angular distance from the point of computation of an element of area ds with 

 gravity anomaly &g, and Stokes function S(i|;) is given by 



where 



Sdi;) = -J- F((p) 

 sin4) 



F(ijj) = cos i^i + i sinijj [1-5 costjj - 6 sin ilj) 

 - 3 costj; ln(sin i^ + sin* i^) ] 



In order to reduce computing time, the value of F {^) was tabulated in the 

 following way (where ii is in degrees): For .1<i|j<1 it was tabulated at every hundredth 

 of a degree; for 1<4'<5 it was tabulated at every tenth of a degree and for i)>5 

 tabulated at every degree. The value of F((|)) at any ip was then obtained by 

 interpolation between tabulated values. For i|)<.l the constant value of 1.007. 

 for FCP) was used. 



In carrying out the Stokes integration the elements of area were the 1x1° 

 or 5x5° squares. In either case, since S (.\li) changes rapidly near the origin, the 

 effect of a square cannot be obtained for a point of computation very close to 

 the square simply by using the value of SCP) corresponding to ^ the distance from 

 the point of computation to the center of the square. The percentage error in 

 such a procedure is plotted as a function of ii in Figure 12. The square must be 

 subdivided into n smaller squares, the value of S(il)) being obtained for each of 

 the smaller squares and then averaged for the entire square. In this study we have 

 in all cases calculated geoid heights at corners of squares. Thus the minimum 

 distance from a point of computation is 0.5° to the center of a 1x1° square and 2.5° 



23-20 



