534 



SCIENCE. 



[N. S. Vol. XIV. No. 353. 



on the side of scientific precision without be- 

 coming less agreeable to read or less easy to 

 understand. 



It would, of course, be absurd to expect a 

 work of the magnitude and scope of the present 

 one to be free from errors of both omission and 

 commission.* The present writer may be per- 

 mitted to point out one of the former sort 

 which seems particularly serious, viz : the 

 omission of the fundamental proof of Cauchy 

 relative to the continuity of the roots of an 

 algebraic eqviation. On page 181 of the new 

 edition, as on page 162 of the old edition, the 

 author simply takes it for granted that when 

 the independent variable changes continuously, 

 so will every root of the algebraic equation. 



Thomas S. Fiske. 

 Columbia University. 



DISCUSSION AND CORRESPONDENCE. 



PEEGLACIAL DRAINAGE IN" SOUTHWESTERN 



OHIO. 



To THE Editor op Science : In Science 

 for August 9, reference is made, in a review 

 of Professor W. M. Davis, to recent papers 

 by Tight, Bownocker, Todd and Fowke upon 

 the subject of ' Preglacial Drainage of Ohio.' 

 In particular Mr. Fowke is represented as 

 advocating for the Licking and Kentucky 

 rivers a continuance of their courses north- 

 ward by way of a reversed Miami river or 

 some of its tributaries. There seems to me to 

 be an objection to this theory, which will be- 

 come apparent to any one who will study the 

 relation of the channels of the Miami river and 

 its principal tributaries to the boundary out- 

 crop of the lower and upper Silurian formations 

 in that region. In a district where the dip of 

 the rocks is very slight, not over four feet to 

 the mile to the northward, all the reentrant 

 angles, formed in a retreating Clinton limestone 

 escarpment, look as if they had been formed 

 by up-stream cutting action of southward- 

 flowing streams. Note on the accompanying 

 map not only the major northeastern reentrant 



*For a careful analysis of the first edition see Pro- 

 fessor Osgood's review published in the Bulletin of the 

 American Mathematical Society, Vol. I. (1894-5), pp. 

 142-154. Some of the criticisms which appear there 

 apply equally to the present edition. 



of the Big and Little Miami rivers combined, 

 bat also the minor reentrants of the tributaries 

 to the Big Miami from the northwest — those of 

 Four Mile, Seven Mile, Twin and Stillwater 

 Creeks, and that of the upper Miami itself. 

 This Clinton escarpment only here and there 

 peeps out from under its heavy mantle of gla- 

 cial drift. Evidently there has been no retreat 

 of these escarpments since the glaciers them- 

 selves retreated. The veneering of glacial drift 

 has stereotyped this preglacial topography. 

 It is true that geological boundary reentrants 



of Q BvsVnct \A So\i\hYl£.sWnO\liO 



Socaa 



2, mAt.4 



may point down stream. South of the Ohio, 

 one is seen in the lower course of the Ken- 

 tucky River — the Trenton — Hudson boundary 

 reentrant. This is accounted for by the aver- 

 age dip of the rocks to the northwest on this 

 slope of the Lexington uplift being 12 feet to 

 the mile, while the fall of the river in the same 

 is only 1.2 feet per mile. In order that the re- 

 entrants northwest of the Miami River should 

 have been made by streams in that region hav- 

 ing a reversed drainage, the average gradients 

 of these streams could not have been greater 

 than four feet to the mile. Four feet to the 

 mile is about the present southwest fall of the 

 Miami River itself, a much steeper gradient) 



