Hooke's law and its experimental verification

HOOKE'S LAW states that, for a small deformation within the elastic limit, the strain produced in a body is directly proportional to the stress that produces it -- equivalently, $\text{stress}\propto\text{strain}$ as long as the elastic limit is not exceeded. EXPERIMENTAL VERIFICATION. The law can be verified with a simple apparatus: a thin, straight wire of uniform cross-sectional area A and natural length L is suspended from a rigid support; a pan to hold weights and a pointer are attached at its free lower end, with the pointer's position read off against a fixed graduated scale (a vernier arrangement) so that the extension produced by each load can be measured precisely. Loads are added to the pan in steps, and for each load the corresponding stretching force F and the resulting elongation $\Delta L$ are recorded. Plotting F on the horizontal axis against $\Delta L$ on the vertical axis produces a straight line through the origin -- direct experimental proof that, within the elastic limit, the elongation is directly proportional to the applied stretching force, and hence that stress (which depends on F) is proportional to strain (which depends on $\Delta L$). Algebraically: since $\Delta L=(\text{slope})\,F$, and multiplying and dividing by the volume $V=AL$ gives $F(\te …