Edinburgh New Philosophical Journal Edinburgh New Philosophical Journal edinburghnewphil1918unse Year: 186 Mr Sang on the manner in which produce SA to meet the arc described from S with the radius SG, and draw the horizontal line HKI; HI will be the ten- dency down the arc, and SI will be the pressure of the knife edge against the plate : wherefore, since the friction is propor- tional to the pressure, IK will represent the friction in the posi- tion SA, leaving the surplus HK to accelerate the descent of the pendulum. From S with the radius SF describe an arc, produce SH to meet it in L,
Edinburgh New Philosophical Journal Edinburgh New Philosophical Journal edinburghnewphil1918unse Year: 186 Mr Sang on the manner in which produce SA to meet the arc described from S with the radius SG, and draw the horizontal line HKI; HI will be the ten- dency down the arc, and SI will be the pressure of the knife edge against the plate : wherefore, since the friction is propor- tional to the pressure, IK will represent the friction in the posi- tion SA, leaving the surplus HK to accelerate the descent of the pendulum. From S with the radius SF describe an arc, produce SH to meet it in L, and draw HN, LO, perpendicular to SF. The trigon KHN is clearly similar to FSG, whence KH : HN :: FS : SG : : LS : SH :: LO : HN to that HK is equal to LO. Now, if gravity, instead of acting in the direction of and with the intensity SG, were to act in the direction of and with the intensity SF, LO would just be the tendency of the pendulum to descend from the point A ; and, therefore, the first oscilla- tion will be performed equally on each side of the line SF, and will be accelerated just as if gravitation were increased from SG to SF. The next oscillation would be performed equally on each side of a line, making with SG an angle equal to FSG, and thus the arcs of oscillation would decrease in arithmetical progression ; the extreme distances from the vertical line being diminished at each oscillation by twice the angle GSF.
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