The physics
Pull a wire and it gets longer. Stress is the pull on each square metre of its cross-section. Strain is the stretch over the length.
stress σ = F / A strain = ΔL / L
Below the elastic limit, stress is proportional to strain. That is Hooke's law. The ratio is Young's modulus Y. Steel has Y = 2 × 10¹¹ Pa, and brass 1 × 10¹¹ Pa.
Y = (F/A) / (ΔL/L) ΔL = F L / (A Y)
Change mm² to m² first: 1 mm² = 10⁻⁶ m². A hanging mass pulls with its weight mg.
A wire acts as a spring of stiffness k = AY/L. Wires in a line carry the same pull, and their stretches add. A cord under its own weight feels half its weight on average.
k = A Y / L ΔL (own weight) = ρ g L² / (2Y)
Searle's rig hangs loads on a test wire, and a vernier reads each length. The slope of reading against load gives Y.