GRAVITATIONAL METHODS 259 



two points on it. (A level surface is not necessarily a horizontal surface.) 

 Because the potential is constant on a level or equipotential surface it is 

 impossible for equipotential surfaces corresponding to different values of 

 potential to intersect, for the two surfaces would have the same values 

 of the potential at the points of intersection and hence the same values at 

 all other points on the surfaces. 



A level or equipotential surface has the following very important 

 property: The force of gravity is perpendicular to the surface at every 

 point.** Hence, if a line is drawn at a point (or points) which is normal 

 to the equipotential surface through the point (or points) selected, the 

 direction of the force of gravity will be along this line, as shown in Figure 

 153. Such a line is called a vertical line. Ordinarily, over distances which 

 are not too large, the vertical lines will be practically straight. 



Gravitational Prospecting and the Science of Geodesy. — The 



science of geodesy deals with measurements of large areas of the earth's 

 surface by triangulation and astronomical observations. One department 

 of geodesy comprises the study of the figure of the earth. This branch 

 investigates deviations from homogeneity of segments of the earth's 

 crust which have a large areal extent and thickness.t The main problem 

 in gravitational prospecting, on the other hand, concerns the deviation 

 from homogeneity of relatively small portions of the near-surface crust 

 of the earth. However, the methods of geodesy are instructive because 

 similar principles of measurement are applied. 



In geodetic terminology, the term sea level applies to the equipotential 

 surface that most nearly coincides with the average level of the ocean. 

 This surface is called the geoid. The determination of the shape of the 

 geoid involves a combination of surveying, astronomy, and gravitational 

 methods. 



Geodetic latitude and longitude determinations at a point involve a 

 determination of the direction of the plumb line at that point. The direc- 

 tion of the plumb line may be greatly affected by the presence of large 

 bodies of abnormal density near the point of measurement. If the body 

 is denser than the surrounding material, it will exert an unduly large force 

 of attraction on the plumb bob and cause the plumb line to deflect toward 

 it. Differences in latitude or longitude due to this effect are usually only 

 a few seconds of arc. Although these differences generally do not exceed 

 ten seconds, except in mountainous areas, they are occasionally quite 

 large. For example, between the north and south coasts of Puerto Rico 

 the anomalous deflection of the plumb line produced by local inhomo- 

 geneities if not taken into account would lead to an error in distance of 

 about 1 part in 50. This example is sufiicient to show that the effects of 



_**The mean surface of a body of water such as an ocean is a portion of a gravi- 

 tational equipotential surface. 



t National Research Council, Physics of the Earth II ; The Figure of the Earth, Washington, 



