232 



SCIENCE. 



Vol. XXI. No. 534 



cases, 89 per cent of the color cases, and, as I have said, 92 per 

 cent of the nevTspaper cases. At nearer distances we find the 

 remarkable uniformity with which the safe-distance association 

 works. At 14 inches only 14 per cent of all the cases were re- 

 fused, and at 13 inches only about 8 per cent. The fact that 

 there was a larger percentage of refusals at 11 and 13 inches than 

 at 13 and 14 inches is seen from the table (I.) to be due to the in- 

 fluence of the brown, which was refused consistently when more 

 than 10 inches away. The fact that there were no refusals to 

 reach for anything exposed within reaching distance (10 inches) 

 — other attractive objects being kept away — shows two things: 

 (1) the very fine estimation visually of the distance represented 

 by the arm-length, thus emphasizing the element of muscular 

 sensation in the perception of distance generally; and (3) the 

 great uniformity at this age of the phenomenon of " sensori- 

 motor suggestion"' upon which this method of child study is 

 based. 



In regard to the relative use of the two hands in these and 

 other experiments, — this is a topic to which I wish to devote an- 

 other paper, giving details upon which certain conclusions (an- 

 nounced in an earlier note in this journal) are based." 



LETTERS TO- THE EDITOR. 



**# Correspondents are requested to be as brief as possible. The writer's name 

 is in all cases required as proof of good faith. 



On request in advance, one hundred copies of the number containing his 

 communication will be furnished free to any correspondent. 



The editor will be glad to publish any queries consonant with the character 

 of the journal. 



The Convex Profile of Bad-Land Divides. 



Under this caption Professor W. M. Davis, in Science, Oct. 28, 

 1893, discusses the "missing factor" in Gilbert's "Law of Di- 

 vides," and concludes that it is "the creeping of the surface 

 soil." 



In my class-room lectures, and in a paper forwarded four 

 months ago to the secretary of the Geological Society of America, 

 but not yet published, I also have attempted an explanation of 

 this missing factor. I mention this merely for the truth of his- 

 tory, not that I care much for the credit of priority, or fear the 

 charge of plagiarism when my explanation appears. Its indepen- 

 dent origin will be self-evident, because I have approached the 

 problem in a very different way. 



Both Professor Davis and Mr. Gilbert seem inclined to regard 

 bad-land forms as something apart from land-sculpture in general 

 — something which requires special explanation — while I have 

 cited general laws and deduced these forms from them. My 

 paper is entitled "Some Elements of Land-Sculpture: Water 

 Curves, Weather Curves, and Structural Angles." Water curves 

 are either horizontal, e.g., the serpentine course of a river, or 

 vertical. The vertical water curve of erosion is concave upwards, 

 e.g., the normal gradient of a stream excavating its channel in 

 homogeneous material (be. Fig. 8) ; and the vertical water curve 

 of deposition is convex upward, e.g., a debris fan, or alluvial 

 cone. 



All weather curves are convex upward. This fundamental law 

 of the weather curve I have deduced theoretically in two ways, 

 and that it is confirmed by observation almost goes without say- 

 ing. An angular structural block. A, Fig. 1, is rounded by 



^^^. 



Fig. 1. — A structural blocfe rounded by weathering. The dotted line Is the 

 weather curve, convex upward. 



weathering, that is, its outline becomes a flowing curve, convex 

 upward, like the dotted line in the figure, because the protruding 

 angles are more exposed to attack, and at the same time the pro- 

 ducts of disintegration are in a position to be quickly removed. 



' See my article on " Suggestion In Infancy," Science, xvU., 1891, p. 113 ; also 

 my " Handbook of Psychology," Vol. II., pp. 897 ff. 

 ' Science, xvi., 1890, p. 347, 



The complex forces included under the general term weathering 

 have a double advantage at a as compared with 6, because the 

 attack comes from two directions. Moreover, the removal of 

 loosened particles, whether by falling raindrops, by winds, or by 

 gravitation (one effect of which is creeping), proceeds many 

 times faster at a than at b. By a similar but slightly modified 

 process of reasoning, it may be shown that a sharp crest triangu- 

 lar in cross-section would be rounded also by weathering (c.f, La 

 Noe and Margarie, Les Formes du Terraines). 



Another method of deducing the upward convexity of weather 

 curves is that which is based upon the law of slopes in relation to 

 hardness. The harder the rock the steeper the slope, other things 

 being equal. Let 1, 3, 3, and 4 (Fig. 2) denote strata which grade 

 regularly downward in hardness. No. 1 being hardest of all. 

 Then, if the products of disintegration are at once and completely 



Fig. 3. — Convex slope formed by the weathering of rooks which regularly 

 increase in hardness downwards, 



removed, as, for instance, by a stream flowing at a, the hard 

 rock, No. 1, will form a cliff ab, while be will be^less steep, cd 

 still less steep, and de very gentle. Each elementjof the slope, 

 e.g., be, is a straight line in cross-section, but thejgeneral effect is 

 that of a curve ; and if the beds were very thin it would pass from 

 a broken line to a true flowing curve, convex upward. Now we 

 may conceive the series 1, 3, 3, 4 to have been originally homo- 

 geneous, and that weathering has softened the upper members. 

 In that case the downward gradation in hardness would be by in- 

 flnitessimal laminae, and the resultant slope a typical weather 

 curve. 



Ordinarily, the convexity does not extend to the bottom, be- 

 cause the weather curve is there replaced by the vertical water 

 curve of erosion. This combination of weather and water curves 

 modifying structural blocks yields the form shown in Fig. 3, the 



Fia. 3. — Cross-section of any ordinary ridge or hill. 



most typical, as it is also the most familiar and universal of earth- 

 forms. The upper part, ab, of each slope is a weather curve, 

 convex upward, and the lower part, bo, is a water curve, concave 

 upward. Bad-land divides are excellent examples of the gen- 

 eral law, instead of being exceptions to it. The convex profile of 

 the summit which puzzled Gilbert is simply the familiar and 

 omnipresent weather curve. The only thing exceptional about 

 it in the bad-lands is its narrowness and sharpness of curvature. 

 That depends'chiefly upon the early stage of the base-levelling in 

 those regions, as I have shown in my forthcoming paper. 



Creeping is a real factor in the rounding of divides, but is only 

 one phase of the secondary process of transportation. Disinte- 

 gration is the primary process. And in the subsequent movement 

 of loosened particles, falling raindrops, gusts of rain driven aslant 

 by winds, the winds themselves, the rolling and tumbling effects 

 of gravitation as distinguished fronj the slow process of creeping 

 — all these are active and efBcient agents of removal. Their 

 combined effects overshadow the results of creeping, especially 

 on the bare, sharp ridges of the bad-lands. The clays are com- 

 pact and firmly adherent. It is on gentle and turf-bound slopes 

 that the slow process of creeping is relatively most effective. 



Nor do I agree that the weather curve on the summit of bad- 

 land ridges would be obliterated if the rainfall should increase. 

 The effect of falling raindrops belongs to the category of weather- 

 ing, and produces convex curves. It is only when the fallen 

 drops gather into rills and begin to flow that the concave water 

 curve of erosion begins to form. Hence increased rainfall would 



