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of size and tone we could not judge of distance, or rather distance would have no existence for us. If two trees, one of which was a hundred paces from us and the other ten, looked equally large and distinct, we should think they were side by side. If we perceived the real dimensions of things, we should know nothing of space; everything would seem close to our eyes.
The angle formed between any objects and our eye is the only means by which our sight estimates their size and distance, and as this angle is the simple effect of complex causes, the judgment we form does not distinguish between the several causes; we are compelled to be inaccurate. For how can I tell, by sight alone, whether the angle at which an object appears to me smaller than another, indicates that it is really smaller or that it is further off.
Here we must just reverse our former plan. Instead of simplifying the sensation, always reinforce it and verify it by means of another sense. Subject the eye to the hand, and, so to speak, restrain the precipitation of the former sense by the slower and more reasoned pace of the latter. For want of this sort of practice our sight measurements are very imperfect. We cannot correctly, and at a glance, estimate height, length, breadth, and distance; and the fact that engineers, surveyors, architects, masons, and painters are generally quicker to see and better able to estimate distances correctly, proves that the fault is not in our eyes, but in our use of them. Their occupations give them the training we lack, and they check the equivocal results of the angle of vision by its accompanying experiences, which determine the relations of the two causes of this angle for their eyes.
Children will always do anything that keeps them moving freely. There are countless ways of rousing their interest in measuring, perceiving, and estimating distance. There is a very tall cherry tree; how shall we gather the cherries? Will the ladder in the barn be big enough? There is a wide stream; how shall we get to the other side? Would one of the wooden planks in the yard reach from bank to bank? From our windows we want to fish in the moat; how many yards of line are required? I want to make a swing between two trees; will two fathoms of cord be enough? They tell me our room in the new house will be twenty-five feet square; do you think it will be big enough for us? Will it be larger than this? We are very hungry; here are two villages, which can we get to first for our dinner?
An idle, lazy child was to be taught to run. He had no liking for this or any other exercise, though he was intended for the army. Somehow or other he had got it into his head that a man of his rank need know nothing and do nothing—that his birth would serve as a substitute for arms and legs, as well as for every kind of virtue. The skill of Chiron himself would have failed to make a fleet-footed Achilles of this young gentleman. The difficulty was increased by my determination to give him no kind of orders. I had renounced all right to direct him by preaching, promises, threats, emulation, or the desire to show off. How should I make him want to run without saying anything? I might run myself, but he might not follow my example, and this plan had other drawbacks. Moreover, I must find some means of teaching him through this exercise, so as to train mind and body to work together. This is how I, or rather how the teacher who supplied me with this illustration, set about it.
When I took him a walk of an afternoon I sometimes put in my pocket a couple of cakes, of a kind he was very fond of; we each ate one while we were out, and we came back well pleased with our outing. One day he noticed I had three cakes; he could have easily eaten six, so he ate his cake quickly and asked for the other. "No," said I, "I could eat it myself, or we might divide it, but I would rather see those two little boys run a race for it." I called them to us, showed them the cake, and suggested that they should race for it. They were delighted. The cake was placed on a large stone which was to be the goal; the course was marked out, we sat down, and at a given signal off flew the children! The victor seized the cake and ate it without pity in the sight of the spectators and of his defeated rival.
The sport was better than the cake; but the lesson did not take effect all at once, and produced no result. I was not discouraged, nor did I hurry; teaching is a trade at which one must be able to lose time and save it. Our walks were continued, sometimes we took three cakes, sometimes four, and from time to time there were one or two cakes for the racers. If the prize was not great, neither was the ambition of the competitors. The winner was praised and petted, and everything was done with much ceremony. To give room to run and to add interest to the race I marked out a longer course and admitted several fresh competitors. Scarcely had they entered the lists than all the passers-by stopped to watch. They were encouraged by shouting, cheering, and clapping. I sometimes saw my little man trembling with excitement, jumping up and shouting when one was about to reach or overtake another—to him these were the Olympian games.
However, the competitors did not always play fair, they got in each other's way, or knocked one another down, or put stones on the track. That led us to separate them and make them start from different places at equal distances from the goal. You will soon see the reason for this, for I must describe this important affair at length.
Tired of seeing his favourite cakes devoured before his eyes, the young lord began to suspect that there was some use in being a quick runner, and seeing that he had two legs of his own, he began to practise running on the quiet. I took care to see nothing, but I knew my stratagem had taken effect. When he thought he was good enough (and I thought so too), he pretended to tease me to give him the other cake. I refused; he persisted, and at last he said angrily, "Well, put it on the stone and mark out the course, and we shall see." "Very good," said I, laughing, "You will get a good appetite, but you will not get the cake." Stung by my mockery, he took heart, won the prize, all the more easily because I had marked out a very short course and taken care that the best runner was out of the way. It will be evident that, after the first step, I had no difficulty in keeping him in training. Soon he took such a fancy for this form of exercise that without any favour he was almost certain to beat the little peasant boys at running, however long the course.
The advantage thus obtained led unexpectedly to another. So long as he seldom won the prize, he ate it himself like his rivals, but as he got used to victory he grew generous, and often shared it with the defeated. That taught me a lesson in morals and I saw what was the real root of generosity.
While I continued to mark out a different starting place for each competitor, he did not notice that I had made the distances unequal, so that one of them, having farther to run to reach the goal, was clearly at a disadvantage. But though I left the choice to my pupil he did not know how to take advantage of it. Without thinking of the distance, he always chose the smoothest path, so that I could easily predict his choice, and could almost make him win or lose the cake at my pleasure. I had more than one end in view in this stratagem; but as my plan was to get him to notice the difference himself, I tried to make him aware of it. Though he was generally lazy and easy going, he was so eager in his sports and trusted me so completely that I had great difficulty in making him see that I was cheating him. When at last I managed to make him see it in spite of his excitement, he was angry with me. "What have you to complain of?" said I. "In a gift which I propose to give of my own free will am not I master of the conditions? Who makes you run? Did I promise to make the courses equal? Is not the choice yours? Do not you see that I am favouring you, and that the inequality you complain of is all to your advantage, if you knew how to use it?" That was plain to him; and to choose he must observe more carefully. At first he wanted to count the paces, but a child measures paces slowly and inaccurately; moreover, I decided to have several races on one day; and the game having become a sort of passion with the child, he was sorry to waste in measuring the portion of time intended for running. Such delays are not in accordance with a child's impatience; he tried therefore to see better and to reckon the distance more accurately at sight. It was now quite easy to extend and develop this power. At length, after some months' practice, and the correction of his errors, I so trained his power of judging at sight that I had only to place an imaginary cake on any distant object and his glance was nearly as accurate as the surveyor's chain.
Of all the senses, sight is that which we can least distinguish from the judgments of the mind; as it takes a long time to learn to see. It takes a long time to compare sight and touch, and to train the former sense to give a true report of shape and distance. Without touch, without progressive motion, the sharpest eyes in the world could give us no idea of space. To the oyster the whole world must seem a point, and it would seem nothing more to it even if it had a human mind. It is only by walking, feeling, counting,