752 



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 develop- 

 ment, and new results are being constant- 

 ly 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 sci- 

 entific and medical circles. It is such a 

 work as every teacher of physiology, es- 

 pecially in our higher schools, should have 

 at hand, to illustrate the exact state of pres- 

 ent 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 or .Mathematics, Real 

 and Applied. Editor-in-Chief J. J. Syl- 

 vester, LL. D., F. R. S. Published un- 

 der the auspices of the Johns Hopkins 

 University. Second notice. 



The second number of the American 

 Journal of Mat hematics 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 cer- 

 tainly is such a thing as economy in re- 

 search ; and, fully admitting that each prin- 

 ciple 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 w ill have its effect 

 through all future time. Here is a little 

 question which we may leave to the mathe- 

 maticians 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 sec- 

 tions have found, but only after a thousand 

 years. What, upon the principles of com- 

 pound 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 so- 

 lution of this or that problem, but the exist- 

 ence of the mathematician himself. The 

 civilization of our time has been more pro- 

 moted 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, not- 

 withstanding the smallness of the class who 

 read mathematics, the influence of the great 

 geometers spreads in concentric circles, un- 

 til 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 applica- 

 tions of mathematics. Their business is es- 

 pecially 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 amuse- 

 ment tends toward corruption, but every 

 one tends also toward culture. An amuse- 



