Page:Elementary Text-book of Physics (Anthony, 1897).djvu/134

120 regarded as incompressible. Thus, for example, the alteration of volume for sea-water by the addition of the pressure of one atmosphere is 0.000044. The change in volume, then, at a depth in the ocean of one kilometre, where the pressure is about 99.3 atmospheres, is 0.00437, or about $$\tfrac{1}{230}$$ of the whole volume.

107. Modulus of Voluminal Elasticity of Solids.—The modulus of voluminal elasticity of solids is believed to be generally greater than that of liquids, though no reliable experimental results have yet been obtained.

The modulus, as with liquids, differs for different bodies.

108. Elasticity of Traction.—The first experimental determinations of the relations between the elongation of a solid and a tension acting on it were made by Hooke in 1678. Experimenting with wires of different materials, he found that for small tractions the elongation is proportional to the stress. It was afterwards found that this law is true for small compressions.

The ratio of the stretching weight to the elongation of unit length of a wire of unit section is the modulus of tractional elasticity. For different wires it is found that the elongation is proportional to the length of the wires and inversely to their section. The formula embodying these facts is where $$e$$ is the elongation, $$l$$ the length, $$s$$ the section of the wire, $$S$$ the stretching weight, and $$\mu$$ the modulus of tractional elasticity.

The behavior of a body under traction may be examined in the following way: We assume for convenience that the traction is applied to the upper and lower faces of a cube with sides of unit length. As already shown, the traction $$P$$ is equivalent to a hydrostatic tension $$\frac{P}{3}$$ and two shearing stresses equivalent to two tensions $$\frac{P}{3}$$ in the direction of the traction, and a pressure $$\frac{P}{3}$$ in each of two directions at right angles to this and to each other. The