luti Bowii — Recent Gravity Work in the Untied States. 



The attraction at the station of an elementary mass which is 

 higher than the station is given by the expression 



h cos 



. e . 2 



sin — sin 



' + 2l)h sin 



o — owl 6 



kdm- 



2> , + A a + 2Z)/tsin 6 



9 



In this A is the difference in elevation between the elemen- 

 tary mass and the station. 



The attraction at the station of an elementary mass which is 

 lower than the station is given by the expression 



h cos — 

 

 sin h sin" 



4/ &* + /?— 2Dh Bin -?- 



2 

 kdm 



Z> 2 + /r-2Z>Asin — 



For masses near the station the following formula was used, 

 which gives the attraction of a mass having the form of a right 

 cylinder, upon a point outside the cylinder and lying in its axis 

 produced : 



Attraction in dynes = k2nh { a/c 2 + /t 2 — y'c 2 + (h + tf + 1 j . 



8 is the density of the material, c is the radius of the cylinder, 

 t is an element of the cylinder and h is the distance from the 

 attracted point, the station, to the nearest end of the cylinder. 



For a mass which has the form of a cylindrical shell, which 

 is the difference in the effect of two solid cylinders of the same 

 length, having different radii c s and c„ this expression was 

 used : 



Attraction in dynes = 



font j yV a + V- ^c\ + h* - y/e\ + (h + ty + ytf, + (h + 1)' } . 



In order to apply the formulae to the computation of the 

 effect of topography and the compensation, the whole surface 

 of the earth was divided into zones, each having the station as 

 the center. Each zone was divided into equal compartments 

 by radial lines from the station. The division adopted is 

 shown in the following table : 



