Abstract

The implication of the author's hypothesis, that the conventional free-air correction factor is difficult to justify and can lead to large errors (e.g., 14 mGal from 300 m of topographic relief), would be very serious indeed for many interpretations of gravity data if it were true. He predicts a normal vertical gradient of 0.264 mGal/m near sea level, 14 percent lower than the conventional theoretical value. However, precise measurements of the free-air gradient near sea level have been reported (Kuo et al., 1969) which differ by less than 1½ percent from the theoretical value; moreover these differences correlate with small local (isostatic) anomalies. My own observations at Leicester, England (elevation 100 m) and Nairobi (elevation 1 650 m) (made with students) also differ by less than 1½ percent from the theoretical values and again the differences correlate with small local anomalies. If these values represent the normal free-air gradient, it would appear that the author's analysis must be wrong. The formula he derives gives, correctly, the mean vertical gradient at some level over and within the Earth to a good approximation. This can be seen simply by considering the well-known formulas for the gradient at a point within the Earth where the density is ρ  
gr2gR+4πγρ
and at a point outside the Earth  
qr2qR
and taking averages at this radius. However, the average value has no practical significance. It does not apply to any point on the Earth's surface; it is merely a mean.
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