THE GEODETIC EVIDENCE OF ISOSTASV 27 



for geographical purposes did not relieve us of the duty of trying to 

 explain the discrepancies between it and the existing geoid. 



The discussion of the arcs hitherto published proceeded along the 

 conventional lines of treating these anomalies, that is, the deflection 

 of the vertical as though they were accidental errors of observation, 

 though it was well understood that such is not the case. When, 

 however, the arcs were all connected it became possible to treat the 

 triangulations in a much more general way and to have regard to the 

 surface within the area covered by them, which would most nearly 

 represent the geoid. To this very difficult task Mr. Hayford addressed 

 himself. He first devised methods of computation which brought the 

 investigation within reach of the limited force of computers at his 

 disposal. What he will tell you to-night in brief, will be submitted 

 in more detail to the International Geodetic Association as a contribu- 

 tion from this country to a problem which all are trying to solve. 



The results will, I believe, make evident to you the great power of 

 geometry, using the word in its etymological sense, to disclose facts 

 which are of the greatest importance to geology and geophysics. 



The Paper. 

 By John F. Hayford, C.E. 1 



My intention is to present to you a general view of an investi- 

 gation which is still in progress, to state some of the principal 

 conclusions reached, and to indicate very briefly some of the 

 relations of these conclusions to conclusions reached by others 

 along very different lines of investigation. 



At the outset it is necessary to have a clear conception of the 

 condition called isostasy. 



If the earth were composed of homogeneous material, its 

 figure of equilibrium, under the influence of gravity, and of its 

 own rotation, would be an ellipsoid of revolution. The earth is 

 composed of heterogeneous material which varies considerably 

 in density. If this heterogeneous material were so arranged 

 that its density at any point depended simply upon the depth of 

 that point below the surface, that is, if all the material in each 

 horizontal stratum were of one density, the figure of equilibrium 

 would still be an ellipsoid of revolution. 



1 Chief of Computing Division and Inspector of Geodetic Work, Coast and 

 Geodetic Survey. 



