An illusion of eccentricity

The illusion investigated here is that two concentric arcs, drawn in different (though possibly overlapping) circular sectors and having the same angular extent, appear to be eccentric. Three possible explanations of the illusion are tested. The first hypothesis is that concentricity judgments are made by elongating the arcs to see if they intersect, the illusion being due to the tendency, when elongating a curve, to follow the end-tangent. The second hypothesis is that concentricity judgments are based on a test of coincidence of centers, the illusion being due to the overestimation of the radius of short arcs. The third hypothesis is that both of these factors contribute in equal measure. These hypotheses make different predictions about the effect (on the magnitude of the illusion) of the following variables: (1) the angular distance between the arcs; (2) the radial distance between the arcs; (3) the degree of curvature of the arcs; and (4) the angular extent of the arcs. The observed values of the illusion angle (obtained by the method of limits) in relation to these variables did not uniformly support any of the hypotheses. A more complex model that is consistent with the observed results is therefore proposed.