516 



SCmNGE. 



[N. S. Voi.V. No. 117. 



berlin that when pronounced upon by ' experts ' 

 in glacial topography, there will be seen to be a 

 difference between the two types as illustrated 

 by the photographs. If so, it should be a 

 requisite that such an expert should have been 

 to the top of some of the unsubdued peaks 

 to prove that they have not been glaciated. 

 The mere conclusion based upon a conception 

 of what seems probable should not suffice. I 

 know for my own part that until I got to the 

 top of some of the high peaks on the Upper 

 Nugsuak I could not believe they had been 

 ice-covered ; yet I found that the ice had not 

 only covered them, but had extended at least 

 twenty miles further. From my studies the 

 conclusion was forced upon me that isolated 

 peaks, as well as those rising well above the 

 general level, may be glaciated for a long time 

 and still remain very angular. 



I am not engaged in an ' attempt ' to place Pro- 

 fessor Chamberlin in error, as he states, but in- 

 tend to point out what I believe is an error of 

 judgment. What glacial geology needs above 

 all other things at present is a greater body of 

 fact upon which to base our conclusions. We 

 now have the fact that many parts of the Green- 

 land coast are angular ; we have the further 

 fact that a region of angular topography has 

 been glaciated. It is the truth that we wish to 

 see discovered, whether this proves that all of 

 Greenland has been glaciated or only a part ; 

 but until more facts are obtained I hold that 

 Professor Chamberlin' s conclusion that the ice 

 did not extend into the heart of Bafiin's Bay is 

 based upon evidence of such a questionable 

 nature that it ought not to be accepted. I, 

 therefore, say again, let us get facts and trust 

 more in them than in 'expert judgment.' 

 When this is done glacial geology will have a 

 better reputation. K. S. Taee. 



COENELL UNIVEESITY. 



So long as Professor Tarr continues to insist 

 that a glaciated and a partially subdued topo- 

 graphy cannot be distinguished by its contours, 

 although his own observations show the dis- 

 criminations of two observers, on separate 

 trips, to have been essentially correct, and so 

 long as he persists in calling a topography un- 

 qualifiedly angular which these observers have 



distinguished from the unqualifiedly angular, it 

 seems idle to continue to discuss the subject. 

 In pursuance of his urgency of the importance 

 of fact and truth and better methods in glaci- 

 ology there is but one defense which he can 

 properly make, and that is to publish in 

 Science, whose readers he seeks to influence, 

 the photographs which accompany his Wash- 

 ington paper. Glacialists will then be able to 

 judge for themselves whether glaciation is or is 

 not indicated by the topography. 



T. C. Chambeelin. 



HISTOEY OP ELEMENTAEY MATHEMATICS. 



In Professor Blake's appreciative review of 

 my ' History of Elementary Mathematics ' there 

 are two or three statements which appear to 

 me open to objection. It must be admitted 

 that, if the logarithm of x be defined by the re- 

 lation a;=6'''S5:^ J being constant, then, strictly 

 speaking, Napier's numbers are not logarithms. 

 It is the knowledge of this fact which led me to 

 write in my history (p. 160) : "In determining, 

 therefore, what the base of Napier's system 

 would have been, we must divide each term in 

 the geometric and arithmetic series by 10'." In 

 the light of this remark, my statement that the 

 base ' demanded by his [Napier's] reasoning is 

 the reciprocal of that of the natural system ' 

 seems correct. The real question raised by Pro- 

 fessor Blake's criticism is this : In considering 

 the matter of a base, what is the best method 

 of describing the nature of Napier's logarithms 

 to a modern student ? My claim is that the 

 method of dividing each of Napier's numbers 

 and logarithms by 10' and then finding the 

 fixed base — a method which I followed in imi- 

 tation of W. R. MacDonald, M. Marie and 

 others — is more readily grasped by the elemen- 

 tary student than the one involving the difii- 

 cult notion of a variable base, suggested by 

 Hagen and Blake. 



The sentence ' V^ cannot be exactly repre- 

 sented by any number whatever ' is correct 

 from the Greek point of view, for on page 29 I 

 say that 'by the Greeks irrationals were not 

 classified as numbers. ' 



I am unable to find anything on page 74 

 which would ' lead one to suppose that rigor 

 demands our ability to construct* * *every in- 



