352 THE POPULAR SCIENCE MONTHLY. 



physics, -witli that of its incessant registration in chemistry and in all 

 the biological sciences ; registi'ation often effected, moreover, by a 

 relatively mediocre order of minds. 



The child, like the race, begins at once with two sets of mental ac- 

 tivities — 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.* It is this very 

 incapacity which makes the complexity of objects a matter of indif- 

 ference, 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 co»;prehension. Whatever does not 

 do so, whatever demands the intervention of abstract reasoning and 

 inference, is ditlieult — 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 rea- 

 sons that I have preferred to introduce the world of plants by the 

 flower, Avith its marvelous variety in form and color, in port and ex- 

 pression 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 asymmet- 

 rical 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 rela- 

 tions presented by these exquisite organic forms. Not only through 

 study of their geometric outline, but in their multiple arithmetic com- 

 binations of insertion and section, may the pupil be led to the fruit- 

 ful modern methods which involve the application of mathematics to 

 the non-mathematical sciences. f 



* The effect of this is shown in the autobiography of John Stuart Mill, as the author 

 himself points out in a striking; chapter. 



f See "Etudes comparees dcs Feuillcs," par M. Fermond, ISGi. 



