Pendulum-clock

is a clock having its motion regulated by the vibration of a pendulum. It is controverted between Galileo and Huygens, which of the two first applied the pendulum to-a clock. After Huygens had discovered that the vibration made in arcs of a cycloid, however unequal they might be in extent, were all equal in time; he soon perceived, that a pendulum applied to a clock, so as to make it describe arcs of a cycloid, would rectify the otherwise unavoidable irregularities of the motion of the clock; since, though the several causes of those irregularities should occasion the pendulum to make greater or smaller vibrations, yet, by virtpe of the cycloid, it would still make them perfectly equal in point of time 3 ‘and the motion of the clock governed by it would therefore be preserved perfectly equable. But the difficulty was, how to make the pendu- ‘lum describe ares of a cycloid; for naturally the pendulum, being tied to a fixed point, can only ‘describe circular arcs about it. Here Mr. Huygens contrived to fix the.iron ‘rod or wire, which bears the ball or weight at the top, to a silken thread, placed between two cycloidal cheeks, or two little arcs of a cycloid, made of metal. Hence the motion of vibration, applying succe ively from one of those arcs to the other, the thread, which is extremely flexible, easily a umes the figure of them, and by that means causes the ball or weight at the bottom te describe a just cycloidal arc. This is doubtle an ingenious invention, more especially as it gave rise to the whole doctrine of involute and evolute curves, with the radius and degree of curvature, . But it is not of any e ential service in the practice of clock-making; for the isochronism of vibrations in cycloidal arcs is demonstrated upon the supposition that the whole ma of the pendulum is concentrated in a point: a supposition which cannot actually take place in any vibrating body. Many other reasons have induced the artists to abandon the use of the cycloidal pendulum. The principal are, the difficulty with which the metallic cheeks are bent into the true cyclordal form; the improbability of their long retaining it, supposing it once given; and the changes of which the pendulum is susceptible in consequence of the expansion and contraction by heat and cold. These sources of error are such as the pe- culiar property of the cycloid cannot obviate: and as the variations from isochronism in very small circular arcs is extremely trifling, the cycloidal pendulum is now wholly disused in practice (Gree - gory’s Mechanics, vol. i. p. 230.) 186