SECT. 3] APPLICATIONS OF THE GYKOPENDULUM 337 



B. Figure of the Earth 



The Gyro Erected Optical Navigation system (or Geon as the navigational 

 device has been called) provides fixes of position which are indistinguishable in 

 principle from those obtained by sextant, transit, zenith tube or other standard 

 astronomical methods making reference to the local direction of gravity. 

 Owing to deflections of the vertical, it is to be expected that the course of given 

 meridians and latitude circles over the face of the earth must be somewhat 

 irregular as well as being arranged on an ellipsoidal format. On the other hand, 

 the proposed system of satellite navigation {Transit) will tend to take 

 reference to the geocenter as the altitude of the satellites is increased and, 

 therefore, to describe geographic position in terms of a system of meridians 

 and latitude circles which have more regular geometrical configurations. 

 Transit navigation, as now proposed, promises to provide geocentric 

 position to an accuracy of about 0.1 nautical mile; or 6 seconds of arc. If 

 Geon can be made to match this precision it would be possible from a compari- 

 son of Geon and Transit positions to measure directly the more conspicuous 

 configurations of the geoid. For example, the rotational flattening of the earth 

 produces a discrepancy of 11 minutes of arc (0.3 xl0~ 2 rad) between the 

 direction of the geocenter and gravity at latitude 45°. Deflections of the vertical 

 associated with higher order harmonics of the earth's figure and local effects of 

 inhomogeneities in the crustal composition in the order of 10 -4 rad could be 

 sensed and measured at sea if these two systems were made equally precise. 



C. Regional Slopes of the Sea Surface 



Because of rotation, the earth's figure is nearly ellipsoidal and the field of 

 plumb-line verticals is roughly described in terms of the resultants of the 

 centrifugal force of rotation and geocentric gravitation at each point on the 

 earth. While this yields an approximation of the field of gravity verticals, it is 

 distinguished from it by its high degree of physical idealization. 



There are local anomalies in the density distribution within the substance of 

 the earth which cause the true field of verticals to depart from ellipsoidal sym- 

 metry. Gravity verticals tend to converge toward local excesses of mass and to 

 diverge in the vicinity of local mass deficiences. Were the solid earth to be 

 entirely covered by motionless water of uniform density the surface would be 

 horizontal (at right angles to local gravity), have uniform geopotential and 

 represent the actual figure of the earth — the geoid. 



For oceanographic considerations we would wish to measure the regional 

 departures of the sea surface from horizontal. Such departures presumably 

 arise from organized motion within the fluid produced by wind stress or 

 horizontal gradients of water density. 



Fluid dynamical reasoning suggests that the regional slopes of the sea 

 surface associated with either the baroclinic or barotropic modes of geostrophic 

 motion become important when they reach the order of 10 -6 rad or about 0.2 

 second of arc. Only the strongest surface currents, such as the Gulf Stream or 



12— s. ii 



