the following means. Let K I (in fig. 52.) be prolonged upwards to L, till I L is equal to I K. Then let the line L M H equal and like to K H be applied, as in the figure between the points L and H, so that the point which in this line L M H answers to the point H in the line K H shall be applied to the point L, and the point answering to the point K shall be applied to the point H. Also let such another line L N C be applied between L and C in the same manner. This preparation being made; if a pendulum be hung at the point L of such a length, that the ball thereof shall reach to K; and if the string shall continually bend against the lines H M L and L N C, as the pendulum swings to and fro; by this means the ball shall constantly keep in the line C K H. 64. NOW in this pendulum, as all the swings, whether long or short, will be performed in the same time; so the time of each will exactly bear the same proportion to the time required for a body to fall perpendicularly down, through half the length of the pendulum, that is from I to K, as the circumference of a circle bears to its diameter. 65. IT may from hence be understood in some measure, why, when pendulums swing in circular arches, the times of their swings are nearly equal, if the arches are small, though those arches be of very unequal lengths; for if with the semidiameter L K the circular arch O K P be described, this arch in the lower part of it will differ very little from the line C K H. 66. IT may not be amiss here to remark, that a body will fall in this line C K H (fig. 53.) from C to any other point, as Q or R in a shorter space of time, than if it moved through the straight line drawn from C to the other point; or through any other line whatever, that can be drawn between these two points. 67. BUT as I have observed, that the time, which a pendulum takes in swinging, depends upon its length; I shall now say something concerning the way, in which this length of the pendulum is to be estimated. If the whole ball of the pendulum could be crouded into one point, this length, by which the motion of the pendulum is to be computed, would be the length of the string or rod. But the ball of the pendulum must have a sensible magnitude, and the several parts of this ball will not move with the same degree of swiftness; for those parts, which are farthest from the point, whereon the pendulum is suspended, must move with the greatest velocity. Therefore to know the time in which the pendulum swings, it is necessary to find that point of the ball, which moves with the same degree of velocity, as if the whole ball were to be contracted into that point.