continents and islands can be traced with an exactness hitherto unknown; that the findings of modern physics have revealed the theoretical laws of vapors and thermodynamics, which are applied daily to supplement and multiply man's labor in all industries; that the discoveries of chemistry respecting gases, combustion, and the preparation of iron and steel, added to the inventions of rational and applied dynamics, control the fabrication and operation of our machines, ships, and locomotives. In short, these marvelous advances have been accomplished through science alone, and not through a blind empiricism. I will not here dwell upon the wonderful facilities that have been given to life by such subtle discoveries of the physics of our time as the electric telegraph, the telephone, photography, and electric lighting; and I only refer by way of a reminder to the complete modification of the conditions of war effected through the very recent discoveries of science concerning explosive matters. I can not, however, pass in silence over the prolongation of human life, the mean duration of which has been doubled among civilized peoples during the past two centuries by the discoveries of physiology, hygiene, and medicine, in which some new advance is marked nearly every day.
All this progress and all this transformation of life have not been accomplished and will not be continued by chance or accident, but are the fruits of modern science. And this is why public opinion is every day demanding an increasing intervention of the methods and teaching of science in public instruction. This participation is, furthermore, not destined to be for the profit of the community alone, but by a necessary consequence is primarily profitable for individuals to whom, prepared by scientific instruction in their secondary education, it is all the time opening new professional careers.
While the necessity of science in secondary education is thus demonstrated by the most imperative reasons from the material and social point of view, it must not be supposed that science is less well adapted to the mental and moral education of the individual, and that it can not form minds capable of elevated conceptions and develop good citizens.
There are two courses in science corresponding to different aptitudes, but not contradictory—the mathematical course, deductive and rational, and the physical and naturalistic direction, founded on observation and experiment, combined with reason. Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for the truth. In addition to all this, mathematics, and chiefly algebra and
