262 EXPLORATION GEOPHYSICS 



and a commonly accepted value of a is 0.005294. On substituting these 

 values into Equation 20, one obtains 



g^ = 978.039 ( 1 + 0.005294 sin^ <^ - 0.000007 sin^ <f>) (21 ) * 



In general, it is not possible to make gravitational measurements on 

 the surface of the ellipsoid corresponding to sea level. If the height of 

 the point of observation above the level surface is h, the value of gravity 

 is obtained by adding a correction proportional to h to the observed value 

 of gravity. The factor by which h must be multiplied amounts to a varia- 

 tion of gravity of about seven one hundred millionth of the total value of 

 gravity for each foot of elevation. This correction for h may be the "free 

 air correction" or the Bouguer correction, as described. 



Stokes showed as early as 1849 that it was possible by gravitational 

 observations to determine not only the flattening of the terrestrial ellipsoid, 

 but also the deviation of the geoid from this assumed elHpsoid. When the 

 suggestion was first made, it seemed to be of speculative interest only 

 because it required that gravity be observed at intervals over the entire 

 globe including the sea. No practical method existed for observing the 

 value of gravity at sea at that time. An interesting method for carrying 

 out observations at sea was devised later by Hecker. In this method the 

 boiling point of water and the height of the mercury barometer are deter- 

 mined simultaneously. Because the atmospheric pressure governs both 

 the boiling point of water and the height of a column of liquid of given 

 density, the boiling point and fluid height data may be used to determine 

 the density of the mercury which is proportional to the value of gravity. 

 Recently, a much more accurate method has been developed by Vening 

 Meinesz. By an arrangement of three pendulums the effect of the motion 

 of the vessel is decreased. By using this apparatus in submarines sub- 

 merged deeply enough to avoid most of the surface motion, it has been 

 possible to make gravity determinations on the ocean floor.f 



If there were no irregularities on the surface of the earth, the water 

 would stand at a uniform depth over the whole earth. The plumb line 

 at all places would be normal to the spheroid and the value of gravity 

 would be the same for all points having the same latitude, and would in- 

 crease uniformly north and south of the equator. Actually, the surface 

 of the earth is not a regular mathematical surface but is quite irregular. 

 However, it is found that the surfaces of the oceans and the imaginary 

 sea levels continued under land areas approximate the surface of the 

 spheroid which would exist if there were no irregularities. For any large 

 area the plumb line will, on an average, be normal to the spheroid and the 

 va,lues of gravity after applying a correction for the elevation of the 

 station above sea level will be very nearly the same. 



* This formula is sometimes referred to as the Bowie Formula, Number 2. 



t F. A. Vening Meinesz, "Projet d'un nouvel appareil pendulaire," Bulletin Geodesique Nr. 

 5, 1925; "Theory and Practice of Pendulum Observations at Sea," Puhliet Netherl. Geod. Comm. 

 1929 



W. Heiskanen. Handbuch der Geophysik (Gutenberg) Vol. I, p. 765-780. 



