Fig. 116.
Illusions of this kind become more striking when the distances to be compared run in different directions. If we look at A and B (fig. 116), which are perfect squares, A appears greater in length than width, whilst B, on the contrary, appears to have greater width than length. The case is the same with angles. On looking at fig. 117, angles 1, 2, 3, 4 are straight, and should appear so when examined. But 1 and 2 appear pointed, and 3 and 4 obtuse. The illusion is still greater if we look at the figure with the right eye. If, on the contrary, we turn it, so that 2 and 3 are at the bottom, 1 and 2 will appear greatly pointed to the left eye. The divided angles always appear relatively greater than they would appear without divisions.
The same illusion is presented in a number of examples in the course of daily life. An empty room appears smaller than a furnished room, and a wall covered with paperhangings appears larger than a bare wall. It is a well-known source of amusement to present someone in company with a hat, and request him to mark on the wall its supposed height from the ground. The height generally indicated will be a size and a half too large.
We will relate an experience described by Bravais: “When at sea,” he says, “at a certain distance from a coast which presents many inequalities, if we attempt to draw the coastline as it presents itself to the eye, we shall find on verification that the horizontal dimensions have been correctly sketched at a certain scale, while all the vertical angular objects have been represented on a scale twice as large. This illusion, which is sure to occur in estimates of this kind, can be demonstrated by numerous observations.”
M. Helmholtz has also indicated several optical illusions.
Fig. 117.
Fig. 118.