296 EXPLORATION GEOPHYSICS 



The difference of potential 



AU=U„ -Up = -W = Gm(- --) (31) 



a positive quantity. 



It is thus apparent that Pz (at radius rz) is at a higher potential than 

 Pi (at radius ri). If the opposite were true, a particle in going from a 

 higher to a lower potential would move away from the earth rather than 

 toward it. 



If now, point P2 is considered as removed to infinity and Up =0, then 



2 



U = -G— (32) 



1 ^1 



It is thus possible to define the gravitational potential at a point Pi as 



1 

 00 



Fdr (33) 



or, in words, the potential at Pj is the negative of the work done by the 

 field in moving a particle from infinity to the point Pi. 



Equipotential surfaces can be drawn about the spherical mass m (Fig- 

 ure 158). They are obviously spheres (the loci of all points a distance 

 r from m). Likewise the equipotential surfaces arising from cylindrical 

 masses are cylindrical in shape and coaxial with the cylindrical mass. 



Equipotential surfaces can converge, but they do not touch each other, 

 as such contact would represent one point having two different values of 

 potential, which is not possible. Such surfaces follow the contours of 

 heavy (dense) masses or configurations in smooth, gently-curved shapes. 



Equipotential surfaces in the earth's gravitational field, as the term 

 implies, are surfaces having at every point thereon the same value of 

 gravity potential. They are also called level or niveau surfaces. Equipo- 

 tential surfaces are not planes of equal gravity force, as they relate to a 

 function of m/r, while gravity force is a function of m/r^. The surface 

 of a lake or other still body of water is an equipotential surface. Such 

 surfaces are everywhere perpendicular to the direction of the force of 

 gravity. 



The equation for a level surface may be written as : -7- = where s 



is a direction in the surface; or the equation may be written as C/ = a 

 constant. 



It also follows from the above that equipotential surfaces are arched over anti- 

 clines, since they are at all points perpendicular to the direction of the force of gravity. 

 No work is involved in moving a unit mass from one point to another in an equipoten- 

 tial surface. 



