Try to find out without any instrument of course, simply by the aid of your eyes which you suppose exact and true. It will appear to you at first sight that the artist has made a mistake, and has made a bad drawing. The last _seems_ the tallest, whereas the first seems shortened. [Illustration] However, measure with a pair of compasses, and the illusion will at once disappear. The draughtsman was not mistaken; the first _is_ the tallest, and the two others go diminishing in height. * * * * * This terminates our experiments on optical illusions and you will now enter upon another field of knowledge altogether. The Insensible Coin. Cut a piece of cardboard about six inches long, and by sticking the extremities together with a pin, or with gum, form a circle or ring. Balance it carefully on the neck of a wine bottle or decanter, and on the top of the ring place a dime, exactly over the neck of the bottle. Now the trick to be performed is to take off the ring so that, without touching it, the coin falls into the bottle. On the inner side of the ring give a sharp knock with the finger, or, better still, with the thumb and forefinger, as in shooting a marble, as shown in figure. The ring will come off, and the coin which on account of its inertia, does not participate in the movement, will infallibly fall into the bottle. It is absolutely necessary to strike the interior of the circle, because in striking it from the outside one would not get any result at all, on account of the elasticity of the cardboard. [Illustration] The Asses’ Bridge. Every schoolboy knows which is the famous geometrical theorem, commonly called the Asses’ Bridge, and which is propounded as follows: [Illustration] The square constructed on the hypotenuse of a right angled triangle is equivalent to the sum of the squares constructed on the two other sides. If we had only to propound this terrible theorem, it would be an easy matter, but the question is to prove it by A and B, and by means of the triangles, similar angles, equivalents, etc. Well, instead of all this, we give here a very simple way to prove the truth; if not quite pedagogic, it is none the less real. Trace on a piece of cardboard or thick paper a square, and divide into 49 parts. This done, cut it out in following the big lines. Take out on the center one division, which add to the small square, and then construct the figure 2. [Illustration: Fig. 2.] The right-angled triangle A C D will be found by the sides of the three squares, and the sum of the two small squares constructed on the two sides of the triangle will be equivalent to the great square constructed on the hypotenuse. Effectively: Square No. 1 has 9 divisions. Square No. 2 has 16 divisions. -- Together 25 == And the square No. 3 has also 25 divisions. Therefore the theorem is proved. Another Way to Prove the Preceding Theorem.