Émile; Or, Concerning Education; Extracts

by Jean-Jacques Rousseau

In order to prove the angles of a triangle equal to two right angles, a circle is usually drawn. I, on the contrary, will call Émile's attention to this in the circle, and then ask him, "Now, if the circle were taken away, and the straight lines were left, would the size of the angles be changed?"

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 that are within his own power, and discover others by inference. But it would be better he should know nothing about these things than that you should tell him all he is to know about them.

We have an organ that corresponds to that of hearing, that is, the voice. Sight has nothing like this, for though we can produce sounds, we cannot give off colors. We have therefore fuller means of cultivating hearing, by exercising its active and passive organs upon one another.

The Voice.

Man has three kinds of voice: the speaking or articulate voice, the singing or melodious voice, and the pathetic or accented voice, which gives language to passion and animates song and speech. A child has these three kinds of voice as well as a man, but he does not know how to blend them in the same way. Like his elders he can laugh, cry, complain, exclaim, and groan. But he does not know how to blend these inflections with the two other voices. Perfect music best accomplishes this blending; but children are incapable of such music, and there is never much feeling in their singing. In speaking, their voice has little energy, and little or no accent.

Our pupil will have even a simpler and more uniform mode of speaking, because his passions, not yet aroused, will not mingle their language with his. Do not, therefore, give him dramatic parts to recite, nor teach him to declaim. He will have too much sense to emphasize words he cannot understand, and to express feelings he has never known.

Teach him to speak evenly, clearly, articulately, to pronounce correctly and without affectation, to understand and use the accent demanded by grammar and prosody. Train him to avoid a common fault acquired in colleges, of speaking louder than is necessary; have him speak loud enough to be understood; let there be no exaggeration in anything.