hayford's reduction of gravity observations 291 



the outer portions of the earth's crust and of the curvature. This was 

 an important advance. He had previously applied the same methods to 

 the study of plumb-line deflections. As the force of gravity at any point 

 on the earth's surface depends on the summation of the attractions of all 

 the particles of the earth's mass, as well as the centrifugal force, the 

 mathematical problem of computing a theoretical value of gravity to 

 compare with the observed value was one of considerable magnitude, and 

 to bring it within the range of practicability Hayford made a number of 

 assumptions, 6 as follows : That the earth's crust is in a state of perfect 

 isostasy, with each topographic feature, however small, compensated for 

 by a deficiency or excess of mass directly under it; that this compensa- 

 tion is uniformly distributed from the surface to a depth of 113.7 kilo- 

 meters (70.6 miles) below the surface, and that the mean density of the 

 solid portion of the earth's crust is 2.67. It was stated that it was not 

 believed that any one of these assumptions is exactly true. In the orig- 

 inal reports and in subsequent papers by Bowie, each of the assumptions 

 is studied and alternate results given for possible variations. This work 

 constitutes the most thorough study that has been made of the results of 

 the determinations of the relative force of gravity as bearing on the 

 problems of the condition of the earth's crust. Aside from the strength- 

 ened proof which it affords of the truth of the isostatic theory of the 

 crust, it also develops local and regional anomalies which are probably 

 more significant than any heretofore. Nevertheless the authors do not 

 claim that the comparative smallness of the residuals affords proof of the 

 complete correctness of any one of the assumptions made. 



The Gravity Eeductions of 1895 compared with earlier and 



later Methods 



To obtain a comparison between the observed and theoretical value of 

 the force of gravity, the observations of 1894 were reduced to sealevel by 

 three methods, depending on different conceptions as to the condition of 

 the earth's crust. 7 It appears useful now to briefly review these reduc- 

 tions and the results, in the light of the methods since developed of ap- 

 plying the isostatic compensation corrections. 



1. The Bouguer, or no compensation, reduction was the original of the 

 three methods, and the other two are based on this. Bouguer's reduction 

 was on the theory of an uncompensated earth's crust, and the attraction 

 of the topography above sealevel was subtracted from observed gravity. 



6 Coast and Geodetic Survey Special Publication No. 10, 1912, p. 10. 



7 Report Coast and Geodetic Survey, 1894, App. No. 1. Phil. Soc. of Washington, vol. 

 xiii, 1895, p. 31. 



