330 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 31 



formed by the surfaces of the waters of the ocean and of the waters 

 of sea-level canals (extended, in imagination, through the continents) 

 deviates from a true mathematical figure. This deviation is un- 

 doubtedly a maximum under the great mountain systems like the 

 Himalayas and the Alps, where the geoid, or water surface, is above 

 the mathematical one. Conversely, over the deepest parts of the 

 ocean the geoid, or water surface, is probably depressed to the maxi- 

 mum amount below this spheroid. In any event, there is an angle 

 between the water surface and the mathematical surface at any 

 point at which astronomical observations may be made. This angle 

 means a deviation of the direction of gravity, or the plumb line, and 

 affects the observations for astronomical latitudes and longitudes 

 accordingly. 



EFFECT OF TOPOGRAPHY ON GEODETIC DATA 



Geodesists had noticed this condition in a number of parts of the 

 earth where surveying and mapping operations had been under- 

 taken, and efforts were made to apply a correction for the influence 

 of the irregularities of the surface. It was evident to each investi- 

 gator that a mountain system, such as the Himalayas, would have 

 an attractive effect on the plumb line at stations within a reasonable 

 distance of it. Efforts were made to compute the effect of these 

 great masses which lie above sea level, but when such corrections 

 were applied it was found that they were larger than were necessary 

 to bring the theoretical and observed values into accord. The moun- 

 tains, apparently, were lighter than normal, but impossibly small 

 densities would have to be assumed for the materials composing the 

 mountains to bring the two values into exact agreement. 



Pratt and Airy, working on geodetic data about the middle of the 

 last century, arrived at the conclusion that the reason why moun- 

 tains and continents stand above sea level is because lighter materi- 

 als lie below them. While they did not, so far as I am aware, make 

 any definite statement that the abnormal densities could only extend 

 to a moderate depth, yet this idea was implied in their statements 

 regarding the deficiencies in densities that must lie below mountains 

 and continents. They advanced their ideas about 75 years ago, but 

 it is only within the last 10 years that their ideas and those of But- 

 ton, expressed 41 j'^ears ago, have been accepted generally by stu- 

 dents of the earth as a working principle in earth studies. 



VARIATIONS OF GRAVITY 



Geodesists have used geodetic data in the form of triangulation, 

 of astronomical determinations of longitude and latitude, and of 



