Two divergently oblique lines attached to the ends of a straight line as at A, Fig. 27, suggest to the mind the idea of lengths greater than that of the straight line itself; the latter, being thought of as comparatively small, is therefore estimated in terms of a smaller unit than would be employed if the attachments were absent, and consequently appears longer. If, on the other hand, the attachments are made convergent, as at B, shorter lengths are suggested; the length of the given line is regarded as exceeding an average or mean; the standard applied in estimating it is accordingly increased, and the line is made to seem unduly short. In spite of appearances to the contrary, the two lines A and B are actually of the same length. By duplicating the attached lines, as shown in Fig. 28, their misleading effect becomes intensified. Here we have a well-known illusion of which several explanations have been proposed. The fallacy is, I think, sufficiently accounted for by variation of the mental standard, in accordance with the law to which I have called attention. [Illustration: _Fig. 28.--Illusion of Length._] A number of other paradoxical effects may be referred to the operation of the same law. Fig. 29 shows a curious specimen. At each end of the diagram is a short upright line; exactly in the middle is another; between the middle and the left hand end are inserted several more lines, the space to the right of the middle being left blank. Any one looking casually at the diagram would be inclined to suppose that it was not equally divided by what purports to be the middle line, the left hand portion appearing sensibly longer than the other. [Illustration: _Fig. 29.--Illusion of Distance._] It is not difficult to indicate the source of the illusion. When we look at the left hand portion we attend to the small subdivisions, and the mental unit becomes correspondingly small; while in the estimation of the portion which is not subdivided a larger unit is applied. As one more example I may refer to a familiar trap for the unwary. Ask a person to mark upon the wall of a room the height above the floor which he thinks will correspond to that of a gentleman's tall hat. Unless he has been beguiled on a former occasion, he will certainly place the mark several inches too high. Obviously the height of a hat is unconsciously estimated in terms of a smaller standard than that of a room.