A number of different theories have been attempted concerning the filled-unfilled illusion. Obonai, for example, has denied previous theories based on perception of the intervening lines since he demonstrated the filled-unfilled illusion even when the interpolated lines were not seen. Among the important characteristics of the illusion, (1) the amount of illusion was found to increase and then decrease as the increase of the interpolatated lines, and (2) even though the filled distance is “overestimated”, the two end lines were found to be under the field force to be “underestimated”. In order to explain this apparent inconsistency, a “repelling force” was assumed. Related to this position are Obonai's “psycho-physiological induction”, Spiegel's “Z-Kraft”, and Wada's “diffusion-effect”. On the other hand, the same apparent inconsistent result may be explained by Yokose's theoretical formulas which deal with how two visual lines are perceptually displaced being influenced with each other. Further Yokose assumed the “enhancement of energy” which acts as a “repelling force” in the filled-unfilled illusion. The purpose of the present experiment is to test whether Yokose's formula can be applied to the perception of three parallel lines of identical size as one of the simplest cases of the filled-unfilled illusion. In addition, the experiment was designed to examine the relationship between the visual displacement of the two end lines and the amount of illusion in the filled-unfilled illusion. Main results are: (1) the finding concerning the visual displacement of each of the lines when the position of the middle line of the three parallel lines was experimentally altered, was very close to that predicted by the Yokose model, and (2) the amount of illusion increased and decreased as the increase of the number of intervening lines, and the two end lines of the filled lines were found to be under the force to be “underestimated ” as previously shown. However, the two phenomena were found to be closely related. It was concluded that the visual displacement of the lines is related to the formation of the filled-unfilled illusion.
Experiments were designed to investigate the inner structure of the interaction between the two different kinds of refracting lines in Lipps figure (Fig. 9). Stimulus conditions operated were as follows; (1) conditions disjointing and simplifying Lipps figure (Fig. 10-11, 14-17), (2) d: distance between principal lines (Fig. 12-13), (3) φ: interior angle of parallelogram composed of principal lines (Fig. 12-13). Results obtained were as follows: (a) The positive illusory effects in Lipps figure were stronger when it contained one kind (or both kinds) of refracting lines than when it contained none (or one) of them (b) The illusory effect of the distance between principal lines increased with the increase of the distance. (c) The illusory effect of the interior angle φ of parallelogram composed of principal lines increased with the decrease of φ in case of φ≤90°, and with the increase of φ in case of φ≥90°. Here, in the interaction between refracting lines, two kinds of effects are assumed; one is the E-effect and the other the P-effect. The former effect has the power to start Lipps illusion and is similar to Ebbinghaus illusory effect of direction caused by the deflection of the line laid obliquely to another line (Fig. 17). On the other hand, the latter has the power to obstruct the former effect-the power is regulated by the forms (φ, d) of parallelogram-and does not exist in Ebbinghaus illusion of direction. Though these two effects vary together and act simultaneously, the former is always active and the latter is, by istelf, potential. In conclusion, the positive illusory effects of Lipps figure were mainly due to the interaction between the two different kinds of refracting lines, and the mode of interaction could be accounted for by the manner of the composition of E-and P-effects. Accordingly, it was considered that Lipps and Ebbinghaus illusions of direction were of the same type as they had E-effect in common. Further, it was assumed that P-effect in Lipps illusion would exist in Zöllner illusion as well.