H0 HILLS AND DALES. 



On Hills and Dales. 



Hence each point of the earth's surface has a line of slope, which begins 

 at a certain summit and ends in a certain bottom. Districts whose lines of 

 slope run to the same bottom are called Basins or Dales. Those whose lines 

 of slope come from the same summit may be called, for want of a better name, 



Hills. 



Hence the whole earth may be naturally divided into Basins or Dales, and 

 also, by an independent division, into hills, each point of the surface belonging 

 to a certain dale and also to a certain hill. 



On Watersheds and Watercourses. 



Dales are divided from each other by Watersheds, and Hills by Watercourses. 



To draw these lines, begin at a pass or a bar. Here the ground is level, 

 so that we cannot begin to draw a line of slope ; but if we draw a very small 

 closed curve round this point, it will have highest and lowest points, the 

 number of maxima being equal to the number of minima, and each one more 

 than the index number of the pass or bar. From each maximum point draw 

 a line of slope upwards till it reaches a summit. This will be a line of Water- 

 shed. From each minimum point draw a line of slope downwards till it reaches 

 a bottom. This will be a line of Watercourse. Lines of Watershed are the 

 only lines of slope which do not reach a bottom, and lines of Watercourse 

 are the only lines of slope which do not reach a summit. All other lines of 

 slope diverge from some summit and converge to some bottom, remaining 

 throughout their course in the district belonging to that summit and that 

 bottom, which is bounded by two watersheds and two watercourses. 



In the pure theory of surfaces there is no method of determining a line 

 of watershed or of watercourse, except by first finding a pass or a bar and 

 drawing the line of slope from that point. In nature, water actually trickles 

 down the lines of slope, which generally converge towards the mathematical 

 watercourses, though they do not actually join them ; but when the streams 

 increase in quantity, they join and excavate courses for themselves ; and these 

 actually run into the main watercourse which bounds the district, and so cut 

 out a river-bed, which, whether full or empty, forms a visible mark on the 





