700 



SCIENCE 



[N. S. Vol. XXXIX. No. 1011 



not sufficient, for the value of gravity does 

 not follow any known definite law, owing 

 to the disturbing influences of masses above 

 sea level and the deficiency of mass in the 

 oceans. 



Helmert derived a formula in 1901 from 

 the observed values of gravity at about 400 

 selected stations. This formula gives theo- 

 retical values which will agree well, on an 

 average, with the observed values, but for 

 any one station the difference may be large, 

 even after one of the values has been cor- 

 rected for the elevation of the station above 

 sea level. 



Helmert 's formula, in the Potsdam sys- 

 tem, is 



7„ = 978.030 (1-f 0.005302 sm=0 — 0.000007 sin^ 2«i) 



in which yo, expressed in dynes, is the 

 theoretical value at sea level in latitude <f>. 



It is evident that the difference between 

 the theoretical and the observed values of 

 gravity, and the deflections of the plumb 

 line (which, as stated above, are the differ- 

 ences between the observed and the theoret- 

 ical astronomic positions) are due to the 

 disturbing influence of the topography and 

 the effect of deviations from the normal 

 densities in the earth's crust. The term 

 "topography" is applied to the visible 

 land masses and the deficiency of mass in 

 the oceans. But when the attractions of 

 the topography are applied as corrections, 

 the differences may still be large, but of 

 the opposite sign. 



About sixty years ago Archdeacon Pratt 

 of England arrived at the conclusion, from 

 a study of the deflections in India, that 

 there must be a deficiency of mass under 

 the Himalayan Mountains and that the 

 deficiency extended to a limited depth. 

 The advancement of this theory marked 

 an epoch in geodesy. Prom time to time, 

 writers in different countries have elabo- 

 rated on the mere statement of Pratt. But 



it was Hayford who gave this theory a 

 quantitative expression when, as a member 

 of the United States Coast and Geodetic 

 Survey, he corrected the astronomic lati- 

 tudes, longitudes and azimuths in the 

 United States for the effect of topography 

 and its negative equivalent, called "iso- 

 static compensation," when making two 

 determinations of the figure of the earth. ^ 



A preliminary report on the application 

 of the theory of isostasy to the study of the 

 deflections in the United States was made 

 by Messrs. Tittmann and Hayford to the 

 Fifteenth General Conference of the Inter- 

 national Geodetic Association, held at 

 Budapest, Austria-Hungary, in 1906.* 



Isostasy was also considered by Hayford 

 and the writer in reducing the gravity sta- 

 tions in the United States.^ 



In order that a clear idea of isostasy*^ 

 may be obtained, I shall quote Hayford : 



If the earth were composed of homogeneous ma- 

 terial, its figure of equilibrium, under the influ- 

 ence of gravitation and 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 on the depth 

 of that point below the surface, or, more accu- 

 rately, if all the material lying at each equipoten- 

 tial surface (rotation considered) were of one den- 

 sity, a state of equilibrium would exist and there 



3 ' ' The Figure of the Earth and Isostasy from 

 Measurements in the United States," by John F. 

 Hayford, U. S. Coast and Geodetic Survey, 1909; 

 "Supplementary Investigation in 1909 of the 

 Figure of the Earth and Isostasy, ' ' by John F. 

 Hayford, U. 8. Coast and Geodetic Survey, 1910. 



* ' ' Geodetic Operations in the United States,. 

 1903-06." 



" "The Effect of Topography and Isostatie Com- 

 pensation Upon the Intensity of Gravity," Spec. 

 Pub. No. 10, U. S. Coast and Geodetic Survey,, 

 1912, by John F. Hayford and William Bowie; 

 same, second paper, by Wm. Bowie, 1912, 



6 The term isostasy was first proposed by E. C. 

 Button. See TraTisactions of the PhilosopMcal 

 Society of Washington, D. C, Vol. XI., pp. 51-64. 



