Chap. XI.

MECHANICS.

981

tions for each oscillation of the balance, which enables us to dispense with such Hies as theordinary winch would require to produce the same effect.

We are indebted to Edmund Cartwright for a motion of rotation communicatedby steam, whose velocity may be increased at pleasure, without the necessity ofany gear-work. The upper part, a b, of the frame which embraces the furnace,cylinder, fly, and all movable parts of the machine, aretraversed by an axle, on which a pulley, c, revolves, roundwhich a chain is wound, fixed to the top of the piston rodt. The pulley, c, is put into alternate circular motion bythe piston and its counterpoise p; this axle is armed with awinch, which, by means of a lengthened rod, communicates toa lever f placed horizontally above, on the side of the furnace.

There is another axle, placed above or below, or at the side ofthe first, which traverses the fly g , and which is terminated onthe other side by a winch, which communicates in the samemanner with the preceding by means of the rod, h, with thehorizontal lever, f, just mentioned of. It is evident thatwhen the pulley, c, is put into motion by the action of the piston, t, the winch which ter-minates its axle will move that of the axle of the fly, g , because they are both attached tothe same lever,/! If then the pulley moves in the direction from a to b, and from b to a, bythe action of the piston and its counterpoise, and if the winch of the axle of the pulleymoves in the same direction, tliat of the axle of the fly will make the same movements,unless its length be so determined that at the end of its course it cannot passbeyond it; the motion of rotation will then take place. If the winch of the axle of thepulley, c, is so disposed that when it moves in any space not exceeding a complete revolu-tion, the winch will pass from c to a by f, or in the direction gone over by a given point ofthe pulley; then the winch will cause the lever to make two vibrations at every stroke ofthe piston, and at the same time the fly, g, will make two revolutions. If the diameter ofthe pulley is so proportioned that at each stroke of the piston the pulley will make a revo-lution and a half, and as much backwards, the lever will receive three vibrations by eachstroke of the piston. If the diameter of the pulley is so proportioned as to make two back-ward and forward revolutions for each stroke of the piston, the lever will make fourvibrations, and the fly four revolutions.

Ordinary Pedal. — If we suppose that the crank of the flycommunicates with the extremity of the lower lever or pedalby an inflexible rod, the ratio between the constituent parts ofpedal and their play ceases to be indeterminate, as they are to acertain point when we employ a flexible body. In fact, if wesuppose that we have given, first, the length of the lower lever,secondly, its centre of rotation; thirdly, the value of the angle itshould pass over at each oscillation ; fourthly, the position of thecentre of the fly relative to the centre of rotation of the lowerlever; the length of the crank, and that of the inflexible rod, aredeterminate quantities. To find their value, place the pedal,properly so called, viz. the lower lever, in its two positions, thelowest and the highest, and draw two right lines from the centreof the fly to the extremity of the pedal; the first of these twodistances is known, and it should be equal to the length ofthe inflexible rod, minus the length of the crank. The second, also known, should beequal to the sum of these two quantities ; consequently the inflexible rod, which shouldbe greater than the crank, is equal to half the sum of the two distances between thecentre of rotation of the fly and the extremity of the pedal in its two extreme positions, andthe crank should be equal to half the difference of these same distances.

If we suppose the angular velocity of the pedal uniform, that of the fly will be variablein all its points: but these inequalities become less sensible in proportion as the angle goneover by the pedal or lower lever is less, and the greater the distance between the centre ofthe fly and that of the rotation of the pedal.

Quadrature of the Pendulum , which marks the true time,invented by the Vicar of St. Cyr. The angular wheel ocarries a curve of equation bed; on the breadth of this curve iscut a groove parallel to the edge of the curve; in this groovea button i slides, adapted to the piece ef movable at thepoint e; this button also holds a second piece attached to the tubewhich carries the minute hand g, in such a manner that it followsthe vibration of the curve over more than half the circumferenceof the dial minutes, and is sufficient to mark the inequalitieswhich show the equation.

3 u 3

Fig. 1429.

Fig. 1430.