# Horologium Oscillatorium

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.

Horologium Oscillatorium: sive de motu pendulorum ad horologia aptato demostrationes geometricae (Latin: The Pendulum Clock: or geometrical demonstrations concerning the motion of pendula as applied to clocks),[1] often abbreviated Horologium Oscillatorium, is a book published by Christiaan Huygens in 1673; it is his major work on pendulums and horology.[2] This work is regarded as one of the three most important work done in mechanics in the 17th century, the other two being Galileo Galilei’s Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638) and Isaac Newton’s Philosophiæ Naturalis Principia Mathematica (1687).[3]

The book is divided into five parts, where the first part contains the 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 then uses these three rules to re-derive Galileo's original study of falling bodies, based on clearer logical framework.[4] 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.[5] 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. In the process, Huygens obtained solutions to dynamical problems such as the period of an oscillating simple pendulum as well as a compound pendulum, center of oscillation and its interchangeability with the pivot point, and the concept of moment of inertia.[6] 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.[7]

Levy & Wallach-Levy (2001) write that, as well as being known for its science, the book is also known for its strangely worded dedication to Louis XIV.[8] Joella G. Yoder writes that the appearance of the book in 1673 was a political issue, since at that time Netherlands was at war with France; and Huygens was anxious to show his allegiance to his patron, which can be seen in the obsequious dedication to Louis IV.[9]

## 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.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
2. Herivel, John. "Christiaan Huygens". Encyclopedia Britannica. Retrieved 14 November 2013.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
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5. 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.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
6. 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.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> gives a detailed description of Huygen's methods
7. Huygens, Christian (Aug 2013). "Horologium Oscillatorium (An English translation by Ian Bruce)". Retrieved 14 November 2013.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
8. Levy, David H.; Wallach-Levy, Wendee (2001), Cosmic Discoveries: The Wonders of Astronomy, Prometheus Books, ISBN 9781615925667<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
9. Yoder, Joella G. (2005), "Christiaan Huygens book on the pendulum clock 1673", Landmark Writings in Western Mathematics 1640-1940, Elsevier, ISBN 9780080457444<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.