physics, with that of its incessant registration in chemistry and in all the biological sciences; registration often effected, moreover, by a relatively mediocre order of minds.
The child, like the race, begins at once with two sets of mental activities—sense-impressions, and speculations suggested by them and by emotional experience. Since complex objects are capable of making impressions on its senses, and of suggesting speculation, it is often both possible and profitable to study the external and perceptible characters of these objects, as well as those of simpler ones. The child, like the infant humanity, is incapable of profound anlysis, and a premature habit of analysis is morally destructive.[1] It is this very incapacity which makes the complexity of objects a matter of indifference, since it is only by analysis that the difference between simple and complex objects can be recognized or felt. Whatever makes a large impression upon the senses is, other things being equal, easy of apprehension, even when not of comprehension. Whatever does not do so, whatever demands the intervention of abstract reasoning and inference, is difficult—often so difficult as to be really impossible—even though the child pretend and appear to understand.
And thus, to return to our starting-point, it is for all of these reasons that I have preferred to introduce the world of plants by the flower, with its marvelous variety in form and color, in port and expression and inflorescence, in contrivance of petal and stamen and pistil, and in manifold destiny of fruit. I would, undoubtedly, and in accordance with the principle already laid down of indicating many things on the mental horizon before the time should arrive for paying systematic attention to them, bring forward a few salient leaves as types: the needles of the pine, the rounded floating leaves of the water-lily, the truncated leaves of the tulip-tree, the five-fingered leaves of the maple, the pinnated leaves of the sumach, the asymmetrical leaves of the begonia, the woolly leaves of the mullein. But I should reserve the systematic study of "hundreds of specimens" to a much later period, and then enter upon it with all possible enthusiasm, and prepared to especially consider the numerous mathematical relations presented by these exquisite organic forms. Not only through study of their geometric outline, but in their multiple arithmetic combinations of insertion and section, may the pupil be led to the fruitful modern methods which involve the application of mathematics to the non-mathematical sciences.[2]
