592 



SCIENCE 



[N. S. Vol. XLHI. No. 1113 



years old with active membersliip ranging 

 from 600 to over 900, the American, the 

 German, and the Italian in Palermo. 

 Taken with other things, these are signs of 

 a flourishing condition of scientific thought. 

 Possibly the most striking proof of this, so 

 far as mathematics is concerned, is found 

 in the annual quantity of published re- 

 search which more than doubled during the 

 last thirty years of the century. 



No one understands the group of trans- 

 formations which we call the flight of time, 

 yet it acts unceasingly upon all human 

 possessions. Nor are its invariants known ; 

 nor yet can we determine what part of 

 scientific energy is conserved and what part 

 is entropy, or waste. It seems to us now 

 that the few great lines of development that 

 I have so briefly traced do show permanent 

 tendencies of organized knowledge — that 

 in these directions science will at least not 

 retrograde while our civilization endures. 

 Yet it is already evident that the last word 

 has not been spoken in physics, and con- 

 ceivably the time may come when the 

 names of Helmholtz, Kirchoff, Maxwell and 

 Hertz will be venerated as that of Archi- 

 medes now is — hardy pioneers indeed, but 

 no longer in the vanguard. Let me make 

 the trite remark, that the transformations 

 of time work more slowly on the body of 

 treasure that we call pure mathematics 

 than ithey do upon the far greater and more 

 rapidly growing pile of natural science. 

 The reason is obvious ; natural science deals 

 with an infinite number of data, and can 

 never apprehend them all ; hence she makes 

 hypotheses serve temporarily. Mathematics 

 does the same, but perfects her products by 

 the progressive exclusion of conflicting 

 data ; that is to say, by increasing precision 

 of terms. The Pythagorean theorem con- 

 cerning the sides of a right triangle will be 

 tnxe longer, in the very nature of things, 

 than Sir George Darwin's magnificent 



theory of the tides. This which is from one 

 point of view a reproach to pure mathe- 

 matics, constitutes on the other hand one 

 of its titles to immortality. 



That the literature of our science is vast 

 and complicated shows only how many are 

 the things that men have wished to know. 

 More numerous, with every advancing de- 

 cade, are the ciuestions pressing for solution. 

 It will not be your lot, members of the 

 Sigma Xi, to discover anything so simple, 

 necessary and universally useful as the 

 multiplication table, or the common the- 

 orems upon volumes and areas; but you 

 may find something as useful to mankind as 

 Napier's logarithms, which were new only 

 three centuries ago ; or some theory as beau- 

 tiful and perfect as that of elliptic func- 

 tions applied to plane cubic curves. You 

 may contribute to the labor of other 

 scholars something as helpful as the great 

 " Encyclopaedic " of the mathematical sci- 

 ences, now almost completed by the untir- 

 ing labor and devotion of cooperating 

 mathematicians in all lands, but chiefly 

 by Germans. But in whatever large do- 

 main or narrow field you may elect to labor, 

 I give you the cheering assurance that 

 there are fruitful discoveries that can be 

 made by every toiler ; that to each one who 

 has the will to know, will come those rare 

 and golden moments when he shall shout in 

 triumph, with the ancient truth-seeker 

 Archimedes, Eureka! 



Henry S. White 

 Vassar College 



SEEING YOURSELF SINQi 



It is possible to make vibrations which pro- 

 duce a tone to the ear also produce a picture to 

 the eye — a picture which reveals details of 

 pitch faithfully and far more finely than the 

 ear can hear, and which may, therefore, be 



1 A part of a paper read before the meeting of 

 the National Music Teachers Association in 

 Buffalo, New York, December, 1915. 



