b. Vertical.-Turn the whole figure through 90° and make sidewise adjustments until the whole figure looks square. Measure the varied dimension only.

12. The Illusion of Length in the Cylinder. a. Vertical. Lay the tissue-paper over Fig. C, Pl. III, so that the cylinder base on the tissue-paper telescopes with the cylinder top in the book; adjust up and down until the length of the cylinder appears to be equal to its width. Measure the vertical distance between the top and bottom at the middle.

b. Horizontal. Repeat the same measurement with the cylinder in the horizontal position.

If the observer has shown fidelity and self-control and has been honest enough in these experiments not to sight or check-measure, he has passed a good test of character and may be recommended for a position of trust. The records also constitute a measure of the power of discrimination in visual perception of space.

The first lesson one learns in the study of sense-perception is that "the senses deceive". The second lesson is that "there is system in the deception"; being warned of the presence of danger, we may become the masters of our senses and avert the deception. Both these lessons are contained in the above experiments, which are intended to show that there are certain universal motives for illusion and that it is possible to determine their approximate force and thus become able to make due allowance for them.

Now, let the observer turn back to the figures and records and reproduce the setting for each figure (1)

according to the record, (2) according to the standard measurement given below, and (3) according to the average record given below. In stating the magnitude of the normal illusions, it will be given with reference to a normal adult male who is a reliable observer and is not acquainted with the illusion. The illusion varies with age, sex, knowledge of the illusion, power of concentration, etc. Thus, one of the laws of illusion is that knowledge of the nature and force of the illusion. decreases it, often by as much as one half its force; hence the illusion measurement in the first record should now seem too large.

The standard distance in Exp. 1 is 114 millimeters for dollars or disks. The average normal observer makes the distance about 100 millimeters in 1 a, which means an illusion of 12 per cent. The error is much greater in 1 b; normally it amounts to more than 20 per

cent.

This form of the terminal illusion is very common in ordinary perception. The simplest form of it is where we compare the distance between two more or less round bodies with the diameter of one, as in Fig. 30.* Of course the illusion does not rest upon the comparison. The diameter of the figure is underestimated and the distance between the two figures is overestimated, independently of the comparison, as may be determined by measuring each in terms of a plain line. We need only

*

Fig. 30. This is a copy of a small section of wall-paper. The aim of the artist has been to produce the effect of the ratio 1:1, which is the impression obtained by the average observer, but the distance between the figures is actually 10 per cent smaller than the distance across one figure.

look intelligently at our wall-papers, carpets, bed-covers, table-linen, and patterns in dress goods to find evidence of this illusion. The commonest effects sought by artists are approximately the ratios 1:1 and 1:1.6. Find designs which give these effects to the eye when the terminals of the distance are arc-formed, and measure them, and you will find that the artist has made allowance for the illusion, usually 8 to 12 per cent. The designer of patterns makes free-hand sketches by eye

estimate and thus naturally makes the proper allowance for the illusion. Where distances of this kind are made equal they do not look equal.

In Exp. 2 the true distance is 34 millimeters. The force of the illusion is approximately the same as in Exp. 1 a; that is, the measured section is made about 12 per cent too short. This is a double figure, because one section has the lengthening effect and the other has the shortening effect. It combines two complementary

illusions. Each of these might be measured separately in terms of a plain line. The left end has the lengthening effect and the right end has the shortening effect. The figure is also called "full-fledged" because it has a full set of end lines; a single line would produce the illusion, though not so forcibly.

This illusion is very common in objects around us, as in trees, fences, and lawn-patches, as well as in designs and structural effects, in fact in all sorts of objects in which a linear distance is marked off at one or both ends by one or more end lines.

In Exp. 3 the true distance is again 34 millimeters, but the measured section is usually made from 3 to 6 per cent too short. This means that the center of the base-line is shifted to the left by that amount.

When we bear in mind that it is not necessary that all the end lines should be present, we can realize how commonly the conditions for the shifting effect are present in nature and art. farther up than they are. two branches, one above the to be. The cross-line on the letter A seems lower than it really is.

The twigs on a limb seem The middle point between other, is not where it seems

In Exp. 4 the true length is 52 millimeters, but the varied line is probably made from 4 to 8 per cent too long. This again is a very common situation in all that we see. Technically we say the perception of a primary stimulus is influenced by secondary stimuli. The visual length of an object, whatever it may be, varies with the presence of other objects near its ends.

The first four experiments deal with the terminal