256 POPULAR SCIENCE MONTHLY. 



infinitesimal analysis, excite to a high degree the conception of 

 the signs and symbols necessary instruments to extend the power 

 and reach of the human mind by summarizing an aggregate of 

 relations in a condensed form and in a kind of mechanical way. 

 These auxiliaries are of especial value in mathematics, because 

 they are there adequate to their definitions, a characteristic which 

 they do not possess to the same degree in the physical and mathe- 

 matical sciences. There are, in fact, a mass of mental and moral 

 faculties that can be put in full play only by instruction in math- 

 ematics ; and they would be made still more available if the teach- 

 ing was directed so as to leave free play to the personal work of 

 the student. Mathematics is the indispensable instrument of all 

 physical research. But the physical sciences introduce new and 

 most important elements into education. They rest chiefly upon 

 other methods than mathematics, the teaching of which con- 

 tributes to the evolution of the child and the manifestation in 

 him of new faculties no less essential, mentally and morally. I 

 mean the faculties of observation and experiment, the object of 

 which is the knowledge of Nature, a thing which, different from 

 geometry, is not acquired by reasoning. In the physical sciences 

 we are slaves to a truth which is exterior to us and which we can 

 not know except by observing it. The teaching of facts is worth 

 most here, and should be given from the tenderest infancy. On 

 this side, scientific teaching, and especially natural history, are 

 necessary from the first years of secondary instruction, and it is a 

 great mistake, I believe, to postpone it till the later years of study. 

 Nothing is more suggestive or better fitted to develop the taste for 

 the knowledge of things and for comparing them than the study 

 of zoology and botany. Children acquire very early the fancy for 

 collections, and morphological notions, so useful for the develop- 

 ment of the arts and sciences, enter their young minds, we might 

 say, insensibly and without forcing. They acquire at the same 

 time the general idea of classification, which plays a very impor- 

 tant part in all human knowledge, and the still more general one 

 of the harmonious combination of organic systems into living 

 beings. A delicate aesthetic sentiment thus gently insinuates 

 itself into their minds. 



In order that the elements of the natural sciences may have 

 their full educational virtue, it is indispensable that they shall 

 not be presented to children under the form of arid nomencla- 

 tures, dictated and learned by heart as a kind of task ; a method 

 very well fitted to give them a disgust for these sciences, which 

 are, on the other hand, really most interesting and most entertain- 

 ing. The teaching of natural history should be based on the sight 

 of the objects themselves. 



The teaching of the experimental sciences, such as physics and 



