ISOCHRONAL

, or Isochronous, is applied to such vibrations of a pendulum as are performed in equal times. Of which kind are all the vibrations of the same pendulum in a cycloidal curve, and in a circle nearly, whether the arcs it describes be longer or shorter; for when it describes a shorter are, it moves so much the slower; and when a long one, proportionably faster.

Isochronal Line, is that in which a heavy body is supposed to descend with a uniform velocity, or without any acceleration.

Leibnitz, in the Act. Erud. Lips. for April 1689, has a discourse on the Linea Isochrona, in which he shews, that a heavy body, with the velocity acquired by its descent from any height, may descend from the same point by an infinite number of Isochronal curves, which are all of the same species, differing from one another only in the magnitude of their parameters (such as are all the quadratocubical paraboloids), and consequently similar to one another. He shews also, how to find a line, in which a heavy body descending, shall recede uniformly from a given point, or approach uniformly to it.