[5] This and the following letters in parentheses refer to Fig. 7
Fig. 7
A great many experiments performed in this way, with the squares set both vertically and horizontally, and with several persons, brought a striking and very uniform result. The point selected by the subject as the middle is regularly too far toward the smaller square. Not a little, indeed, but a very appreciable amount. The amount of the displacement, or, roughly speaking, of the illusion, increases as the larger square is made larger and the smaller one smaller; or, put in a sentence, the amount varies directly with the ratio of the smaller to the larger square side.
Finding such an unmistakable illusion by this method, Mr. B. thought that if it could be tested by an appeal to people generally, it would be of great gain. It occurred to him that the way to do this would be to reverse the conditions of the experiment in the following way: He prepared the figures given in Plate I, in which the two squares are made of suitable relative size, a line is drawn between them, and a point on the line is plainly marked. This he had printed in a weekly journal, and asked the readers of the journal to get their friends, after merely looking at the figure (i. e., without knowing the result to be expected), to say—as the reader may now do before reading further—whether the point on the line (Plate I) is in the middle or not; and if not, in which direction from the true middle it lies. The results from hundreds of persons of all manner of occupations, ages, and of both sexes, agree in saying that the point lies too far toward the larger square. In reality it is in the exact middle. This is just the opposite of the result of the experiments in the laboratory, where the conditions were the reverse, i. e., to find the middle as it appears to the eye. Here, therefore, we have a complete confirmation of the illusion; and it is now fully established that in all cases in which the conditions of this experiment are realized we make a constant mistake in estimating distances by the eye.[6]
[6] In redrawing the figure on a larger sheet (which is recommended), the connecting line may be omitted, only the mid-point being marked. Some get a better effect with two circles, the intervening distance being divided midway by a dot, as in Plate II.
For instance, if a town committee wish to erect a statue to their local hero in the public square, and if on two opposite sides of the square there are buildings of very different heights, the statue should not be put in the exact middle of the square, if it is to give the best effect from a distance. It should be placed a little toward the smaller building. A colleague of the writer found, when this was first made public, that the pictures in his house had actually been hung in such a way as to allow for this illusion. Whenever a picture was to be put up between two others of considerable difference of size, or between a door (large) and a window (small), it had actually been hung a little nearer to the smaller—toward the small picture or toward the window—and not in the true middle.
It is probable that interesting applications of this illusion may be discovered in æsthetics. For wherever in drawing or painting it is wished to indicate to the observer that a point is midway between two lines of different lengths, we should find that the artist, in order to produce this effect most adequately, deviates a little from the true middle. So in architecture, the effect of a contrast of masses often depends upon the sense of bilateral balance, symmetry, or equality, in which this visual error would naturally come into play. Indeed, it is only necessary to recall to mind that one of the principal laws of æsthetic effect in the matter of right line proportion is the relation of "one to one," as it is called, or equal division, to see the wide sphere of application of this illusion. In all such cases the mistake of judgment would have to be allowed for if masses of unequal size lie at the ends of the line which is to be divided.