THE NATURE AND INTERPRETATION OF GEODETIC EVIDENCE. 13 



This, which lie called the solution G, was afterwards modified 1 

 on the inclusion of additional observations, and the depth of com- 

 pensation increased to 122 km., but as the difference is trivial, 

 and the earlier value has been used in the investigations published 

 by the Great Trigonometrical Survey of India, and was used by 

 Mr. Hayford himself in his investigation of the effect of compensa- 

 tion on the vertical force of gravity, it may be accepted as a (-lose 

 approximation #to average conditions. The results of calculations 

 based on it are so little different from those which would have been 

 obtained from a slightly different depth of uniform compensation, 

 that no useful purpose Would be served by a revision of the calcula- 

 tions. 2 



It must not, however, be supposed that these depths of 113-7 

 or 122 km. have any real meaning; all that the calculations imph 

 is that the effect of such compensation as actually exists is not 

 materially different from that which would have resulted from 

 a defect of mass equal to that of the material above sea level, if 

 this were produced by a defect of density extending uniformly 

 through a depth of 113-7 km. and everywhere proportionate to 

 the excess of mass represented by the surface elevation above sea 

 level. Any other form of distribution of density^ which would 

 bring about the same result would be equally in accord with ob- 

 servation, and this conclusion is borne out by certain calculations 

 made by Mr. Hayford. In addition to the hypothesis of uniform 

 compensation he considered four others, namely — 



(1) A compensation uniformly distributed between the 

 depths of 25 and 35 miles. 



1 Supplementary Investigation in 1909 of the Figure of the Earth and Isostasy. 

 Washington, 1910. 



2 In Mr. Hayford's calculation, as in other treatments, it is assumed that compen- 

 sation should be applied directly to the elevations above, or depressions below, sea 

 level. The sea level is. however, an artificial datum for these purposes and the differences 

 of level should, strictly, be measured from a datum representing the mean level of the 

 solid earth, or the mean level as it would be if the oceans were supposed to be solidified 

 and condensed to the mean density of the rock forming (heir Soon This datum would 

 lie at about .'5,000 ft. below sea level and its introduction would require an extensive 

 re-calculation of tables, which ought properly to be undertaken in a discussion of the 

 effect of compensation, which included observations at stations near the sea coast. 

 Where, as is the case in this investigation, the distances from the shore line are measured 

 in hundreds of miles, and where, as will appear further on, the modification introduced 

 by considering the effect of topography beyond a distance of one hundred miles is 

 trivial, as compared with the differences indicated by observation, we may confine atten- 

 tion to the difference of effect due to difference of elevation above an arbitrarily assumed 

 datum, such as the mean sea level, the effect of the mass of the crust below this level. 

 but above the mean level of the solid spheroid, and of its compensation, being the same 

 in amount at all stations. 



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