440 



SCIENCE. 



[N. S. Vol. XXIV. No. 614. 



Manson's theory of the ice age has been 

 favorably received by some eminent geologists. 

 Thirteen years ago, shortly after Manson's 

 memoir entitled ' Geological and Solar Cli- 

 mates ' was first published, I wrote,^ from an 

 astronomer's point of view, as follows: 



Under the above title Dr. Marsden Manson has 

 published a thesis, issued by the University of 

 California, of more than ordinary merit. Geol- 

 ogists tell us that large areas of now densely 

 populated regions of the earth were at one time 

 covered with ice to a depth of many feet. To most 

 scientists the explanations hitherto given, to ac- 

 count for the cause of the so-called Glacial Epoch, 

 seem wholly inadequate. Dr. Manson's treat- 

 ment of the problem is unique, and to many it 

 M'ill appear quite convincing. We do not hesitate 

 to recommend it for careful study to those in- 

 terested in astro-geological physics. 



I now copy, word for word, the last para- 

 graph of a recent paper entitled ' The Causes 

 of the Glacial Epoch,' written by a recognized 

 leader in science. He concludes as follows: 



It does seem to the writer that imless it 

 can be shown that the temperature prevailing 

 at the beginning of the glacial epoch could not 

 have been high enough to maintain a cloud en- 

 velope, Manson's theory as outlined above must 

 be considered as the most probable among those 

 that have heretofore been suggested, as fulfilling 

 both qualitatively and quantitatively the postu- 

 lates of the great Ice Age; not excluding of course 

 the probable influence of the agencies claimed by 

 Arrhenius and Chamberlin as the chief ones, but 

 which appear to the writer to be inadequate to 

 account for the phenomena in actual evidence. 



Such is the testimony of a geologist of 

 world-wide fame. 



J. M. SCHAEBERLE. 



Ann Arbob, 



August 30, 1906. 



NON-EUCLIDEAN GEOMETRY. 



To THE Editor of Science: My attention 

 has been called to some quotations from a 

 private letter of mine in an article by Pro- 

 fessor George Bruce Halsted on * The Value 

 of the Non-Euclidean Geometry,' which ap- 

 peared in the November number of the Popular 



^ See No. 32, ' Publications of the Astronomical 

 Society of the Pacific' 



Science MoniMy, 1905. The letter referred 

 to was written by me to the author in answer 

 to a query of his of March 21, 1904, couched 

 in the following words : 



I am curious to know, if in the face of such a 

 statement as Poincare's in his review of Hilbert, 

 ' The postulate of Euclid then can not be demon- 

 strated; and this impossibility is as certain as 

 any mathematical truth whatsoever,' you actually 

 still think that you have proved it, or that you 

 have proved that external space is necessarily 

 Euclidean. 



In view of the fact that the quotations do 

 not adequately express my views, I beg you 

 for the privilege of being granted some of 

 your valuable space for the publication of my 

 letter in full. The true copy of my letter 

 dated March 25, 1904, follows. The quotations 

 are enclosed in brackets : 



My dear Professor Halsted — Your letter of the 

 21st inst. has just reached me. From its tone 

 I conclude that you are in earnest about the 

 matter, and I am glad to have found in you a 

 man who intends to read the work. The disser- 

 tation was written for the purpose of bringing 

 before the mathematical world certain conten- 

 tions — no matter how seemingly heterodox — for 

 which a scientific basis is claimed to have been 

 laid down in the new treatment and in the new 

 point of view; and, of course, if the claim is not 

 well established, then either the treatment or the 

 point of view is open to criticism — and fair criti- 

 cism, whether favorable, or unfavorable, is cor- 

 dially invited, even solicited. [As to Poincarg's 

 assertion about the impossibility of proving ^ the 

 Euclidian postulate, it is no more than a belief — 

 though an enthusiastic one — never proved mathe- 

 matically, and in its very nature incapable of 

 mathematical proof,] unless we are certain that 

 space is non-Euclidian. [Poincar6 is undoubtedly 

 a great mathematician, perhaps the greatest now 

 living; but his assertion of his inmost conviction, 

 no matter how strongly put, can not pass for 

 mathematical truth, unless mathematically 

 proved. His conclusion — shared also by many 

 another noted mathematician, as well as by the 

 founders of the non-Euclidian geometries — can 

 only be based on the fact of the existence of these 

 last geometries, self-consistent and perfectly log- 



^ I stand corrected with regard to the german- 

 isms, ' impossibility to prove,' ' impossibility to 

 establish,' which appeared in the original text of 

 the letter. 



