SCIENCE 



Editorial Committee : S. Newcomb, Mathematics ; E. S. Woodward, Mechanics ; E. C. Pickering, 



Astronomy; T. C. Mendenhall, Physics; E. H. Thurston, Engineering; Ira Eemsen, Chemistry; 



J. Le Conte, Geology; W. M. Da VIS, Physiography; O. C. Marsh, Paleontology; W. K. Brooks, 



C. Hart Merriam, Zoology; S. H. Sciiddbe, Entomology; C. E. Bessey, N. L. Britton, 



Botany; Henry F. Osborn, General Biology; C. S. Minot, Embryology, Histology; 



H. P. Bowditch, Physiology; J. S. Billings, Hygiene ; J. McKeen Cattell, 



Psychology; Daniel G. Brinton, J. W. Powell, Anthropology. 



Friday, January 7, 1898. 



CONTENTS: 



The PMlosophy of Hyper-space: Professor S. 

 Newcomb 1 



Report upon some Preliminary Experiments with the 

 Sontgen Bays on Plants: Professor G. F. 

 Atkinson 7 



Some Considerations upon the Functions of Stomata : 

 Professor Charles E. Bessey 13 



Recent Progress in Agricultural Chemistry : De. H. 



W. Wiley 16 



The American Society of Nattiralists : Professor 



H. C.Bdivipus 21 



tiflc Notes and News 23 



f and Educational News 27 



I and Correspondence : — 

 Water Surface Temperature of Lake Titicaca: 

 E. DeC. Ward. ZirTcelite—A Question of Prior- 

 ity: President M. E. Wadswoeth 28 



Scientific Literature : — 



Catalogvs Mammalium tarn viventium quam fos- 

 silimn : Dr. C. Haet Mereiam. Guide to the 

 Genera and Classification of the North . American 

 Orthoptera found north of 31exico : Peofessor 

 A. S. Packard. Les Ballons-Sondes : De. A. 

 Lawrence Eotch. EusselVs Volcanoes of North 

 America: Professor Wm. North ElCE 30 



Societies and Academies : — 



New York Academy of Sciences — Section of Geol- 

 ogy : Professor EicHARD E. Dodge 36 



MSS. intended ior publication and books, etc., intended 

 for review should be sent to the responsible editor, Prof. J. 

 MoKeen Cattell, Garrlson-on-Hudson, N. Y. 



TSE PHILOSOPBY OF HYPER-SPACE* 

 There is a region of mathematical 

 thought which might be called the fairyland 

 of geometry. The geometer here disports 

 himself in a way which, to the non- 

 mathematical thinker, suggests the wild 

 flight of an unbridled imagination rather 

 than the sober sequence of mathematical 

 demonstration. Imaginative he certainly 

 does become, if we apply this term to every 

 conception which lies outside of our human 

 experience. Yet the results of the hypoth- 

 eses introduced into this imaginary uni- 

 verse are traced out with all the rigor of 

 geometric demonstration. It is quite fit- 

 ting that one who finds the infinity of space 

 in which our universe is situated too nar- 

 row for his use should, in his imaginative 

 power, outdo the ordinary writer of fairy 

 tales, when he evokes a universe sufficiently 

 extended for his purposes. 



The introduction of what is now very 

 generally called hyper-space, especially 

 space of more than three dimensions, into 

 mathematics has proved a stumbling block 

 to more than one able philosopher. The 

 question whether a fourth dimension may 

 possibly exist, and whether it can be legiti- 

 mately employed for any mathematical pur- 

 pose, is one on which clear ideas are not 

 universal. I do not, however, confine the 

 term ' hyper-space ' to space of more than 



*Address of the President before the American 

 Mathematical Society, December 29, 1897. 



