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This is an annotated translation of Huygens' Horologium Oscillatorium , taken from the 'Gallica' website of the French National Library from the Oeuvres of Huygens, this also includes a French translation of the latin text; here the latin text is inculded last, from my own transcription. I am indebted both to the editors of Huygens' works, and to the Bibliotheque numerique This work inspired a generation of physicists and mathematicians, including Newton, Johanne Bernoulli, and Euler, for it reaches far beyond the working of pendulum clocks, and it still deserves a place in the historical presentation of the subject as presented today in elementary physics text books.
For example, most of the intuitive ideas about centripetal forces are presented here in Part V. I am indebted on several points to the translation of Richard J. Blackwell, which I discovered only after most of my own translation; this admirable translation does not however include mathematical notes, apart from an introduction by H. It must be stressed that this present work is my own independent translation, in which I have gone through most of the relevant mathematics, and the Huygens scholar will of course be aware of Blackwell's work as well as French and German translation.
This work also has the advantage of accessibility, and comes to you free of charge. Part 1 describes the work on clocks carried out by Huygens, and his attempts at the determination of longitude at sea. The tautochronous behaviour of the cycloid curve is used as a means of correcting the erratic behaviour of pendulums on ships.
Most of the first part is concerned with the making and testing of such clocks. Part IIA relates to a careful geometrical examination of the speed and distance travelled by a body falling from rest in successive time intervals both vertically and down inclined planes; before embarking on motion down the cycloid curve, which is set out in part IIB.
Huygens makes use of traditional Greek geometry and leans on Galileo in establishing the tautochronic behaviour of the cycloid, which is rather heavy going with such limited mathematical tools. If nothing else, it demonstrates the beauty of the analytical methods that were soon to appear. One presumes that Huygens made use of such tools in his derivation, which remain hidden.
Part III is a rather wonderful essay on the properties of the Evolutes of Curves and their lengths, starting with the cycloid, the parabola, and others derived from conic sections and higher order curves. Some results are only quoted, unfortunately, but this work gives a real insight into the state of mathematics in the middle of the 17th century.
One can understand why Huygens' book made such an impression on his peers, including Newton. Part IVA is a recipe for finding the centre of oscillation for a suspended shape. It is the first time the quantity that Euler later called the moment of inertia was investigated. You will find many familiar propositions here in an unfamiliar guise.
Part IVB evaluates the centre of oscillation for many familiar shapes in two and three dimesions as canditates for the pendulum bob. The later theorems return to the clock, which is now standardised, and a use in determining a standard of length, as well as the acceleration of gravity, are investigated. Truly, a wonderful piece of work : Huygens is seen as the outstanding physicist of the pre-Newton age who pointed the way forwards.
This work deserves to be read by all physicists and mathematicians with an interest in physics. Part V shows a different kind of clock, where the motion of the pendulum is circular, and the string unwinds from the evolute of a parabola. This clock was presumably used to conduct experments on circular motion, and on the misnamed centrifugal force in particular, for which a number of theorems are set out without proof.
XVI, pp , by M. Mahoney can be found on the web, which provides the analysis for the final theorems. Huygens' Pendulum Clock. Part I : Huygens' Pendulum Clock. Part IIa : The motion of falling bodies. Part IIb : The motion of a body falling along a cycloid. Part III : The evolutes and lengths of curves.
Part IVA : Concerning the centre of oscillation. Part IVB : Concerning the centre of oscillation. Part V : The construction of another kind of clock, and the enunciation of some theorems on centrifugal force. Ian Bruce. July latest revision. Copyright : I reserve the right to publish this translated work in book form.
However, if you are a student, teacher, or just someone with an interest, you can copy part or all of the work for legitimate personal or educational use. If you wish to send me a message, then click on my name. Christian Huygens : Horologium Oscillatorium.
Sale Price realised USD , Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae. Paris: F.
“THE HOROLOGIUM OSCILLATORIUM OF CHRISTIAN HUYGENS”
Horologium Oscillatorium: sive de motu pendulorum ad horologia aptato demonstrationes geometricae Latin for "The Pendulum Clock: or geometrical demonstrations concerning the motion of pendula as applied to clocks"  is a book published by Christiaan Huygens in ; it is his major work on pendulums and horology. The book is divided into five parts. The first part of the book contains the descriptions of clock designs. 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.