The induced effect is an apparent slant of a frontal plane surface around a vertical axis, resulting from vertical magnification of the image in one eye. It is potentially important in suggesting a role for vertical disparity in stereoscopic vision, as proposed by Helmholtz. The paper first discusses previous theories of the induced effect and their implications. A theory is then developed attributing the effect to the process by which the stereoscopic response to horizontal disparity is scaled for viewing distance and eccentricity. The theory is based on a mathematical analysis of vertical disparity gradients produced by surfaces at various distances and eccentricities relative to the observer. Vertical disparity is shown to be an approximately linear function of eccentricity, with a slope or gradient which decreases with observation distance. The effect of vertical magnification on such gradients is analyzed and shown to be consistent with a change in the eccentricity factor, but not the distance factor, required to scale horizontal disparity. The induced effect is shown to be an appropriate stereoscopic response to a zero horizontal disparity surface at the eccentricity indicated. However, since extraretinal convergence signals provide conflicting evidence about eccentricity, they may attenuate the induced effect from its mathematically predicted value. The discomfort associated with the induced effect is attributed to this conflict.In binocular vision, the consequence of vertically magnifying one retinal image (usually done with an afocal lens) is an apparent slant of a frontal plane surface around a vertical axis (Ogle, 1950). This mysterious, apparently stereoscopic phenomenon is known as the induced effect. It appears similar, but opposite in sign, to the geometric effect, a slant around a vertical axis that occurs when one image is magnified horizontally (see Figure I). However, there is no straightforward geometric explanation in the case of the induced effect. Since the eyes are separated horizontally, not vertically, a depth difference between two points produces a horizontal, not a vertical, disparity in their images. In the real world, no arrangement of objects on the median plane would produce vertical disparity. Therefore, the induced effect cannot· be predicted by triangulation of the lines of sight as the geometric effect can. Ogle (1938, 1939, 1950), who has investigated the induced effect

The present study investigated the possible ecological role of vertical disparity. Specifically, the stereoscopic slant response to vertical magnification of one eye's view (i.e., the induced effect) was measured as a function of degree of magnification and observation distance. As a control, the stereoscopic response to equivalent amounts of horizontal disparity (i.e., the geometric effect) was measured under the same conditions. Unlike the geometric effect, the induced effect did not vary with observation distance, and at all distances it reached an asymptote at approximately 2% magnification. There was evidence that at very low magnification values the induced effect was greater than the geometric effect. These data are discussed in relation to theories in which the stereoscopic effect of vertical disparity is attributed to the process by which horizontal disparity is scaled for surface eccentricity and distance. The data are consistent with such a theory only if the assumption is made that the scaling effect of vertical disparity is attenuated by conflicting indicators of eccentricity given by convergence. It is argued that direct computational theories, which do not postulate an explicit representation of eccentricity or distance as part of the scaling process, cannot account for the differences obtained between the magnitude of the induced effect and that of the geometric effect.The binocular induced effect is an apparent slant around a vertical axis caused by vertical disparity. It occurs when one eye's image is subject to vertical magnification by an afocallens (Ogle, 1950). The slant is opposite in direction to the geometric effect, which results from horizontal magnification of one eye's image. The induced effect is regarded as somewhat mysterious since vertical disparity, unlike horizontal disparity, would not normally result when a surface is slanted.One obvious way to study the induced effect (Arditi, Kaufman, & Movshon, 1981) is to examine the effect of vertical magnification on orientation disparity, which is a geometric stimulus for depth perception. Figure 1 shows that the orientation disparities produced by vertical magThis work was supported by National Science Foundation Grant BNS 8311613 and carried out while the authors were at the Schnurmacher Institute, Slate University of New York, Slate College of Optometry.The writing was carried out while the senior author was at Oxford University on a Guggenheim Fellowship. She wishes to thank Brian Rogers for helpful discussions. Correspondence concerning this article should be addressed to Barbara Gillam at the School of Psychology, University of New South Wales, P.O. Box I, Kensington, N.S.W., Australia 2033.nification of one image of several nonvertical lines are indeed consistent with a tilt of the lines in depth, but that these tilts do not cumulatively result in a planar surface for lines of different orientation. It seems that at some degree of stimulus complexity, a planar solution, in the form of the induced effect, takes over from the indi...

S5895th Meeting: Acoustical Society of America S58 could only be a matter of time after joining a handbell choir that two physicists with a well-equipped vibration analysis lab at their disposal subjected the bells to test. This paper presents the results of analysis of the overtones produced by the handbell. There seemed little agreement with some early literature that suggested that the frequency of bell partials should be 1:2: 2.4: 3:4. In some bells, the fundamental tone was completely missing and the ratio was 2:4:6 indicating a single family of modes while in others it was strongly present and the ratios were 0.4:1:1.6:2 (if 2 is assigned to the labeled tone of the bell) indicating two separate mode families. Spectra are compared for different loudness settings of the bell as well as at impact and later during the after tone.•

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