422 Mr. J. C. Maxwell on Hills and Dales. 



place, and defining every other level surface by the work required 

 to raise unit of mass from the standard station to that level 

 surface. This work must, of course, be expressed in absolute 

 measure, not in local foot-pounds. 



At every step, therefore, in ascertaining the difference of level 

 of two places, the surveyor should ascertain the force of gravity, 

 and multiply the linear difference of level observed by the nu- 

 merical value of the force of gravity. 



The height of a place, according to this system, will be defined 

 by a number which represents, not a lineal quantity, but the 

 half square of the velocity which an unresisted body would 

 acquire in sliding along any path from that place to the standard 

 station. This is the only definition of the height of a place con- 

 sistent with the condition that places of equal height should be 

 on the same level. If by any means we can ascertain the mean 

 value of gravity along the line of force drawn from the place to 

 the standard level surface, then, if we divide the number already 

 found by this mean value, we shall obtain the length of this line 

 of force, which may be called the linear height of the place. 



On the Forms of Contour-lines. 



Let us begin with a level surface entirely within the solid part 

 of the earth, and let us suppose it to ascend till it reaches the 

 bottom of the deepest sea. At that point it will touch the sur- 

 face 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 deep- 

 est bottom of the sea ; and as it ascends it will form another con- 

 tour-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 surround- 

 ing 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 depres- 

 sion. 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. 



