In a square A B D C, trace four similar and equal triangles; cut them out and dispose them as shown in Fig. 1. You will have in the middle an empty space forming a great square, which just has one of the sides of the hypotenuse of the right-angled triangle A E B. [Illustration] Trace the outlines of this square and remount the triangles one against the other, H C E, against A E B, and C D G, against B F G, you will get the Fig. below. [Illustration: Fig. 1.] The successively covered and uncovered parts of the two squares have not changed in extent. But this time the uncovered part is formed of the two squares 2 and 3 which correspond to those constructed on the two other sides of the triangle, A E B. This very simple demonstration has the advantage of being applicable to any rectangle. Indented Angles. Given two sheets of paper of the same size and form of a rectangle, fold them both in four equal parts, one lengthwise and the other sideways, as shown below. [Illustration: Fig. 1.] When so folded take a fourth part off each. Part A in the figures. The question is now to cover quite exactly one of the remaining surfaces with the other, in cutting the latter in two perfectly equal parts. [Illustration: Fig. 2.] To resolve this question take the surface (parts A having been detached), with which it is intended to cover the other, fold it again into equal parts, but this time in the opposite way to the one in which it was folded first, as indicated in Fig. 4: cut it out then in following the dotted line, F L, formed by the marks of the fold; this done one will obtain two parts absolutely equal, F L. [Illustration: Fig. 3.] In order to cover the other surface, Fig. 3, all that is now necessary is to lower the angles, viz.: angle A’, must be in front of angle A, angle B’ in front of angle B, and angle C’ in front of angle C. When the angles are lowered in this way, the two surfaces will be quite similar, and can be covered one by the other. [Illustration: Fig. 4.] This experiment can be made either with one or the other sheet, in lowering or raising the angles. In the example shown here it is the fourth Figure which is destined to cover the other one. When the operation is terminated as indicated above, part M, of Fig. 4, will be at M’ of Fig. 3, and part O at O’ of the covert figure. A Cheap Shooting Gallery. With a whalebone stay busk, make a bow and draw a target on a card. For the arrows, divide lengthwise a steel nib, choosing long shaped ones in the form of a lance and fix each part at the end of a match. You now have complete a saloon shooting gallery, inoffensive and sufficiently recreative at least for your smaller friends. [Illustration] The Coin in Equilibrium. Here is a curious demonstration of the balancing of bodies having their center of gravity displaced by a counterpoise.