Chap. 2. PHILOSOPHY. 91

provided they be such, as the geometers call similar ; thatis, if the arches bear the same proportion to the whole cir-cumferences of their respective circles. Suppose (in fig. 4.8.)

A B, C D to be two pendulums. Let the arch E F be describ-ed by the motion of the pendulum A B, and the arch G Hbe described by the pendulum C D ; and let the arch E F bearthe same proportion to the whole circumference, whichwould be formed by turning the pendulum A B quite roundabout the point A, as the arch G H bears to the whole cir-cumference, that would be formed by turning the pendu-lum C D quite round the point C. Then I fay, the propor-tion, which the length of the pendulum AB bears to thelength of the pendulum C D, will be two fold of the propor-tion, which the time taken up in the description of the archE F bears to the time empi yed in the description of the archGH.

6z. Thus pendulums, which swing in very small arches,are nearly an equal measure of time. But as they are not suchan equal measure to geometrical exactness; the mathematicianshave found out a method of causing a pendulum so to swing,that, if its motion were not obstructed by any resistance, itwould always perform each swing in the same time, whetherit moved through a greater, or a lesser space. This was firstdiscovered by the great Huygens, and is as follows. Up-on the straight line A B (in fig. 49.) let the circle C D E be soplaced, as to touch the straight line in the point C. Then letthis circle roll along upon the straight line AB, as a coach-wheel rolls along upon the ground. It is evident, that, as

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