cer points out the unequal values of logic and different branches of mathematics for this purpose.
As the first division takes into account only ideal relations, the second division takes up relations among realities. It includes concrete things, and gives rise to a division which Mr. Spencer, therefore, calls the abstract concrete-sciences. These are mechanics, physics, and chemistry. They deal with the laws of forces as manifested by matter, but when artificially separated from one another. Mechanics, physics, and chemistry have, for their object, to generalize the laws of relation of their several phenomena, when disentangled from those actual conditions of Nature in which they are mutually modified. For example: "In works on mechanics, the laws of motion are expressed without reference to friction and resistance of the medium. Not what motion ever really is, but what it would be, if retarding forces were absent, is asserted. If any retarding force is taken into account, then the effect of this retarding force is alone contemplated: neglecting the other retarding forces." This group of sciences introduces a new order of ideas which call out a different form of mental exercise. They deal with causation, and have great value in giving "distinctness and strength to the consciousness of cause and effect." By familiarizing the mind with numberless simple and separate cases of the action of forces, "they make it impossible to think of any effect as arising without a cause, or any cause as expended without an effect; and they make it impossible to think of an effect out of proportion to its cause, or a cause out of proportion to its effect."
Mr. Spencer's third division comprises what he terms the concrete sciences, or the real, as contrasted with the wholly or partially ideal sciences. They include astronomy, geology, biology, and psychology, which consider phenomena in their totalities or aggregates. These sciences, being far more complex than the preceding, and presenting their various phenomena in combination, are suited to cultivate the synthetical habit of mind, and to familiarize it with complex causation. Mr. Spencer shows that, while the concrete sciences cannot be made to give the mental discipline of the simpler groups, they are indispensable to exercise the mind upon the fundamental conceptions of continuity, complexity, and contingency in causation, and which are of the highest importance in the judgment of common affairs.
The authorities cited above, and which might have been greatly multiplied, establish the fact, beyond cavil, that there is a profound deficiency in the discipline of the current classical system of study; and they all agree that the introduction of science is alone competent to afford a remedy. Mr. Spencer has shown not only how comprehensive and varied is the discipline which the sciences are capable of yielding, but he has pointed out the radical insufficiency of limited portions of science for that complete mental training which it is the object of the higher education to give. In the interests of mental discipline, therefore, we are compelled to demand a reconstruction of the curriculum of "liberal culture," with not merely more of science in it, but with such an organized scheme of scientific studies as will accomplish the end desired.
Popular Lectures on Scientific Subjects. By H. Helmholtz Professor of Physics in the University of Berlin. Translated by E. Atkinson, Ph.D., F.C.S., Professor of Experimental Science, Hoff College. With an Introduction by Prof. Tyndall. New York: D. Appleton & Co., 1873.
This is, in several respects, the most important scientific publication of the sea-