December 5, 1913] 



SCIENCE 



791 



successful, varies from partial failure to 

 failure that, if not total, would at all 

 events be fatal in any universe that had the 

 economic decency to forbid, under pain of 

 death, the unlimited wasting of its re- 

 sources. The dominant animal of such a 

 universe would be in fact a superman. In 

 our world the natural resources of life are 

 superabundant, and man is poor in reason 

 because he has been the prodigal son of a 

 too opulent mother. But, ladies and gentle- 

 men, our speaker will conclude, you will 

 know better what rigorous thinking is not 

 when once you have learned what it is. 

 This, however, can not well be learned in 

 a course of lectures in which that knowl- 

 edge is presumed. I have, therefore, to 

 adjourn this course until such time as you 

 shall have gained that knowledge. It can 

 not be gained by reading about it or hear- 

 ing about it. The easiest way, for some 

 persons the only way, to gain it is to exam- 

 ine with exceeding patience and care some 

 specimens, at least one specimen, of the 

 literature in which rigorous thinking is 

 embodied. Such a specimen, he could say, 

 is Dr. Thomas L. Heath's magnificent edi- 

 tion of Euclid where an excellent transla- 

 tion of the "Elements" from the definitive 

 text of Heiberg is set in the composite light 

 of critical commentary from Aristotle down 

 to the keenest logical microscopists and 

 histologists of our own day. If you think 

 Euclid too ancient, and too stale even when 

 seasoned with the wit of more than two 

 thousand years of the acutest criticism, you 

 may find a shorter and possibly a fresher 

 way by examining minutely such a work as 

 Veronese's "Grundziige der Geometric" or 

 Hubert's famous "Foundations of Geom- 

 etry" or the late Fieri 's "Delia Geometria 

 elementare come sistemi ipotetieo-dedut- 

 tivo. ' ' In works of this kind, of which the 

 growing number is rather large, and not 

 elsewhere, you will find, in its nakednoss. 



purity and spirit, what you have neglected 

 and what you need. You will note that in 

 the beginning of such a work there is 

 found a system of assumptions or postu- 

 lates, discovered the Lord only and a few 

 men of genius know where or how, selected 

 perhaps with reference to simplicity and 

 clearness, certainly selected with respect to 

 their compatibility and independence, and, 

 it may be, with respect also to categoricity. 

 You will not fail to observe with the utmost 

 minuteness, and from every possible angle, 

 how it is that upon these postulates as a 

 basis there is built up by a kind of divine 

 masonry, little step by step, a stately struc- 

 ture of ideas, an imposing edifice of 

 rigorous thought, a towering architecture 

 of doctrine that is at once beautiful, aus- 

 tere, sublime and eternal. Ladies and 

 gentlemen, our speaker will say, to accom- 

 plish that examination will require twelve 

 months of pretty assiduous application. 

 The next lecture of this course will be given 

 one year from date. 



On resuming the course what will our 

 philosopher and historian proceed to say? 

 He will begin to say what, if he says it con- 

 cisely, will make up a very large volume. 

 Koom is lacking here, even if competence 

 were not, for so much as an adequate out- 

 line of the matter. It is possible, however, 

 to draw with confidence a few of the larger 

 lines that woiUd have to enter such a 

 sketch. 



"What is it that our speaker will be 

 obliged to deal with first? I do not mean 

 obliged logically or obliged by an orderly 

 development of his subject. I mean 

 obliged by the expectation of his hearers. 

 Every one can answer that question. For 

 presumably the audience represents the 

 spirit of the times, and this age is, at least 

 to a superficial observer, an age of engi- 

 neering. Now, what is engineering ? Well, 

 the charter of the Institution of Civil 



