ENERGY 107 



zero potential. Since the potential energy of a drop 

 of water depends upon where it is, that is, upon the 

 point which we are considering, we are justified in 

 speaking of the gravitational potential of any point 

 as meaning the available potential energy of a drop of 

 water placed at that point. All the points about the 

 earth where such a drop of water would have the same 

 potential energy form an equipotential surface. For 

 example, if we consider a point a foot above sea level 

 it will have a certain potential, but every other point 

 which is one foot above sea level will have the same 

 potential. Through these we may think of a surface 

 as existing, not a real surface like that of the sea itself, 

 but an abstract one like those which are considered in 

 geometry. Similarly, other equipotential surfaces may 

 be imagined. 



This idea of potential is of peculiar value in the 

 study of electricity, but we are limiting our present 

 discussion to gravitational potential. Although this 

 terminology is largely used only in such study, equi- 

 potential surfaces are frequently dealt with. The 

 surveyor, locating a railroad route, endeavors as far 

 as possible to find it on an equipotential surface. He 

 does not call it that, for he usually says he wishes to 

 obtain a level line or else a line of low grades. In 

 passing from a point of lower to one of higher poten- 

 tial, that is, from one nearer to the center of the earth 

 to one farther therefrom, work must be done in moving 

 a body ; and as far as possible the engineer wishes the 

 only work to be that required to overcome the friction 

 of the moving train. Of course, if his road was going 

 to carry freight only one way, he would seek for a 



