HILLS AND DALES. 235 



sea. At that point it will touch the surface of the earth; and if it continues 

 to ascend, a contour-line will be formed surrounding this bottom (or Immit, as 

 it is called by Professor Cayley) and enclosing a region of depression. As the 

 level surface continues to ascend, it will reach the next deepest bottom of the 

 sea; and as it ascends it will form another contour-line, surrounding this point, 

 and enclosing another region of depression below the level surface. As the level 

 surface rises these regions of depression will continually expand, and new ones 

 will be formed corresponding to the different lowest points of the earth's 

 surface. 



At first there is but one region of depression, the whole of the rest of 

 the earth's surface forming a region of elevation surrounding it. The number 

 of regions of elevation and depression can be altered in two ways. 



1st. Two regions of depression may expand till they meet and so run 

 into one. If a contour-line be drawn through the point where they meet, it 

 forms a closed curve having a double point at this place. This contour-line 

 encloses two regions of depression. We shall call the point where these two 

 regions meet a Bar. 



It may happen that more than two regions run into each other at once. 

 Such cases are singular, and we shall reserve them for separate consideration. 



2ndly. A region of depression may thrust out arms, which may meet each 

 other and thus cut off a region of elevation in the midst of the region of 

 depression, which thus becomes a cyclic region, while a new region of elevation 

 is introduced. The contour-line through the point of meeting cuts off two 

 regions of elevation from one region of depression, and the point itself is called 

 a Pass. There may be in singular cases passes between more than two regions 

 of elevation. 



3rdly. As the level surface rises, the regions of elevation contract and at 

 last are reduced to points. These points are called Summits or Tops. 



Relation between the Number of Summits and Passes. 



At first the whole earth is a region of elevation. For every new region 

 of elevation there is a Pass, and for every region of elevation reduced to a 

 point there is a Summit. And at last the whole surface of the earth is a 



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