March 16, 1900.] 



SCIENCE. 



433 



divided into any multitude of parts whatsoever 

 — or if we replace this by an equivalent defini- 

 tion in purely logical terms — we find it lends 

 itself at once to mathematical demonstrations, 

 and enables us to work with ease in topical 

 geometry. 



3. Professor Eoyce wants to know how I 

 could, in a passage which he cites, attribute to 

 Cantor the above opinion about infinitesimals. 

 My intention in that passage was simply to 

 acknowledge myself, in a general way, to 

 be no more than a follower of Cantor in 

 regard to infinity, not to make him responsible 

 for any particular opinion of my own. How- 

 ever, Cantor proposed, if I remember rightly, 

 so far to modify the kinetical theory of gases 

 as to make the multitude of ordinary atoms 

 equal to that of the integral numbers, and that of 

 the atoms of ether equal to the multitude of 

 possible collections of such numbers. Now, 

 since it is essential to that theory that encounters 

 shall take place, and that promiscuously, it 

 would seem to follow that each atom has, in 

 the random distribution, certain next neighbors, 

 so that if there are an infinite multitude in a 

 finite space, the infinitesimals must be actual 

 real distances, and not the mere mathematical 

 conceptions, like i^ — 1, which is all that I con- 

 tend for. C. S. Peiece. 



MiLFOED, Pa., Feb. 18, 1900. 



CURRENT NOTES ON PHYSIOGRAPHY. 



DEFLECTION OP RIVBES BY SAND-EEEFS. 



An article on ' The effect of sea barriers upon 

 ultimate drainage ' by J. F. Newsom (Journ. 

 Geol., vii, 44.5-451), describes several ex- 

 amples of rivers whose discharge is deflected 

 to the right or left by the formation of an off- 

 shore sand-reef in front of their mouths, and 

 suggests that such deflection may explain the 

 course of rivers that now flow parallel to pre- 

 existent coast lines ; for example, the Delaware 

 below Bordentown, N. J. 



This suggestion is evidently valid as a possi- 

 bility, but it is not accompanied by tests that 

 sufficiently distinguish deflections thus caused 

 from deflections that arise from the spontaneous 

 adjustment of streams to the weak strata that 

 underlie the cuesta-makers of coastal plains 

 having longitudinal relief. The lower Dela- 



ware cannot be a normal example of the latter 

 class, because as the master river of its region 

 it is the very one that should not be deflected 

 by adjustment; on the other hand, it may 

 truly fall under the former class because its 

 deflection is in the sense of the dominant sand- 

 drift along our Atlantic Coast. Examples of 

 sand-reef deflections ought to follow the strike 

 of strong or weak rocks, indifferently ; while 

 normal deflections by adjustment can only fol- 

 low belts of weak rocks. 



DEVELOPMENT OF THE SEVERN. 



The systematic development of rivers seldom 

 finds better illustration than in the interaction 

 of the ' waxing Severn and the waning Thames,' 

 concerning which a number of new details and 

 suggestions are given by S. S. Buckman (Nat. 

 Science, xiv, 1899, 273-289). The growth of 

 the Severn by headward erosion along the 

 weaker strata that underlie the firmer oolites of 

 the Cotteswold hills is advocated on good evi- 

 dence, and a restoration of the original conse- 

 quent headwaters that have now been diverted 

 from the Thames system is attempted. The 

 growth of obsequent branches of the subse- 

 quent Severn on the line of the beheaded con- 

 sequent branches of the Thames is well pre- 

 sented as the reason for the peculiar un- 

 symmetrical arrangement of the Severn tribu- 

 taries in the neighborhood of Gloucester. The 

 Frome, a branch of the Severn, is shown to 

 have captured several of the westernmost 

 headwaters of the Thames in the Cottes- 

 wold hills between Chalford and Edgeworth. 

 The progressive diminution of the Coin, a 

 branch of the Thames, by the successive diver- 

 sion to the Severn of the two large branches 

 that once came from Wales is offered in explana- 

 tion of the very curious features of the present 

 Coin valley in the upland east of Cheltenham : 

 a valley of large-curve meanders is taken as the 

 work of the original river ; a narrower valley 

 of small meanders, cut in the floor of the larger 

 valley, is the work of the river after one of its 

 upper branches was captured by the Severn ; 

 the wriggling course of the present stream on 

 the floor of these smaller meanders is due to 

 the further loss of volume after the second 

 upper branch was captured. 



