If we always measure them, however, our eye, depending on this, will never gain accuracy. Yet the child ought not to pass too soon from measuring to estimating. It will be better for him, after comparing by parts what he cannot compare as wholes, finally to substitute for measured aliquot parts others, obtained by the eye alone. He should train himself in this manner of measuring instead of always measuring with the hand. I prefer that the very first operations of this kind should be verified by actual measurements, so that he may correct the mistakes arising from false appearances by a better judgment. There are natural measures, nearly the same everywhere, such as a man's pace, the length of his arm, or his height. When the child is calculating the height of the story of a house, his tutor may serve as a unit of measure. In estimating the altitude of a steeple, he may compare it with that of the neighboring houses. If he wants to know how many leagues there are in a given journey, let him reckon the number of hours spent in making it on foot. And by all means do none of this work for him; let him do it himself.
We cannot learn to judge correctly of the extent and size of bodies without also learning to recognize their forms, and even to imitate them. For such imitation is absolutely dependent on the laws of perspective, and we cannot estimate extent from appearances without some appreciation of these laws.
All children, being natural imitators, try to draw. I would have my pupil cultivate this art, not exactly for the sake of the art itself, but to render the eye true and the hand flexible. In general, it matters little whether he understands this or that exercise, provided he acquires the mental insight, and the manual skill furnished by the exercise. I should take care, therefore, not to give him a drawing-master, who would give him only copies to imitate, and would make him draw from drawings only. He shall have no teacher but nature, no models but real things. He shall have before his eyes the originals, and not the paper which represents them. He shall draw a house from a real house, a tree from a tree, a human figure from the man himself. In this way he will accustom himself to observe bodies and their appearances, and not mistake for accurate mutations those that are false and conventional. I should even object to his drawing anything from memory, until by frequent observations the exact forms of the objects had clearly imprinted themselves on his imagination, lest, substituting odd and fantastic shapes for the real things, he might lose the knowledge of proportion and a taste for the beauties of nature. I know very well that he will go on daubing for a long time without making anything worth noticing, and will be long in mastering elegance of outline, and in acquiring the deft stroke of a skilled draughtsman. He may never learn to discern picturesque effects, or draw with superior skill. On the other hand, he will have a more correct eye, a truer hand, a knowledge of the real relations of size and shape in animals, plants, and natural bodies, and practical experience of the illusions of perspective. This is precisely what I intend; not so much that he shall imitate objects as that he shall know them. I would rather have him show me an acanthus than a finished drawing of the foliation of a capital.