229. Archimedes's Lever.—Archimedes said that if he could have a lever long enough and a prop strong enough he could move the world by his own weight. But he did not think how far he would have to move to do this, from the vast difference between his weight and the weight of the earth. "He would have required," says Dr. Arnot, "to move with the velocity of a cannon-ball for millions of years to alter the position of the earth by a small part of an inch."
230. An Analogy.—You will remember that in the case of the Hydrostatic Paradox, the Hydrostatic Bellows, and Bramah's Press (§ 131, § 132, and § 133), great effects are produced by a small power. But this small power has to execute an extensive motion in order to produce these effects. Thus, as stated in § 132, if the area of the top of the Hydrostatic Bellows be one thousand times the area of the tube, though the water poured into the tube will raise a very great weight on the bellows, the water in the tube must fall ten inches in raising the weight the hundredth part of an inch. So when the pressure of the hand on the long arm of a lever moves a great weight, as a heavy stone, the weight is moved but a little, while the extent of the hand's motion is comparatively very great.
Fig. 161.
Fig. 162.
Fig. 163.
231. Lever of the Second Kind.—In the second kind of lever the weight is between the fulcrum and the power, as you see in Fig. 161. The same rule of equilibrium applies here as in the case of the lever of the first kind. The 72 pounds of weight can be sustained by 8 pounds of power, because the power acts on the lever at 9 times the distance from the fulcrum that the weight does, for 1×72 = 9×8. The common wheel-barrow, Fig. 162 (p. 180), is an example of this kind of lever. The point at which the wheel presses on the ground is the fulcrum, and the weight is the load, its downward pressure from its centre of gravity being indicated at M. Of course the nearer the load is to the fulcrum the easier it is, on starting, to raise the handles. The crow-bar can be used as a lever of this kind when its point is placed beyond the weight to be raised. The chipping-knife, Fig. 163, is another example. The end, F, attached to the board, is the fulcrum, the hand pressing at P the power, and the resistance of the substance R, which is to be cut, is the weight. Nut-crackers have a similar arrangement. In shutting a door by pushing it near its edge we move a lever of this kind. The hinge is the fulcrum, and the weight is between this and the hand. We see, then, the reason that the slight push of a hand shutting the door may even crush a finger when caught in it at the side where the hinges are. The finger is a resistance so near the fulcrum that the power moving through a great space acts upon it with immense force. The same explanation applies to the severe bite of the finger when it is caught in the hinge of a pair of tongs. The oar of a boat is a lever of this kind, the weight to be moved being the boat, which is between the power, the hand of the rower, and the fulcrum, the resisting water.
