Two postulates, one concerning assimilation and the other concerning attentive fields, are employed to explain the Ponzo, Poggendorff, Wundt, and Hering illusions. Several new configurations are predicted from the theory. In addition, changes in the magnitude or direction of illusion which result from alterations of the basic illusion are explained.

It is argued that the parallel lines illusion is the basic model for many visual distortions that are produced by geometric patterns. An experiment assessed the effect of moving the contextual contour away from the standard contour in two directions-away from the center of the attentive field and toward the center of the attentive field. The degree of illusion declined as the contextual magnitude moved away from the standard magnitude, but the rate of decline was more rapid when the contextual stimulus was moved away from the center of the attentive field. The results necessitated the addition of a new postulate for the assimilation theory of geometric illusions. This postulate states that the effectiveness of a contextual magnitude decreases as the distance between the contextual magnitude and the standard magnitude increases. The postulate was translated into a mathematical form in a manner analogous to the way' in which the "attentive field" postulate was quantified. The new formula was successful in predicting both the pattern of means and the pattern of variances found in this study. The formula was cross-validated with data from the Ponzo and reversed Mueller-Lyer illusions.

The Mueller-Lyer illusion is explained on the basis of rhe central tendency effecc which refers to errors of overestimation and underestimation that occur whenever repeated judgments of a series of stimuli are made. It was noted that the theory could be extended to explain some, but not all, other types of geometrical illusions.One of the oldest and most rncr~guing of the geometrical illusions is the Mueller-Lyer illusion which is shown in Fig. 1. This ill~ision consists of two lines of equal length (AB and CD) which do not appear equal because of "arrow heads" and "arrow feathers" drawn at the ends of the lines. Line AB which is bounded by feathers appears longer than line CD which is bounded by heads.

The mathematical model associated with integrative field theory was used to infer the size of attentive fields in a task involving judgments of size. A compounded Miiller-Lyer task was employed in which fins between or outside the standard shafts were systematically removed. Performance on this task was simulated by a computer that generated families of theoretical functions varying in the parameter of attentive field size. Individual theoretical functions were then correlated with an empirical function obtained from real observers. The value of attentive field size that provided the best fit between functions was then selected. The results showed that, in almost all cases, the optimum size of the attentive field was smaller for the shrinkage form than for the expansion form ofthe Miiller-Lyer pattern, that the attentive field changed more dramatically with changes in stimulus variables in the expansion form than in the shrinkage form, and that changes in viewing distance had little effect on the optimum size of the attentive field. It was concluded that the attention was involved both in figure-ground segregation and in maintaining object constancy. The similarity ofthese results to data obtained in recognition and detection tasks was noted. 423In a perceptual task that requires a response to some attribute involving two or more spatially separated objects, an observer deploys attention in a way that includes those objects. The notion of afield has been proposed to describe such attentional selectivity, and its characteristics have been investigated using tasks involving detection (B. A.

A variant of Ponzo's pattern was devised by drawing converging oblique lines at the ends of each of two horizontal lines that were located directly one above the other. Pairs of converging or diverging fins (either between or outside the horizontal shafts) were systematically removed. The results showed that, as predicted by integrative field theory, oblique lines between the shafts produced more distortion than did oblique lines outside the shafts. Also, it was shown that the attentive field construct in integrative field theory was crucial for predicting patterns of means and variances in this experiment. The modified Ponzo effect was shown to have much in common with the classical Muller-Lyer illusion. The subtle differences between the two were explained by proposing that the size of the optimum attentive field was larger in the Ponzo tasks than in the Muller-Lyer tasks because expansion fins are found on both shafts in the Ponzo-like figure.