion of “length” of a pendulum is extended to compound pendulums, so that Huygens could investigate how the period of a pendulum can be regulated by varying the position of an additional small weight on the arm. These studies form the main contents of Huygens’ Horologium oscillatorium (1673). After 1673, Huygens studied harmonic oscillation in general and attempted to determined longitudes at sea using his pendulum clocks, but his experiments carried on ships were not very successful.

Contents

The book is divided into five parts. The first and last parts of the book contain descriptions of clock designs, while the rest of the book is devoted to the analysis of pendulum motion and a theory of curves. In the second part of the book, Huygens states three hypotheses on the motion of bodies. They are essentially the law of inertia and the law of composition of "motion". He uses these three rules to re-derive Galileo's original study of falling bodies, based on clearer logical framework.[7] He then studies constrained fall, obtaining the solution to the tautochrone problem as given by a cycloid curve and not a circle as Galileo had conceived.[8] In the third part of the book, he outlines a theory of evolutes and rectification of curves. The fourth part of the book is concerned with the study of the center of oscillation. The derivations of propositions in this part is based on a single assumption: that the center of gravity of heavy objects cannot lift itself, which Huygens used as a virtual work principle. In the process, Huygens obtained solutions to dynamical problems such as the period of an oscillating pendulum as well as a compound pendulum, center of oscillation and its interchangeability with the pivot point, and the concept of moment of inertia.[9] The last part of the book gives propositions regarding bodies in uniform circular motion, without proof, and states the laws of centrifugal force for uniform circular motion.

Reception

References

  1. ^ Huygens, Christiaan; Blackwell, Richard J., trans. (1986). Horologium Oscillatorium (The Pendulum Clock, or Geometrical demonstrations concerning the motion of pendula as applied to clocks). Ames, Iowa: Iowa State University Press. ISBN 0813809339.{{cite book}}: CS1 maint: multiple names: authors list (link)
  2. ^ Herivel, John. "Christiaan Huygens". Encyclopædia Britannica. Retrieved 14 November 2013.
  3. ^ Bell, A. E. (30 Aug 1941). "The Horologium Oscillatorium of Christian Huygens". Nature. 148 (3748): 245–248. doi:10.1038/148245a0. S2CID 4112797. Retrieved 14 November 2013.
  4. ^ Huygens, Christian (August 2013). "Horologium Oscillatorium (An English translation by Ian Bruce)". Retrieved 14 November 2013.
  5. ^ Levy, David H.; Wallach-Levy, Wendee (2001), Cosmic Discoveries: The Wonders of Astronomy, Prometheus Books, ISBN 9781615925667.
  6. ^ Yoder, Joella G. (2005), "Christiaan Huygens book on the pendulum clock 1673", Landmark Writings in Western Mathematics 1640-1940, Elsevier, ISBN 9780080457444.
  7. ^ Ducheyne, Steffen (2008). "Galileo and Huygens on free fall: Mathematical and methodological differences". Dynamis : Acta Hispanica Ad Medicinae Scientiarumque. Historiam Illustrandam. 28: 243–274. doi:10.4321/S0211-95362008000100011. ISSN 0211-9536. Retrieved 2013-12-27.
  8. ^ Mahoney, Michael S. (March 19, 2007). "Christian Huygens: The Measurement of Time and of Longitude at Sea". Princeton University. Archived from the original on 2007-12-04. Retrieved 2013-12-27.
  9. ^ Bevilaqua, Fabio; Lidia Falomo; Lucio Fregonese; Enrico Gianetto; Franco Giudise; Paolo Mascheretti (2005). "The pendulum: From constrained fall to the concept of potential". The Pendulum: Scientific, Historical, Philosophical, and Educational Perspectives. Springer. pp. 195–200. ISBN 1-4020-3525-X. Retrieved 2008-02-26. gives a detailed description of Huygens' methods


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