Chap. 7] 



GRAVITATIONAL METHODS 



219 



= [5.77 ^U 



+[0.00379 ^(hi + h) + 0.0061 ^(h + hy) 

 + 0.0221 ^{ki + /i4 + Ae + A8)+0.0160i(/i2 -{-h -h-h) 

 + 0.13046(/ii - h) + 0.09225(/i2 -{- h - ht - h) + Ql, 

 +[0.01173(/ii - h) + 0.00831(/i2 + ;i8 - ^4 - hi)l, 

 +[0.00108(^1 - As) + 0.00077 (/i2 + As - /14 - A«)]p, 

 +[0.00028(/ii - h) + 0.00020(/i2 + Ag - /14 - h)l, 



Uy, = [5.77 i]pi 



+[0.0379 lih + A7) + 0.0061 L{hi + A5) ' 



+ 0.0221 I (/i2 + /14 + Ae + h) + 0.0160 ^(^2 + h - ht 



- h) + 0.13046(/i3 - A7) + 0.09225 (As + h - h - As) 



+ e]p. ^ (7-74) 



+[0.01173(A3 - A7) + 0.00831 (A2 + A4 - Ae - A8)]p, 



+[0.00108(A3 - A7) + 0.00077(A2 + A4 - Ae - A8)]p, 



+[0.00028(A3 - At) + 0.00020(A2 + A4 - Ae - ha)],, 



-Ua = [0.4826(Ai - A3 + As - At)]^, 



+ [0.08194 (Ai - A3 + Ae - A7)]p, 

 +[0.03181(Ai - A3 + Ae - A7)]p, 

 +[0.03077(Ai - A3 + Ae - A7)]pj 



2U,y = [0.4826 (A2 - A4 + Ae - A8)]p2 



+[0.08194(A2 - A4 + Ae - A8)]p, 

 +[0.03181 (A2 - A4 + Ae - A8)]p, 

 + [0.03077 (A2 - A4 + Ae - hti)l, 



These formulas have been simplified yet extended to more unfavorable 

 terrain by Schweydar.^ He eliminated the separate calculation of the 

 innermost ring and developed two methods for calculating gradients 

 for: (1) gentle terrain and elevations not exceeding the height above 

 ground of the center of gravity of the instrument; (2) any topography. 

 The first method follows Eotvos' procedure and considers only the first 



" W. Schweydar, Zeit. Geophys., 1(1), 81-89 (1924); 4(1), 17-23 (1927). 



