Chap. 7] 



GRAVITATIONAL METHODS 



211 



magnetic meridian, a correction would, of course, be necessary. However, 

 this can be avoided by allowing for the declination, and setting it in the 

 direction of the astronomic meridian. 



For calculating the planetary effect on curvature values, formula (7-48i) 

 may be used, which relates the curvature U^ to the two principal radii of 

 curvature of the equipotential surface. The normal surface is assumed to 

 be that of a two-axial elHpsoid of rotation, in which case the planes con- 



dC 60* 40' 20' 20* 40* 60* dtr 



Latitude 



Fig. 7-73a. Planetary variation of gravity, gradients, and curvature values. 



taining the principal radii of curvature are in the astronomic meridian 

 and the prime vertical, so that X = 0. Hence {U ^)noTm. = —g{— ], 



\Py Px/ 



where Px and p„ are the principal radii of curvature. For the meridian 

 ellipse the radius of curvature^' in the latitude (p, is given by 



2 2 



a c 



Px = 



■y/{a^ cos^ <p + c^ sin'* <py 



" K. Jung, Handb. Exper. Phys., 26(3), 150 (1930). 



