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Derivation of a Hypothesis about Monocular Size and Depth Perception from a Simple General Perceptual Principle

A viewer is assumed to look with one eye at a fixation point f and a reference point x of a surface in a frontal parallel plane. He can move his eye along its line of regard for f some distance ΔS; and we suppose that he can assess the ratio ΔR−1/ΔS, where R is the retinal separation between the images of f and x and ΔR−1 is the change in the reciprocal of R that attends his movement of a distance ΔS. A model is proposed that approximates the optical conditions of his stimulation, and that allows him to calculate the physical distance E between f and x and the distance S between f and the center of his eye in terms of ΔR−1/ΔS. His calculations of E and S are treated as perceptions of the linear extent and the distance of the surface on which the points f and x are located.