Between the molecules of a solid, however, the forces of attraction are strong, as is shown by the fact that a solid often requires a great force to pull it apart; some, as steel and iron, show this property in a superlative degree, a high-grade steel rod 1 cm. in diameter requiring nearly 9 tons to pull it apart. Tests show that the breaking strengths of such rods are directly proportional to their areas of cross-section. That is, twice the area has twice the breaking strength. [Illustration: FIG. 16.--Elasticity of bending.] =30. Elasticity.=--Fully as important as a knowledge of the breaking strengths of solids, is the knowledge of what happens when the forces used are not great enough to break the rods or wires. Take a wooden rod (as a meter stick) and clamp one end to the table top, as in Fig. 16. At the other end hang a weight. Fasten a wire to this end so that it projects out in front of a scale. Add successively several equal weights and note the position of the wire each time. Remove the weights in order, noting the positions as before. The rod will probably return to the first position. This simple experiment illustrates a characteristic of solids: that of changing shape when force is applied and of returning to the original shape when the force is removed. This property is called _elasticity_. Tests of elasticity are made by subjecting wire of different materials but of the same dimensions to the same tension. The one changing least is said to have the greatest _elastic force_ or elasticity. If greater forces are applied to the wire and then removed, one will finally be found that will permanently stretch the wire so that it will not return exactly to the former length. The wire has now passed its _elastic limit_ and has been permanently stretched. Just as there are great differences between the _elastic forces_ of different substances, so there are great differences in the _limits of elasticity_. In some substances the limit is reached with slight distortion, while others are _perfectly elastic_ even when greatly stretched. India rubber is an example of a body having _perfect_ elasticity through wide limits. Glass has great _elastic force_ but its _limit_ of _elasticity_ is soon reached. Substances like India rubber may be said to have great "_stretchability_," but little elastic force. In physics, elasticity refers to the elastic force rather than to ability to endure stretching. =31. Kinds of Elasticity.=--_Elasticity may be shown in four ways_: _compression_, _bending_ or _flexure_, _extension_ or _stretching_, _twisting_ or _torsion_. The first is illustrated by squeezing a rubber eraser, the second by an automobile spring, the third by the stretching of a rubber band, the fourth by the twisting and untwisting of a string by which a weight is suspended.