is that the actual numerical integration which is the most laborious part of the 

 procedure is done only for the limited area of the western North Atlantic. It also 

 has the advantage that the "1x1° difference" geoid clearly indicates the extra 

 information not available from the spherical harmonics coefficients of degree and 

 order 16. 



In using averaged surface free-air anomalies in the inner area and those 

 obtained from the spherical harmonic coefficients for the outer area, one must 

 be particularly careful on two accounts. One, that the same reference ellipsoid 

 must be used in both cases. We have used the International Ellipsoid (with 

 flattening 1/297.0). Secondly, the areal average of the anomalies shown in 

 Figure 6 must not be different from the areal average of "G and L" gravity. We have 

 compared these averages and find there is a slight difference (of about 1 mgal) in 

 the two areal averages. The systematic error in geoid height corresponding to this 

 difference is negligible and is not considered further. Errors due to uncertainties 

 in the exact dimensions of the reference ellipsoid are inconsequential for this study. 



In order to convert the gravity or geoidal height data referred to the 

 International Ellipsoid and refer it instead to ellipsoids of flattening 1/298.25 

 (best fitting) and hydrostatic (1/299.7) the curves in Figure 11 can be utilized. 

 Details of Stokes Integration 



As discussed above, the Stokes Integration was carried out over the western 

 North Atlantic using the 1x1° and 5x5° free-air gravity average values shown in 

 Figure 6. 



The geoidal height N at any point is given by Stokes Formula: 



, s 

 N = — i — / S(ip)6g ds where 



4Trgr „ 



g and r are the mean values of gravity and earth radius over the geoid, ii is the 



23-18 



