GEODESY. 



I. Form of the Earth. The Earth's Spheroid. The Geoid. 



The shape of the earth is defined essentially by the sea surface, which embraces 

 about three fourths of the entire surface. The sea surface is an equipotential 

 surface due to the attraction of the earth's mass and to the centrifugal force of its 

 rotation. We may imagine this surface to extend through the continents, and 

 thus to be continuous. Its position at any continental point is the height at 

 which water would stand if a canal connected the point with the ocean. 



Geodetic measurements show that this surface is represented very closely by 

 an oblate spheroid, whose shorter axis coincides with the rotation axis of the 

 earth. This is called the earth's spheroid. The actual sea surface, on the other 

 hand, is called the geoid. With respect to the spheroid the geoid is a wavy sur- 

 face lying partly above and partly below ; but the extent of the divergence of the 

 two surfaces is probably confined to a few hundred feet. 



2. Adopted Dimensions of Earth's Spheroid. 



The dimensions of the earth's spheroid here adopted are those of General A. 

 R. Clarke, published in 1866, to wit : — 



Semi major axis, a = 20 926 062 English feet. 

 Semi minor axis, ^ = 20 855 121 " " 



3. Auxiliary Quantities. 



The following quantities are of frequent use in geodetic formulas : — 



e = y/ 2 — ' ^^^ eccentricity of generating ellipse, 



(t — i> , ^ . ,,. . . 



/ =: » the flattenmg, ellipticity, or compression, 



a — d 

 I — n 



e'=2f-f\ 



e* I ^^ I 5 ^" 



/=I_^I_^2::^ — + — 4--^ + — g + ... 



2 ;/ 



= 2(n - ?r + n'' -«" + .. .). 



