Fig. 1.
The eye is an organ which is very easily deceived, and needs constant training to enable it to judge correctly of the relative proportions of objects of different forms. Most of our readers are probably familiar with the optical test of guessing the height of an ordinary stove-pipe hat by measuring off the supposed height on the wall of a room. Those who have not heard of it will find it interesting to try the experiment. Take a stick, or walking-cane, and measure off on the wall of a room a height to which you suppose a stove-pipe hat would reach if placed on the floor immediately underneath, as represented in Fig. 1. Nine times out of ten the point selected will be a great deal too high.
Another point in which the proportions of a hat are very deceptive is this: The diameter, or distance across the crown, of a silk hat is greater than the height of the crown of the hat from the brim. Most people will be very positive that just the reverse is the case. We have all heard that a horse's head is as long as a flour barrel, and felt very much inclined not to believe it, though such is the fact.
Fig. 2.
There is also an optical test which is little known, and far more surprising: Take three tumblers of the same size, and place them in a row on the table, as represented in Fig. 2; then withdraw the middle tumbler, and request any one present to place it at such a distance on the table from the other two tumblers—as represented in Fig. 3—that the measurements from C to D and from E to F shall be the same as from A to B. This test will prove very amusing at any small gathering. Each person in turn tries his hand; the distance he guesses is marked off on the table. Then the real distance is measured off, and the tumbler put in its right place, when it will probably be found that every one has fallen far short of the right measurement. In Fig. 3 we have only represented the relative positions of the tumblers; the correct distance is not given. Try it before you measure.
Fig. 3.