204 LECTURE XVIII. 



the end of the lever, and the utmost force that he can apply is equal to the 

 whole weight of his body: but when he thrusts the lever under the stone, so 

 that its extremity bears on the ground, it becomes a lever of the second kind, 

 and in order to raise the stone, he must now draw the end of the lever up- 

 wards. In this direction, a strong man can exert a force equivalent to twice 

 his weight; consequently the second kind of lever possesses here a temporary 

 advantage over the first; although, if the operation were continued, the 

 workman would be more fatigued by raising even the same weight by this 

 method, than if he could conveniently apply his weight to a lever of the first 

 kind ; and for this purpose, cross bars have sometimes been added to levers, in 

 order to enable several workmen to stand on them with advantage at once. 

 A bent lever operates precisely with the same power as a straight one, provid- 

 ed that the forces be applied in a similar manner with respect to its arms: 

 and in all cases, the forces capable of balancing each other are inversely as 

 the distances of the points of action from the fulcrum. Some addition of force 

 is necessary for overcoming the equilibrium, and producing motion, but the 

 velocity of the motion being seldom of much consequence, a small preponder- 

 ance is usually sufficient. 



The principal inconvenience of the lever is the short extent of its action : this 

 may, however, be obviated by means of the invention of Perrault, in which two 

 pins are fixed in the lever, at a short distance from each other, sliding in two 

 pairs of vertical grooves, provided with ratchets, so that when the long arm of 

 the lever is pulled by means of a rope, the nearer pin serves as a fulcrum, and the 

 more distant one is elevated at the same time with the weight, and is detain- 

 ed in its place by the click; but when the rope is slackened, the weight sinks 

 a little, and raises the pin, which first served as a fulcrum, to a higher place 

 in its groove. The same effects may also be produced by catches or clicks rest- 

 ing upon ratchets on the opposite sides of a single upright bar, which passes 

 through a perforation in the lever. There must, however, be a considerable 

 loss of force, from the continual intermission of the motion. (Plate XVII. 

 Fig. £13.) 



An axis with a winch, that is, a lever bent at the end, is known from the 

 common machine for raising a bucket out of a well. A vertical or upright 

 axis, with two or more levers inserted into it, becomes a capstan. In these 



