The curve is the rear-face temperature rise of a flash-heated disc, normalized to its maximum, drawn against the Fourier number Fo = αt/L² — diffusion’s natural dimensionless clock. Parker’s method reads one feature, the half-rise at Fo½ ≈ 0.1388, and converts it to diffusivity through α = 0.1388 L²/t½ (the classic Parker/ASTM E1461 coefficient). Stretch the pulse width and the rise starts late: t½ inflates and the uncorrected α comes out low. Add face heat losses and the curve peaks early and sags: t½ shrinks and the uncorrected α comes out high. Two biases, opposite signs, invisible in a single reading — the reason the Cape–Lehman corrections and ASTM E1461 exist.
Model: Parker one-dimensional adiabatic series V₀(Fo) = 1+2Σ(−1)ⁿexp(−n²π²Fo), convolved analytically with a rectangular pulse of width τα/L², then multiplied by exp(−2Y·Fo) as a SIMPLIFIED first-order face-loss factor — the full Cape–Lehman treatment shifts the modal eigenvalues and handles radial losses; this teaching model reproduces the direction and approximate scale of both biases, not their exact magnitudes. The half-rise is located on the curve as displayed (normalized to its own maximum), exactly as an uncorrected analysis would. Axes dimensionless; schematic teaching tool, not an instrument.