166 



GRAVITATIONAL METHODS 



[Chap. 7 



at ebb tide, a rise in water level of 6.5 feet causes a change in gradient of the 

 order of 90 Eotvos units f^ however, this effect decUnes rapidly away from 

 the edge and is only 1 Eotvos unit at a distance of 100 feet. The variation 

 in the curvature values above the edge is 0. The maximum is observed 

 about 10 feet from the edge; thence, the effect declines slowly and reaches 

 1 Eotvos unit about 1000 feet from the edge. These values may be cal- 

 culated by applying the formula for the two-dimensional effect of a vertical 

 step given on page 264. If the coast is sloping, the tide effects must be 

 calculated by using the formula for an inverted sloping edge. The gra- 

 dients and curvature effects are less in this case. The gravity anomalies 

 directly above the edge follow from formula (7-42e). It is seen that, for 

 the same conditions assumed in the calculation of the torsion balance 





Fig. 7-54. Gravity gradients and curvature anomalies produced when the water 

 level in a lock is raised by 8.2 feet (after Schleusener). 



anomalies, the gravity anomaly at the edge is 0.05 milligal, which is within 

 the limits of accuracy of present gravimeters. 



Fig. 7-54 shows the gravity gradients, as well as the curvature values, 

 for a water rise of about eight feet in a lock, all determined by a 

 torsion balance, the distance of which from the edge ranged from 1 to 20 m. 

 At 1 m distance the gradient reaches a maximum of about 100 E.U. At 

 3 m distance a maximum in the curvature occurs with 47 E.U., and at 

 20 m distance the gradient is 1 E.U. and the curvature 7 E.U. De- 

 flections ,of the vertical may be calculated from an integration of the curva- 

 ture variation; near the edge the deviation is 1.2- 10~ arc-sec. De- 

 observed values for all quantities were in good agreement with values 

 calculated from the theory. 



«' Eotvos unit = E.U. = 110-» Gal-cm-». 



