*THE POPULAR SCIENCE MONTHLY.*

community at large that the subject ought to have great prominence in education and to be taught to every child at school. But while many physiological principles and facts are so well established that they require to be understood for practical ends, yet the subject is still undergoing rapid development, and new results are being constantly reached which throw further light upon the operations of the vital economy, and are often immediately useful. *The Journal of Physiology,* therefore, has a valid claim upon the attention of many outside of scientific and medical circles. It is such a work as every teacher of physiology, especially in our higher schools, should have at hand, to illustrate the exact state of present knowledge upon numberless questions in relation to which current text-books may be insufficient or behind the times. Where teaching has not become purely mechanical and perfunctory, and all care and conscience have not died out, the teacher of physiology might give freshness and authority to his instructions by subscribing to this new magazine, and making himself familiar with its contents.

American Journal of Mathematics, Real and Applied. Editor-in-Chief J. J. Sylvester, LL. D., F. R. S. Published under the auspices of the Johns Hopkins University. *Second notice.*

The second number of the *American Journal of Mathematics* reaches us. It is very handsomely printed in quarto, and the formulas look as inviting as formulas can. It undoubtedly belongs to the highest class of mathematical periodicals. We will not presume to pass judgment upon the utility of all those speculations concerning space of four dimensions, the exact movements of the moon, the abstrusities of pure algebra, the phyllotactic numbers, etc. There certainly is such a thing as economy in research; and, fully admitting that each principle of pure mathematics is likely some day to find an application, it is a question to be considered whether it is worth while to spend time upon a theorem a thousand years before it will probably be needed. The principles of compound interest apply as much to brains as to money. If, instead of expending a certain portion of energy upon the resolution of a distantly useful problem, I devote it to something which has immediate applications, an advantage will have been gained which will have its effect through all future time. Here is a little question which we may leave to the mathematicians to solve, if anything so simple can interest them: Suppose that a certain mathematical study is destined to find an application as important as the conic sections have found, but only after a thousand years. What, upon the principles of compound interest, is the present worth of it as compared with that of an equal expenditure of energy in any immediately practical way?

When we call to mind what an army of intellects have devoted themselves to such subjects as, say, the resolution of cubic equations, we can hardly help suspecting that such researches, though of a higher order of activity than chess-playing, are chiefly of value for the amusement they afford. What is really useful is not the solution of this or that problem, but the existence of the mathematician himself. The civilization of our time has been more promoted by engineers, inventors, and popular writers on science, than by almost any other classes of men. But these persons are led by scientific men. The scientific men are certainly led by the physicists, and these in turn by the mathematicians. Thus, notwithstanding the smallness of the class who read mathematics, the influence of the great geometers spreads in concentric circles, until there is no one, not even the common day-laborer, who is not better off for it. It is not necessary that the problems in which the mathematicians most delight should be particularly useful. It is not necessary that the most profound minds, whose real value to civilization is the greatest of all, should ever concern themselves with the applications of mathematics. Their business is especially to work out fruitful conceptions, and to impress them upon other minds; and this they do not only by their writings, but also by their personal conversation.

The truth is, that productive industry only builds the substructure upon which civilization rests. The fairy palace itself is due to the pursuit of pleasure, to luxury, to the doing of useless things. Every amusement tends toward corruption, but every one tends also toward culture. An amuse-