398 ANNUAL EEPOKT SMITHSONIAN INSTITUTION, 1910. 



known as Faj^e's method; but Putnam and Gilbert were the first to 

 put it in practice and to elaborate the idea of the mean plain. 



In the discussion of Hayford's method it will be seen that there is 

 a correction for topography which is analogous to that for mean 

 plain in Faye's method, but which has reference to a " theoretic 

 plain that passes through the station." 



The test which is applied to the results of calculations made under 

 any one of these three different assumptions is that of agi^eement. 

 x\ll the values of gravity calculated by one and the same method 

 should be the same. All the corrections which are applied are in- 

 tended to eliminate from the original observation those items of 

 attraction which may render the observed value greater or less than 

 the normal value. Any difference wdiich remains points to some 

 factor that has been overlooked or to an erroneous assumption. That 

 method of reduction which yields results in closest accord with each 

 other is assumed to be nearest the truth. 



We shall first contrast the assumption of high rigidity with that 

 of partial isostatic balance combined with partial rigid support ; and 

 then compare the latter with the assumption of completed isostatic 

 balance, referring to the three methods, respectively, by the names of 

 their authors, as Bouguer's, Faye's, and Hayford's. 



In Bouguer's time no one doubted but that the earth's crust was 

 very rigid. All masses above sea level were regarded as heaps upon 

 the rigid crust and all depressions below sea level were taken to be 

 defects of mass in the spheroid whose surface should correspond with 

 that of the sea. Bouguer therefore corrected all observations for 

 gravity by subtracting the attraction of the mass between the station 

 and sea level. He obtained very small values. The intensity of 

 gravity appeared to be so slight that Laplace, in the Mecanique 

 Celeste, calculated the density of the material beneath the Andes as 

 about equal to that of water, and he gravely suggested that the ob- 

 served lightness might be due to great caverns within the volcanic 

 zone. This suggestion is now recognized as quite untenable since 

 rocks are not strong enough to maintain open spaces under the pres- 

 sures that exist beneath the Andes. 



A great many observations for gravity were made during the 

 century and a half between 1739 and 1895, and all, bO far as the 

 writer knows, were reduced by Bouguer's method. They jnelded a 

 general result : The intensity of gravity on continents was found to 

 be less than normal and was particularly low on high mountains; 

 whereas the intensity wa-s great on oceanic islands. Hence followed 

 the conclusion that continents are light and suboceanic masses heavy. 



But Bouguer's method yielded extreme results. Oceanic masses 

 appeared to be very heavy and continents seemed excessively light, 

 as Laplace's calculation of the density of the Andes should have 



