192

Mechanic $.

Spring or Machine is wound up. From the Points Band D let fall the Perpendiculars to the Axis B A andDH; in which produced, let there be taken AE andHI proportional to the Force or Strength of the Spring,when the Chain is at B and D. Through E, I, drawthe Right Line ElK intersecting the Axis somewherein K; and from any Point C in the Curve, draw CFperpendicular to the Axis in G ; then will F Cr be asthe Strength of the Spring when the Chain is as G.

7. Now, since the Force acting on the Fusee oughtalways to be uniformly the fame; and this Force be-ing always as the Strength of the Spring exprefs’d byF G, and the Distance at which the Chain acts fromthe Axis of the Fusee conjointly : Therefore the Forceat any Point C will be as the Rectangle FG X GC,and since this is a given Quantity it may be made F G

X GC “ al, and so we have FG —

Cj C

8. Therefore to determine the Equation of the

Curve BCD, let LH -s, HI=Z>, HG = *, andGC —y. Then because of the similar Triangle HKIand G K F, we have H K : H I : : GK : F G = ;

—; that is, a : b : : ax : — ; whence we have aa —

y y

a y -f- xy, which is the Equation of the Curve, andshews it to be of the Hyperbolic Kind.

9. The Form or Figure of the Fusee being thus de-termined by the given Force of the Spring in the PointsB and D, and the Points G taken at Pleasure succes-sively from H towards A; we next consider that it isacted upon, or put into Motion, by an uniform Force;by which means also the Great Wheel, which is fix’dto it, is put into Motion, and that drives the Pinionof the Centre Wheel, which Centre Wheel drives the Pinion

of the Third Wheel, and this drives the Pinion of the jContrate Wheel, and this the Pinion of the Balance Wheel iwhich plies the two Pallets on the Axis of the Balance,and keeps the Balance in Motion.

10. The Balance in a Watch is instead of the Pendu-lum in a Clock; both serving to govern the Motionof the whole Machinery. To this Balance is fix’d asmall Steel spiral Spring which regulates the Motion

thereof.