Chap. 7] GRAVITATIONAL METHODS 167 



D. Artificial Mass Displacements (Mining Operations) and the Like 



There can be no doubt that mass displacements, brought about by the 

 removal of commercial minerals (salt, coal, sulfur, ore), and rock formation 

 underground, and by filling of subsurface cavities produce variations of 

 gravity anomalies with time. Actual measurements of such variations are 

 apparently lacking. The only information now available are some calcula- 

 tions concerning the maximum deflection of equipotential surfaces of 

 gravity to be expected in such cases. For a coal seam 66 ft. in thickness, 

 occupying a square 7.1 km wide, A. Schleusener^" has calculated that the 

 maximum deformation would amount to only 3.4 mm. In the Ruhr 

 district where 4 billion tons of coal have been removed in an area of 1000 to 

 1500 square km., a drop of 3 mm of the niveau surfaces was calculated, 

 assuming the average seam thickness to be 3 m. It should be observed 

 that in these calculations the effect of refilling emptied pillars has not been 

 considered. For a lignite open-pit mine of 50 m depth and 500 ra breadth 

 (200 m length), the maximum drop would be 2 mm and the maximum 

 deflection of the vertical at the edge would be 0.77 -10" arc-sec, corre- 

 sponding to a maximum curvature anomaly of about 140 E.U. at that point. 



VII. DETERMINATION OF THE DEFLECTIONS OF THE 



VERTICAL 



Deflections of the vertical, or "plumb-line deviations," are as the name 

 indicates departures of the direction of gravity from some reference direc- 

 tion. As there is no absolute way of establishing a constant reference 

 direction all over the earth, the direction of gravity is referred to an arbi- 

 trarily adapted standard. It is easier to visualize the attitude of these two 

 directions by considering the surfaces to which they are perpendicular. 

 The first is a niveau surface of gravity (a surface in which no gravity 

 components exist), called a "geoid." This has no regular geometric shape 

 and is affected by all visible and invisible irregularities in mass distribution. 

 The second is an ellipsoid of revolution, also known as reference ellipsoid, 

 since all accurate geodetic surveys are referred to it. The deviations in 

 the direction of the perpendiculars to these planes are, therefore, the 

 deflections of the vertical, that is, the deviation in the direction of actual 

 gravity from that of normal gravity. The meridional deflection of the 

 vertical is equal to the ratio of the horizontal gravity component in the 

 meridian to gravity. It is frequently convenient to refer the deflection 

 of the vertical to a point (P in Fig. 7-55) in which the directions of the 

 normal and actual gravity are assumed to be identical. The magnitude 



" Schleusener, Beitr. angew, Geophys., loc. cit, 



