GRAVITY AND GRAVITY POTENTIAL. 23 



In this case it will, however, be inconvenient to measure the length of the curve 

 in meters ; but the m.t.s. value of g e>m will come out correctly also when the length 

 of the curve s is measured in kilometers and the difference of potential fa fa for 

 each 100 dynamic meters of height is taken for unity. The average value of the 

 component of the acceleration of gravity along a segment limited by two succes- 

 sive level curves on our map of the world will therefore be 



If the map represented the topography of a perfectly hard and smooth surface, 

 and if the curve 5 be the path of a particle forced to slide on it with any initial 

 velocity under the sole action of gravity, this formula would serve to find the 

 average acceleration of the particle in any part of its path. 



