MECHANICS. 



would be lost in time. In theory, a lever is considered 

 inflexible and without weight. There is an equili- 

 brium when the power and weight are inversely as 

 their distances from the fulcrum. Leverage is the 

 distance of the power from the fulcrum. The mecha- 

 nical advantage or purchase is proportional to this 

 distance, compared with that of the weight from the 

 fulcrum. Levers are of three kinds, according to the 

 relative position of the power, the prop, and the 

 weight. In the first, the prop is between the power 

 and the weight. To it belong scissors, snuffers, pin- 

 cers (in which the pivot or joint is the prop,) the 

 handspike, the brake of a pump, &c. A hammer 

 with its claw, is a bent lever of this kind. In the 

 second, the weight lies between the fulcrum and the 

 power. This includes the oar, where the boat is the 

 weight to be moved ; the door, of which the hinge is 

 the fulcrum ; the wheelbarrow, nut-crackers, bellows, 

 and the knife attached at one end, used to chip dye- 

 woods. In a lever of the third kind, the resistance 

 is at one end and the fulcrum at the other. To this 

 belong the pitchfork and spade, the one hand being 

 the power, and the other the fulcrum, sheep-shears, 

 with a bow at one end, giving a greater facility of 

 motion. The bones of animals are levers of this 

 kind, and are moved by muscles so attached as to give 

 rapidity of motion at the expense of power. The 

 ox-yoke is of this kind ; the neck of each ox being 

 the fulcrum with reference to the exertion of the 

 other. The stronger of two oxen must have tlje 

 short arm of the lever, that they may be able to pull 

 together. So a load supported on a pole and borne 

 by two men, must divide the pole unequally, if eithei* 

 is to be favoured. Let W represent the weight, P 

 the power, and F the Fulcrum, this diagram will show 

 their relative positions in the three different kinds of 

 levers. 



Jst kind, 



2d kind, 



3d kind, 



The Wheel and Axle is a kind of lever, so contrived 

 as to have a continued motion about its fulcrum, or 

 centre of motion, where the power acts at the circum- 

 ference of the wheel, whose radius may be reckoned 

 one arm of the lever, the length of the other arm being 

 the radius of the axle, on which the weight acts. 

 If the power acts at the end of a handspike fixed in 

 the rim of the wheel, then this increases the leverage 

 of the power, by the length of the handspike. 1 lie 

 wheel and axle consists of a 

 wheel having a cylindric axis 

 passing through its centre. 

 The power is applied to the 

 circumference of the wheel, 

 and the weight to the circum- 

 ference of the axle. In the 

 wheel and axle, an equilibri- 

 um takes place when the 

 power multiplied by the radius 

 of the wheel, is equal to the 

 weight multiplied by the ra- 

 dius of the axle ; or P : W : 

 wheel and axle being nothing else but a lever so con- 

 trived as to have a continued motion about its fulcrum 

 C, the arms of which may be represented by AC and 

 BC, therefore, by the property of the lever, P : W : : 

 C A . CB. If the power does not act at right angles 

 to CB, but obliquely, draw CD perpendicular to the 

 direction of the power, then, by the property of the 

 lever, P : W : : CA : CD. It will be easily seen, 

 that if two wheels fastened together and turning 



For the 



round the same centre, be so adjusted, that while 

 they turn round they will coil on their circumferences 

 strings to which weights are suspended ; one of 

 those wheels being larger than the other, the larger 

 wheel will coil up a greater length of the string than 

 the smaller one will do in the same time, and this 

 will depend either on the radii or circumferences of 

 the two wheels. The velocity of the weight will be 

 in proportion to the length of string coiled in a given 

 time ; therefore, the velocity of the weight will be 

 greater as the wheel is larger. Now, as in the lever 

 we saw that a small weight required a great velocity to 

 balance a large weight with a small velocity, we may 

 infer, that the rules given for levers will also apply 

 to the wheel and axle ; since the velocity of any body 

 on a lever depends upon its distance from the fulcrum. 



The efficacy of the wheel and axle may be increased, 

 either by enlarging the diameter of the wheel, or 

 diminishing that of the cylinder. The Chinese cap- 

 stan furnishes the means, without resorting to either 

 alternative, of increasing the mechanical efficacy to 

 any degree. It consists of two cylinders of nearly 

 equal diameters, turning upon the same axis, the 

 weight being supported by the loop of a very long 

 cord, one end of which unwinds from the smaller 

 cylinder, while the other end is coiled upon the 

 larger. The elevation of the weight by each revolu- 

 tion is equal to half the difference of the two circum- 

 ferences, the mechanical advantage depending upon 

 the smallness of this difference. In the ship's wind- 

 lass, movable bars or handspikes are substituted for 

 a wheel. The capstan is a vertical wheel and axle, 

 used on board ships to weigh the anchor. The wheel 

 and axle may turn on different centres, and have 

 their circumferences connected and made to act on 

 each other, by means of a strap or belt, or by a system 

 of cogs or teeth. This arrangement is called a wheel 

 and pinion. See JVheel-fVmk. 



Wheels acting on each other by teeth or bands, 

 may be easily calculated in the same way as the 

 wheel and axle. Thus, if a wheel which has thirty 

 teeth, drives another of ten teeth, it is evident, that 

 as the larger wheel has three times as many teeth as 

 the smaller, the smaller wheel will be turned round 

 three times for once that the larger one is turned 

 round ; so that the velocities of the wheels will be 

 inversely as their number of teeth. In like manner, 

 if the larger wheel drives the smaller not by teeth 

 but by a band, their revolutions will be inversely as 

 their circumferences. 



The larger wheel is usually called the wheel, 

 driver, or leader, and the smaller one is called tlie 

 pinion, driven wheel, or follower. When there are a 

 number of wheels 

 A, B, C, D, E, act- 

 ing on the respective 

 pinions, a, b, c, d, e, 

 as then the effect of 

 the whole may be 

 found thus : if the 

 letters which repre- 

 sent the wheels and 



pinions be understood to signify the number of teetli 

 of each, 



power x A X B X C y D y F._ weiahu 

 ay.bycy.dYe 



If the velocity of tiie first wheel be used instead of 

 the power applied, then this rule will give the result- 

 ing velocity instead of the weight. Thus, 



If the numbers of the teeth of the wheels are 9, 6, 

 9, 10, 12, and those of the pinions G, 6, 6, 6, 6: then if 

 the power applied be 14 Ibs., we have 



H X 9X6 X 9 X 10 y '2 _ 105 Ibs., the weight 

 (i X '> X 6 x 6 X 6 



