to the center of a 5x5° square (even at the farthest north latitudes) . 



Table 1 gives the value of n versus the angular distance iJj necessary to keep 

 the error in calculating s (ip) , below 1% for both 1x1° and 5x5° squares. 



Table 1 



5x5° squares 



1x1° squares 



i|'>2.0 

 2.0>ijj>l.l 

 l.l»li>0.7 

 0.7>i(;>0.5 



n = 1 



n = 2 



n = 4 



n = 5 



Economy in computing time was obtained by combining twenty five 1x1° squares 

 into a single 5x5° square when the angular distance of the point of computation 

 from the center of the 5x5° square was greater than 15°. 

 10x10' Difference Geoid 



In the Caribbean the gravity anomalies and the gravity gradients are so large 

 that we suspected that even gravity anomalies of wavelength less than 200 km (the 

 shortest wavelengths represented in the 1x1° maps) might make significant contributions 

 to the geoid heights. In the Eastern Caribbean we used the values of gravity inter- 

 polated at the centers of a 10x10' grid to determine geoidal undulations with wave- 

 lengths as short as nearly 40 km. The 1x1° averaged gravity values were subtracted 

 from the 10x10' grid values and were used in a Stokes integration to obtain a 

 "10x10' difference" geoid (Fig. 13) . This geoid for the Eastern Caribbean represents 

 the extra short wavelength information present in the 10x10' gravity values. The 

 reference surface is the "1x1°" geoid of Figure 10. 



We consider this "10x10' difference" geoid computation a very preliminary one. 

 Having determined that the geoidal undulations corresponding to 10x10' gravity 

 differences are significant, we intend to make a more precise determination of this 

 geoid in the future. 



23-22 



