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 mathematical sciences. There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching 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 contributes 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 zoölogy and botany. Children acquire very early the fancy for collections, and morphological notions, so useful for the development 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 important part in all human knowledge, and the still more general one of the harmonious combination of organic systems into living beings. A delicate æsthetic 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 nomenclatures, 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 entertaining. 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
