MECHANICS. 



to CB. But the arches AD and CB repre- 

 sent the velocities of the ends of the lever, 

 because they are the spaces which they 

 moved over in the same time ; therefore 

 the arms DE and EC may also represent 

 these velocities. Hence, an equilibrium 

 will take place, when the length of the 

 arm AE, multiplied into the power A, 

 shall equal EB, multiplied into the weight 

 B; and, consequently, that the shorter EB 

 is, the greater mus't be the weight B ; 

 that is, the power and the weight must 

 be to each other inversely, as their dis- 

 tances from the fulcrum. Thus, suppose 

 AE, the distance of the power from the 

 prop, to be twenty inches, and EB, the 

 distance of the weight from the prop, to 

 be eight inches, also the weight to be 

 raised at B to be five pounds ; then the 

 power to be applied at A, must be two 

 pounds; because the distance of the 

 weight from the fulcrum eig'ht, multipli- 

 ed into the weight five, makes forty ; 

 therefore twenty, the distance of the 

 power from the prop, must be multiplied 

 by two, to get an equal product ; which 

 will produce an equilibrium. 



The second kind of lever, when the 

 weight is between the fulcrum and the 

 power, is represented by fig. 3, in which 

 A is the fulcrum, B the weight, and C the 

 power. The advantage gained by this 

 lever, as in the first, is as great as the dis- 

 tance of the power from the prop ex- 

 ceeds the distance of the weight from it. 

 Thus, if the point a, on which the power 

 acts, be seven times as far from A as the 

 point , on which the weight acts, then 

 one pound applied at C will raise seven 

 pounds at B. This lever shews the rea- 

 son why two men carrying a burden upon 

 a stick between them, bear shares of the 

 burden, which are to one another in the 

 inverse proportion of their distances from 

 it. 



It is likewise applicable to the case of 

 two horses of unequal strength to be so 

 yoked, as that each horse may draw a 

 part proportionable to his strength ; 

 which is done by so dividing the beam 

 they pull, that the point of traction may 

 be as much nearer to the stronger horse 

 than to the weaker, as the strength of 

 the former exceeds that of the latter. To 

 this kind of lever may be reduced rud- 

 ders of ships, doors turning upon hinges, 

 Sec. The hinges being the centre of 

 motion, the hand applied to the lock is 

 the power, while the door is the weight 

 to be moved. 



If in this lever we suppose the power 

 and weight to change places, so that the 

 power may be between the weight and 



the prop, it will become a lever of the 

 third kind ; in which, that there maybe 

 a balance between the power and' the 

 weight, the intensity of the power must 

 exceed the intensity of the weight just 

 as much as the distance of the weight 

 from the prop exceeds the distance of 

 the power. Thus, let E, fig 4, be the 

 prop of the lever EF, and W a weight of 

 one pound, placed three times as far from 

 the prop as the power P acts at F, by the 

 cord going over the fixed pulley D ; in 

 this case, the power must be equal to 

 three pounds, in order to support the 

 weight of one pound. To this sort of 

 lever are generally referred the bones of 

 a man's arm ; for when he lifts a weight 

 by the hand, the muscle that exerts its 

 force to raise that weight, is fixed to the 

 bone about one tenth part as far below 

 the elbow as the hand is. And the elhow 

 being the centre round which the lower 

 part of the arm turns, the muscle must 

 therefore exert a force ten times as gi*eat 

 as the weight that is raised. As this kind 

 of lever is a disadvantage to the moving- 

 power, it is used as little as possible ; but 

 in some cases it cannot be avoided ; such 

 as that of a ladder, which being fixed 

 at one end, is by the strength of a man's 

 arms reared against a wall. 



What is called the hammer-lever, dif- 

 fers in nothing but its form from a lever 

 of the first kind. Its name is derived 

 from its use, that of drawing a nail out of 

 wood by a hammer. Suppose the shaft 

 of a hammer to be five times as long as 

 the iron part which draws the nail, the 

 lower part resting on the board as a ful- 

 crum ; then, by pulling backwards the 

 end of the shaft, a man will draw a nail 

 with one-fifth part of the power that he 

 must use to pull it out with a pair of pin- 

 cers ; in which case, the nail would move 

 as fast as his hand ; but with the hammer, 

 the hand moves five times as much as the 

 nail by the time that the nail is drawn out. 

 Hence it is evident, that in every species of 

 lever there will be an equilibrium, when 

 the power is to the weight as the distance 

 of the weight from the fulcrum is to the 

 distance of the power from the fulcrum. 

 In experiments with the lever we take 

 care that the parts are perfectly balanced 

 before the weights and powers are applied. 

 The bar, therefore, has the short end so 

 much thicker than the long arm, as will 

 be sufficient to balance it on the prop. 



If several levers be combined tog-ether 

 in such a manner, as that a weight being 

 appended to the first lever may be sup- 

 ported by a power applied to the last, 

 as in fig. 5, which consists of three levers 



