Chap. 2. PHILOSOPHY. 93

manner. This preparation being made; if a pendulum behung at the point L of such a length, that the ball thereofshall reach to K ; and if the string shall continually bend a-gainst the lines H M L and L N C, as the pendulum swingsto and fro ; by this means the ball shall constantly keep inthe line CKH.

64. N o w in this pendulum, as all the swings, whetherlong or short, will be performed in the same time; so the timeof each will exactly bear the fame proportion to the time re-quired for a body to fall perpendicularly down, through halfthe length of the pendulum, that is from I to K, as the cir-cumference 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 oftheir swings are nearly equal, if the arches are small, thoughthose arches be of very unequal lengths ; for if with the fe-midiameter LKthe circular arch OKP be described, this archin the lower part of it will differ very little from the lineCKH.

66 . It may not be amiss here to remark, that a bodywill fall in this line CKH (fig. yz.) from C to any otherpoint, as Q^or R in a shorter space os time, than if it movedthrough the straight line drawn from C to the other point;or through any other line whatever, that can be drawn be-tween these two points.

67. But

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