Chap. 7] GRAVITATIONAL METHODS 163 



elevation (epirogenic movements). They are of practical importance in 

 determining corrections for (torsion balance) coast stations, in ground 

 subsidence problems, and in the investigation of subsurface mass dis- 

 placements leading to earthquakes and volcanic eruptions. The following 

 discussion deals not only with variations of gravity itself but also with re- 

 lated variations of torsion balance quantities and the deflection of the 

 vertical. 



A. Planetary (Lunar) Variations 



Planetary variations of the gravitational field and the well-known 

 "oceanic" and "bodily" tides are related phenomena. Tidal forces are 

 due to the fact that the attractions of sun and moon at the earth's surface 

 deviate in direction and intensity from those attractions effective at the 

 earth's center. They would be present even if the earth did not rotate, 

 would be approximately 

 constant for any given 

 surface point, and would 

 have but semimonthly 

 or semiannual periods. 

 The earth's rotation pro- 

 duces a migration of a 

 double tidal bulge with 

 a period of one-half lunar 

 day, the maximum am- Fig. 7-53. Tidal forces. 



plitudes occurring if the 



tide-generating body is in the zenith or nadir. Superposition of the 

 semidiurnal, semimonthly, or semiannual periods brings about ex- 

 cessive or abnormally reduced tidal amplitudes, the more important of 

 these being known as "spring" and "neap" tide. 



The variations in intensity and direction of gravity which can be calcu- 

 lated from the distance and mass of the sun and the moon are modified by 

 the change of distance of a surface point from the earth's center, brought 

 about by the bodily tide. The observed variations in the direction of the 

 vertical (recorded with horizontal pendulums) are about f to | the theoreti- 

 cal values; the observed variations in gravity are about 1.2 times greater 

 than the theoretical variations. 



In Fig. 7-53, let M be a heavenly body (sun or moon) at a distance r 

 from the earth's center, C, and at a distance e from a point P at the earth's 

 surface in the latitude <p. The angle between r and e is the parallax of 

 the star, or x- If the star is in the zenith, the attraction on P is — {kM/e ) 

 (negative in respect to gravity), and at C it is — (kM/r^). To deduct the 

 latter from the former, it is convenient to resolve either force into its ver- 



