30 HAYFORD 



and unknown. The topographic irregularities and the distri- 

 bution of density each affect the deflections of the vertical. 

 Therefore, each should be taken into account as far as possible 

 in any attempt to derive the figure and size of the earth from 

 geodetic measurements. They are so taken into account in the 

 investigation now in progress in the Coast and Geodetic Survey. 



This investigation seeks to determine not only the figure and 

 size of the earth but also to determine whether the condition 

 called isostasy exists with its peculiar distribution of sub-surface 

 densities, and if so the depth within which the isostatic compen- 

 sation is complete. Several complete and independent solutions 

 by least squares of the problem of determining the figure and 

 size of the earth have been made in this investigation upon 

 different assumptions as to isostasy and depth of compensation. 



The residuals of these different solutions, expressing the 

 degree of harmony brought about by the different assumptions, 

 furnish the evidence as to which of the assumptions is nearest 

 the truth. 



One solution was made on the assumption that the condition 

 called isostasy does not exist, that no isostatic adjustment occurs 

 when vast masses are eroded from high parts of the earth's 

 surface, and are transported and deposited on the low parts — 

 that the earth is so rigid as to support the continents as local 

 excesses of mass. It is equivalent to the assumption that the 

 depth of isostatic compensation is infinite. 



To make this solution it was necessary to compute the effect 

 of all the topography for a considerable distance from each 

 station. The computation was made to cover all topography 

 within 2,564 miles of each of the 304 stations. 



The usual solution was also made. This solution is based 

 upon the tacit assumption that no relation exists between deflec- 

 tions of the vertical and the topography. It is equivalent to the 

 assumption that isostatic compensation exists and is complete at 

 depth zero — that there exists immediately below every elevation 

 (either mountain or continent) the full compensating defect of 

 density, and that at the very surface of the ocean floor there 

 lies material of the excessive density necessary to compensate 

 for the depression of that floor. Under no other condition can 



