It is not customary to pay much attention to the accuracy of figures in geometry; the accuracy is taken for granted, and the demonstration alone is regarded. Émile and I will pay no heed to the demonstration, but aim to draw exactly straight and even lines; to make a square perfect and a circle round. To test the exactness of the figure we will examine it in all its visible properties, and this will give us daily opportunity of finding out others. We will fold the two halves of a circle on the line of the diameter, and the halves of a square on its diagonal, and then examine our two figures to see which has its bounding lines most nearly coincident, and is therefore best constructed. We will debate as to whether this equality of parts exists in all parallelograms, trapeziums, and like figures. Sometimes we will endeavor to guess at the result of the experiment before we make it, and sometimes to find out the reasons why it should result as it does. Geometry for my pupil is only the art of using the rule and compass well. It should not be confounded with drawing, which uses neither of these instruments. The rule and compass are to be kept under lock and key, and he shall be allowed to use them only occasionally, and for a short time, lest he fall into the habit of daubing. But sometimes, when we go for a walk, we will take our diagrams with us, and talk about what we have done or would like to do. Hearing. What has been said as to the two senses most continually employed and most important may illustrate the way in which I should exercise the other senses. Sight and touch deal alike with bodies at rest and bodies in motion. But as only the vibration of the air can arouse the sense of hearing, noise or sound can be made only by a body in motion. If everything were at rest, we could not hear at all. At night, when we move only as we choose, we have nothing to fear except from other bodies in motion. We therefore need quick ears to judge from our sensations whether the body causing them is large or small, distant or near, and whether its motion is violent or slight. The air, when in agitation, is subject to reverberations which reflect it back, produce echoes, and repeat the sensation, making the sonorous body heard elsewhere than where it really is. In a plain or valley, if you put your ear to the ground, you can hear the voices of men and the sound of horses' hoofs much farther than when standing upright. As we have compared sight with touch, let us also compare it with hearing, and consider which of the two impressions, leaving the same body at the same time, soonest reaches its organ. When we see the flash of a cannon there is still time to avoid the shot; but as soon as we hear the sound there is not time; the ball has struck. We can estimate the distance of thunder by the interval between the flash and the thunderbolt. Make the child understand such experiments; try those