Let as suppose, I said to the teacher, that an architect shows you a dome, the form of which interests you. He can follow one of two methods in showing you his work: he can call attention to the beauty of line, the harmony of the proportions, and may then take you inside the building and up into the cupola itself, in order that you may appreciate the relative proportion of the parts in such a way that your impression of the cupola as a whole shall be founded on general knowledge of its parts, or he can have you count the windows, the wide or narrow cornices, and can, in fact, make you a design showing the construction; he can illustrate for you the static laws and write out the algebraic formulæ necessary in the calculation of such laws. In the first place, you will be able to retain in your mind the form of the cupola; in the second, you will have understood nothing, and will come away with the impression that the architect fancied himself speaking to a fellow engineer, instead of to a traveller whose object was to become familiar with the beautiful things about him. Very much the same thing happens if we, instead of saying to the child, "This is a square," and by simply having him touch the contour establish materially the idea of the form, proceed rather to a geometrical analysis of the contour.
Indeed, we should feel that we are making the child precocious if we taught him the geometric forms in the plane, presenting at the same time the mathematical concept, but we do not believe that the child is too immature to appreciate the simple _form_; on the contrary, it is no effort for a child to look at a square window or table,--he sees all these forms about him in his daily life. To call his attention to a determined form is to clarify the impression he has already received of it, and to fix the idea of it. It is very much as if, while we are looking absent-mindedly at the shore of a lake, an artist should suddenly say to us--"How beautiful the curve is that the shore makes there under the shade of that cliff." At his words, the view which we have been observing almost unconsciously, is impressed upon our minds as if it had been illuminated by a sudden ray of sunshine, and we experience the joy of having crystallised an impression which we had before only imperfectly felt.