A Weekly Journal devoted to the Advancement 

 of Science, publishing the official notices and 

 proceedings of the American Association for the 

 Advancement of Science, edited by J. McKeen 

 Cattell and published every Friday by 



THE SCIENCE PRESS 



1 1 Liberty St., Utica, N. Y. Garrison, N. Y. 



New York City: Grand Central Terniinal 



Annual Subscription, $6.00 Single Copies, 15 Cts. 



Entered as second-class matter January 21, 1922, at the 



Post Office at Utica, N. Y., Under the Act of March 3, 1879. 



Vol. lvi October 13, 1922 No. 1450 



CONTENTS 



The British Association for the Advancement 

 of Science: 

 The Theory of NumJiers: Professor G. H. 

 Hardy 401 



Whither? Dr. Martin Fischer 405 



Alexander Smith: Professor Alan W. C. 

 Menzies - 409 



Scientifio Events: 



The Cost of Besearoh WotTc; PeTcing Vnion 

 Medical College; Legal Eestrictions on 

 Types of BaicooJc Glassware; The Confer- 

 ence on Highivays ; The American Psycho- 

 logical Association 409 



Scientifio Notes and News 413 



University and Education Notes 416 



Biscussion and Correspondence: 



The Paleopathology of the Parasuchians : 

 Dr. Kot L. Moodie. Measurement of 

 Human Crania: Professor Eoland B. 

 DisoN. Bibliography and Besearoh: K. C. 

 Walker. An Unusual Solitaire Game: 

 Professor L. E. Dickson. Science in Fic- 

 tion: Dr. Edwin E. Slosson 417 



Quotations : 



The Worlc of General Gorgas 419 



Scientific Books: 



Osgood and Graustein's Plane and Solid 

 Analytic Geometry: Professor G. A. Mil- 

 ler 420 



Special Articles: 



Water Culture Experimentation : Professor 

 W. P. Gericke. The Sperms of Vallisneria: 

 Professor Eobert B. Wylie 421 



The American Mathematical Society: Pro- 

 fessor E. G. D. ElCHARDSON 423 



The American Chemical Society : Dr. Charles 

 L. Parsons 424 



THE THEORY OF NUMBERSi 



There is probably less difference between the 

 methods of a physicist and a mathematician 

 than is generally supposed. The most striliing 

 among them seems to me to be this, that the 

 mathematician is in much more direct contact 

 with reality. This may perhaps seem to you a 

 paradox, since it is the physicist who deals with 

 the subject-matter 'to which the epithet "real" 

 is commonly applied. But a very little reflec- 

 tion will show that the "reality" of the phys- 

 icist, whatever it may be (and it is extraor- 

 dinarily diiflcult to say), has few or none of the 

 attributes which common-sense instinctively 

 marks as real. A chair may be a collection of 

 whirling atoms, or an idea in the mind of God. 

 It is not my business to suggest that one ac- 

 count of it is obviously more plausible than 

 the other. Whatever the merits of either of 

 them may be, neither draws its inspiration from 

 the suggestions of common-sense. 



Neither the philosophers, nor the physicists 

 themselves, have ever put forward any very 

 convincing account of what physical reality is, 

 or of how the physicist passes, from the con- 

 fused mass of fact or sensation with which he 

 starts, to the construction of the objects which 

 he classifies as real. "We can not be said, there- 

 fore, to know what the subject-matter of 

 physics is; but this need not prevent us from 

 understanding the task which a physicist is 

 trying to perform. That, clearly, is to corre- 

 late the incoherent body of facts confronting 

 him with some definite and orderly scheme of 

 abstract relations, the kind of scheme, in short, 

 which he can borrow only from mathematics. 



A mathematician, on the other hand, for- 

 tunately for him, is not concerned with this 



1 Prom the address of the president of the Sec- 

 tion of Mathematics and Physics, given at the 

 Hull meeting of the British Association for the 

 Advancement of Science. 



