The human body is almost entirely supported in water, in fact, many people can easily float in water. It was the consideration of this fact that led the Greek philosopher Archimedes to discover and state the principle that describes the supporting of a body in a liquid. [Illustration: FIG. 25.--Theoretical proof of Archimedes' principle.] =45. Archimedes' Principle.=--"_A body immersed in a liquid is pushed up by a force equal to the weight of the liquid that it displaces._" The proof for this law is simply demonstrated. Suppose a cube, _abcd_, is immersed in water (Fig. 25). The upward force on _cd_ is equal to the weight of a column of water equal to _cdef_. (See Art. 39.) The downward force upon the top of the cube is equal to the weight of the column of water _abef_. Then the net upward force upon the cube, that is, the upward force upon the bottom less the downward force upon the top, or the buoyant force exerted by the liquid is exactly equal to the weight of the displaced water _abcd_. =46. Law of Floating Bodies.=--This same reasoning may be applied to any liquid and to any body immersed to any depth below the surface of the liquid. If the body weighs more than the displaced liquid it will sink. If it weighs less than the displaced liquid it will float or rise in the water. A block of wood rises out of the water in which it floats until its own weight just equals the weight of the water it displaces. From this we have the law of floating bodies. _A floating body displaces its own weight of the liquid in which it floats._ [Illustration: FIG. 26.--A floating body displaces its own weight of water.] To test the law of floating bodies, take a rod of light wood 1 cm. square and 30 cm. long (Fig. 26). Bore out one end and fill the opening with lead and seal with paraffin so that the rod will float vertically when placed in water. Mark upon one side of the rod a centimeter scale, and dip the rod in hot paraffin to make it waterproof. Now find the weight of the stick in grams and note the depth to which it sinks in water in centimeters. Compute the weight of the displaced water. It will equal the weight of the rod. =47. Applications of Archimedes' Principle.= There are numerous applications of Archimedes' Principle and the law of floating bodies. =(a) To Find the Weight of a Floating Body: Problem.=--A boat 20 ft. long and with an average width of 6 ft. sinks to an average depth of 3 ft. in the water. Find the weight of the boat. What weight of cargo will sink it to an average depth of 5 ft.?