a curve on which the doctrine of pendulums and time measuring instruments in a great measure depend; Mr Huygens demonstrated, that from whatever point or height a heavy body, oscillating on a fixed centre, begins to descend, while it continues to move in a cycloid, the time of its falls or oscillations will be equal to each other. It is likewise demonstrable, that it is the curve of quickest descent, i.e., a body falling in it, from any given point above, to another, not exactly under it, will come to this point in a less time than in any other curve passing through those two points.