THE PENDULUM CLOCK

BY CHRISTIAAN HUYGENS

we have applied to clocks, the motion of which has emerged as so constant and certain that, after frequent experiments conducted on land and at sea, it is now manifest that there is a great deal of protection original: "præsidij" - meaning support or utility for the studies of Astronomy and the art of Navigation in them. This is that very line which a nail, fixed on the circumference of a running wheel, designates in the air by its continuous revolution; it was given the name cycloid The curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line. by the Geometers of our age, and has been diligently examined for many of its other properties; but it was by us that its capacity for measuring time was discovered—a quality we found inherent in it while suspecting no such thing, and merely following the tracks of our craft. Although we made this known some time ago to friends who understand these matters (for it was noticed not long after the first edition of the Horologium), we now propose the same to be read by all, strengthened by the most accurate demonstration we could provide. Therefore, the most significant part of this book will be occupied in delivering this demonstration. In this, it was first necessary to establish and further promote, with several new proofs, the doctrine of the great man Galileo regarding the descent of heavy bodies; the most longed-for fruit and, as it were, the highest peak of this doctrine is this very property of the cycloid which we have found.

Furthermore, so that this could be adapted to the use of pendulums, a new consideration of curved lines had to be applied—namely, those which generate other curves by their own "unrolling" evolutes: the curve formed by the centers of curvature of another curve. From this arises a comparison between the length of curves and straight lines, which I have pursued even further than present necessity demanded, because of the elegance and novelty of the theory, as it seemed to me.

Moreover, to explain the nature of the Compound Pendulum, the utility of which I demonstrate in the construction of these automata mechanical clocks, I had to add a contemplation of the Centers of Oscillation. This has been attempted by many before, though with less success; in this section, several theorems will be found worthy of notice, I believe, pertaining to linear, plane, and solid figures. Before all of this, however, the mechanical construction of the clock itself is presented, along with the application of the pendulum in that form which has been found most suitable for astronomical uses, according to the model of which all others can easily be arranged, with the necessary changes.

But because it happened—due to the excellent success of this invention, as usually occurs and as I had predicted would happen—that many desired to be its authors themselves, or if not for themselves, they wished this honor to be granted to someone of their own nation rather than to us, I must here finally encounter their unjust attempts...