STRUCTURAL CURVES AND THEIR PRODUCTION. 1 37 



still water above them are in flat contradiction to the law of increasing 

 gradient upstream and skyward concavity. Time enough being given, 

 the obstruction would no doubt he cut through and the ideal curve 

 established. All streams tend toward its realization as an ultimate goal. 

 Cataracts are temporary departures from the rule, and quite evanescent 

 when compared with the whole life history of a river. 



Combined weather Curve and water Curve. — Another departure from the 

 type is more permanent and universal, so frequent and lasting, indeed, 

 that it almost deserves to he formulated as a distinct and opposite law. 

 it is the fact that while the gradient increases upstream to a certain 

 point and the curve is concave upward, as the definition requires, above 

 that point the gradient diminishes, and the curve is convex upward, as 

 at a />, figure 3. This is usually true of streams rising in extensive 

 swamps and wet meadows. Even the mountain streams often flow 

 sluggishly at first upon broad Hat summits, then pitch headlong over the 

 escarpment. We have seen above that breadth and flatness are the domi- 

 nant elements of structure. The precipitous edges of broad continental 



Figure 3.— Combined weather Curve (a b) and water Curve (b c). 



blocks being rounded off impose their own curves upon the rivers. Thus 

 the convex portion (a 1>, figure 3) is not really a water curve, it is a 

 temporary accommodation of a water gradient to the structural form 

 upon which it flows. The true water curve (b c, figure 3) will moreover 

 gradually encroach upon the upper convex curve a b, and, if the base- * 

 leveling be continued long enough, it will establish itself as a smooth 

 concave curve from c to a. Hence this exception, as in the case of cata- 

 racts, is an incident only of river history, the only differences being that 

 it is more common and less transient; but, as 1 said above, it almost 

 deserves to take rank as a distinct and coordinate law on account of its 

 universality. The convex portion of the curve (a />, figure 3) is not, 

 however, a new kind of curve, but one that has already been defined, 

 viz, the weather curve. The double reversed curve (a /> c, figure 3) is the 

 combination of the weather curve and the water curve of erosion. It is 

 Hogarth's line of beauty, the most universal of earth forms. Almost 

 every hill slope in a rolling country presents an upper convex portion 



