168 



GRAVITATIONAL METHODS 



[Chap. 7 



of the gravity vectors is not defined by the direction of the niveau surface 

 alone, but by the number of niveau surfaces per unit distance in the direc- 

 tion of gravity. 



There are altogether four methods of determining deflections of the 

 vertical. The first consists of a comparison of astronomic and geodetic 

 measurements to establish a difference in the direction of the geoid and 

 reference ellipsoid. The second measures the time variations of the 

 direction of the vertical with horizontal pendulums. The third is based 

 on field measurements of the horizontal component of gravity and is at 

 present of theoretical significance only. The fourth is an indirect determi- 



vio" 



VI 



irtacii 



*''"•;»» 



Undisturbtd 

 nivtau surfaces 



Btf. Ellipsoid 



ce - 9,-9' ^^s 



Aag- mfridtonal 

 defLoffht 

 vertical 



Fig. 7-55. Relations between deflection of vertical, geoid, reference ellipsoid, and 



gravitj' components. 



nation by integration from curvature values measured with the torsion 

 balance. Only the first and last methods are discussed in this section. 

 In the astronomic or star observations, instruments used for the deter- 

 mination of longitude and latitude are set with their axes of revolution 

 vertical, by means of accurate spirit levels which adjust themselves into a 

 niveau surface of gravity. Therefore, astronomic observations give co- 

 ordinates of a station on the geoid. If these coordinates, on the other 

 hand, are determined by geodetic triangulation, the calculation of arcs, 

 distances, and angles is based on the geometric figure of the reference 

 ellipsoid. The difference of astronomic and geodetic latitude, therefore, 

 gives the deflection in the meridian. From differences in astronomic and 

 geodetic longitudes, deflections in the prime vertical may be obtained. 



