Page:Elementary Text-book of Physics (Anthony, 1897).djvu/137

§ 111] this substitution, we obtain $$\Theta = \frac{4 \pi^2 I}{T^2}$$, or if we observe the single instead of the double oscillation.

The torsion balance may therefore be used to measure forces in absolute units.

If the value of $$\Theta$$ just obtained be substituted in equation (47), we obtain Since all these magnitudes may be expressed in absolute units, we may obtain the value of $$n$$, the rigidity, by observing the oscillations of a wire of known dimensions, carrying a body of which the moment of inertia is known.

110. Elasticity of Flexure.—If a rectangular bar be clamped by one end, and acted on at the other by a force normal to one of its sides, it will be bent or flexed. The amount of flexure—that is, the amount of displacement of the extremity of the bar from its original position—is found to be proportional to the force, to the cube of the length of the bar, and inversely to its breadth, to the cube of its thickness, and to the modulus of tractional elasticity. The formula expressing the relations of these magnitudes is

111. Limits of Elasticity.—The theoretical deductions and empirical formulas which we have hitherto been considering are strictly applicable only to perfectly elastic bodies. It is found that the voluminal elasticity of fluids is perfect, and that within certain limits of deformation, varying for different bodies, we may consider both the voluminal elasticity and the rigidity of solids to be practically perfect for every kind of strain. If the strain be carried beyond the limits of perfect elasticity, the body is permanently deformed. This permanent deformation is called set.