to the calculation of eclipses, than to get a thorough understanding of day and night.
Since the sun revolves round the earth it describes a circle, and every circle must have a centre; that we know already. This centre is invisible, it is in the middle of the earth, but we can mark out two opposite points on the earth's surface which correspond to it. A skewer passed through the three points and prolonged to the sky at either end would represent the earth's axis and the sun's daily course. A round teetotum revolving on its point represents the sky turning on its axis, the two points of the teetotum are the two poles; the child will be delighted to find one of them, and I show him the tail of the Little bear. Here is a another game for the dark. Little by little we get to know the stars, and from this comes a wish to know the planets and observe the constellations.
We saw the sun rise at midsummer, we shall see it rise at Christmas or some other fine winter's day; for you know we are no lie-a-beds and we enjoy the cold. I take care to make this second observation in the same place as the first, and if skilfully lead up to, one or other will certainly exclaim, "What a funny thing! The sun is not rising in the same place; here are our landmarks, but it is rising over there. So there is the summer east and the winter east, etc." Young teacher, you are on the right track. These examples should show you how to teach the sphere without any difficulty, taking the earth for the earth and the sun for the sun.
As a general rule—never substitute the symbol for the thing signified, unless it is impossible to show the thing itself; for the child's attention is so taken up with the symbol that he will forget what it signifies.
I consider the armillary sphere a clumsy disproportioned bit of apparatus. The confused circles and the strange figures described on it suggest witchcraft and frighten the child. The earth is too small, the circles too large and too numerous, some of them, the colures, for instance, are quite useless, and the thickness of the pasteboard gives them an appearance of solidity so that they are taken for circular masses having a real existence, and when you tell the child that these are imaginary circles, he does not know what he is looking at and is none the wiser.
We are unable to put ourselves in the child's place, we fail to enter into his thoughts, we invest him with our own ideas, and while we are following our own chain of reasoning, we merely fill his head with errors and absurdities.
Should the method of studying science be analytic or synthetic? People dispute over this question, but it is not always necessary to choose between them. Sometimes the same experiments allow one to use both analysis and synthesis, and thus to guide the child by the method of instruction when he fancies he is only analysing. Then, by using both at once, each method confirms the results of the other. Starting from opposite ends, without thinking of following the same road, he will unexpectedly reach their meeting place and this will be a delightful surprise. For example, I would begin geography at both ends and add to the study of the earth's revolution the measurement of its divisions, beginning at home. While the child is studying the sphere and is thus transported to the heavens, bring him back to the divisions of the globe and show him his own home.
His geography will begin with the town he lives in and his father's country house, then the places between them, the rivers near them, and then the sun's aspect and how to find one's way by its aid. This is the meeting place. Let him make his own map, a very simple map, at first containing only two places; others may be added from time to time, as he is able to estimate their distance and position. You see at once what a good start we have given him by making his eye his compass.
No doubt he will require some guidance in spite of this, but very little, and that little without his knowing it. If he goes wrong let him alone, do not correct his mistakes; hold your tongue till he finds them out for himself and corrects them, or at most arrange something, as opportunity offers, which may show him his mistakes. If he never makes mistakes he will never learn anything thoroughly. Moreover, what he needs is not an exact knowledge of local topography, but how to find out for himself. No matter whether he carries maps in his head provided he understands what they mean, and has a clear idea of the art of making them. See what a difference there is already between the knowledge of your scholars and the ignorance of mine. They learn maps, he makes them. Here are fresh ornaments for his room.
Remember that this is the essential point in my method—Do not teach the child many things, but never to let him form inaccurate or confused ideas. I care not if he knows nothing provided he is not mistaken, and I only acquaint him with truths to guard him against the errors he might put in their place. Reason and judgment come slowly, prejudices flock to us in crowds, and from these he must be protected. But if you make science itself your object, you embark on an unfathomable and shoreless ocean, an ocean strewn with reefs from which you will never return. When I see a man in love with knowledge, yielding to its charms and flitting from one branch to another unable to stay his steps, he seems to me like a child gathering shells on the sea-shore, now picking them up, then throwing them aside for others which he sees beyond them, then taking them again, till overwhelmed by their number and unable to choose between them, he flings them all away and returns empty handed.
Time was long during early childhood; we only tried to pass our time for fear of using it ill; now it is the other way; we have not time enough for all that would be of use. The passions, remember, are drawing near, and when they knock at the door your scholar will have no ear for anything else. The peaceful age of intelligence is so short, it flies so swiftly, there is so much to be done, that it is madness to try to make your child learned. It is not your business to teach him the various sciences, but to give him a taste for them and methods of learning them when this taste is more mature. That is assuredly a fundamental principle of all good education.
This is also the time to train him gradually to prolonged attention to a given object; but this attention should never be the result of constraint, but of interest or desire; you must be very careful that it is not too much for his strength, and that it is not carried to the point of tedium. Watch him, therefore, and whatever happens, stop before he is tired, for it matters little what he learns; it does matter that he should do nothing against his will.
If he asks questions let your answers be enough to whet his curiosity but not enough to satisfy it; above all, when you find him talking at random and overwhelming you with silly questions instead of asking for information, at once refuse to answer; for it is clear that he no longer cares about the matter in hand, but wants to make you a slave to his questions. Consider his motives rather than his words. This warning, which was scarcely needed before, becomes of supreme importance when the child begins to reason.
There is a series of abstract truths by means of which all the sciences are related to common principles and are developed each in its turn. This relationship is the method of the philosophers. We are not concerned with it at present. There is quite another method by which every concrete example suggests another and always points to the next in the series. This succession, which stimulates the curiosity and so arouses the attention required by every object in turn, is the order followed by most men, and it is the right order for all children. To take our bearings so as to make our maps we must find meridians. Two points of intersection between the equal shadows morning and evening supply an excellent meridian for a thirteen-year-old astronomer. But these meridians disappear, it takes time to trace them, and you are obliged to work in one place. So much trouble and attention will at last become irksome. We foresaw this and are ready for it.
Again I must enter into minute and detailed explanations. I hear my readers murmur, but I am prepared to meet their disapproval; I will not sacrifice the most important part of this book to your impatience. You may think me as long-winded as you please; I have my own opinion as to your complaints.
Long ago my pupil and I remarked that some substances such as amber, glass, and wax, when well rubbed, attracted straws, while others did not. We accidentally discover a substance which has a more unusual property, that of attracting filings or other small particles of iron from a distance and without rubbing. How much time do we devote to this game
