Page:Mind (New Series) Volume 8.djvu/101

 T. LIPPS, Baumaesthetik u. yeometrisch-optische Tduschungen. 87 pressing force is greater and greater. But the narrower figure may be squeezed more (1) because it is weaker, or (2) merely because it is more compressed, though it has the same ex- pansiveness. The results will differ according as we incline to one or the other view. Thus in the well-known illusions of ' confluxion,' or approximation (Ausgleichung} where a short line between two long ones looks longer, the same line between two short ones shorter, the lines in each figure all seem to partake of a common impulse (case 2), to have the same expansive force : hence the tendency to equalisation. On the other hand with surfaces like squares and circles the reverse is the case, for these figures seem independent, hence (case 1) the small circle between two bigger ones seems smaller, because of its inherent weakness. This is how Dr. Lipps explains the ' contrast ' in this illusion. Section iv. on Division and Composition is perhaps the best because the most intricate example of Dr. Lipps' method, and certainly the most difficult. It deals with the illusions of divided distances or divided lines (especially the case of symmetrical division into three), as well as of circles divided by a concentric circle, and these illusions stand in the closest connexion with those of approximation just described. They are various and interacting. Primarily the part is underestimated and the whole distance overestimated ; but secondarily the reverse is the case. To explain the primary illusion : take a part, say the middle part, and compare it with an independent distance of the same length. This latter distance, by approximation to the whole divided line, seems bigger; the mere part therefore as a part, and not in- dependent and therefore not thought of prominently as having equal expansive power with the whole distance, seems smaller in comparison with the same independent distance. On the other hand, the whole line may be considered as made up of inde- pendent portions which are overestimated, and is therefore itself overestimated. We may put the same thing from the compres- sive side, but I fear to encumber the statement. The opposite illusion arises from considering the part as sharing in the move- ment of the whole distance, as tending to expand to the limits of the whole. The bigger the part (still the middle part) is, the more it seems to break down its own limits ; or, to put the case otherwise, the more it seems to be compressed by the limits of the whole distance and to be relieved of the compression of its own limits. This is beautifully illustrated by the effect of lightness given to a heavy pillar or cupboard when it supports a light weight (p. 158). The whole line is for similar reasons now under- estimated. Owing to the interaction of these two causes the illusion varies with the size of the middle part, and the character of the variation is traced with great minuteness in a series of chapters (cc. xxix.-xxxvi.). The famous Miiller-Lyer illusions (the ' optical paradox ') are