-Bowie —Recent Gravity Work in the United States. 105 



y = 978-046(1 + -005302 sin 2 <j!>= •000007 sin 2 2</>). 



The value sought is y . The constant 798*04:6 is the theo- 

 retical value of the intensity of gravitation at sea level at the 

 equator, unaffected by topograph}'. The coefficient '000007 

 was adopted by Helmert from the theoretical investigations 

 of Weichert and Darwin, while the coefficient "005302 resulted 

 from a discussion by Helmert of about 400 selected gravity 

 stations. These stations were selected from a total of about 

 1600 stations and were those which showed the smallest anom- 

 alies. In latitude 39°, approximately that of Washington, 

 there is a change of "0013 dyne for 1 minute change in latitude. 



The formula C H = - -0003086 H, in which H is the eleva- 

 tion above sea level in meters, is used to get the correction for 

 elevation of the stations. It follows that a change of -001 

 dyne is caused by changing the elevation about 3 meters. 



The corrections for latitude and elevation, only, are used in 

 the Free Air reduction, which ignores the attraction of the 

 topography altogether. In this reduction it is implied that 

 there is complete isostatic compensation at the depth zero. 



The Bouguer reduction applies corrections for latitude, eleva- 

 tion, and for the topography without compensation. The 

 new, or Hayford, method applies these three corrections and 

 also a correction for the isostatic compensation. 



It is not necessary to discuss in detail the formulae used to 

 obtain the attraction of the topography and compensation. 

 They are based upon the fundamental principle that the attrac- 

 tion of any elementary mass dm for a mass of one gram at the 



station of observation is in dynes -rp— - , where k is the gravita- 

 tion constant, in the C. G. S. system, namely, 6673 (10 -11 ).* 

 All other quantities must, therefore, be expressed in that sys- 

 tem. D is the distance from the station to the elementary mass. 

 The vertical component at the station of this attraction is 



e 



sin — 

 Jcdm , 



ir' sin 2 — 



in which v is the radius of the earth, considered as a sphere 

 (6370 kilometers), and 6 is the angle at the center of this earth 

 subtended between the station and the elementary mass (the 

 station and the elementary mass being considered at sea level). 



*See page 153 of "The Century's Progress in Applied Mathematics" by 

 E. S. Woodward, in Bulletin of the American Mathematical Society, vol. vi, 

 No. 4, pp. 133-163. 



