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EARTHWORK 



outside of the center, the eccentricity is small, and the cor- 

 rection may usually be neglected, even with curves of short 

 radii. But when the eccentricity is large (as is usually the 

 case in side-hill work), the curvature correction may be a 

 very considerable percentage of the volume, and should not 

 be neglected, especially if the radius of the curve is small. 



To apply the general formula for curvature correction, the 

 eccentricities ei and e* are required. These can be determined 

 by using the methods employed in finding the center of grav- 

 ity of plane figures. The section is divided into triangles and 

 their areas are referred to the vertical axis through the center 

 of the track; then the coordinate of the center of gravity of 

 the total area with regard to this axis is found, which coordinate 

 is the eccentricity of the section. 

 Three'- Level Sections. 

 Where the surface of the ground 

 is fairly regular, it is sufficiently 

 accurate to determine the ele- 

 vation of the center point and 

 the distances and elevations of 

 the two slope stakes. The 

 method assumes that the 

 straight lines cq and cp. Fig. 7, 

 that join the center with the 

 slope stakes are on the surface 

 of the ground. When this method is used, the sections are 

 called three-level sections. 



To calculate the volume of a prismoid whose bases are three- 

 level sections distant I from each other, let, in Fig. 7, the area 

 gcpn = At and the area of lmn = T. Then, using the notation 

 of the figure and the sign (') to denote corresponding values at 

 the other base, the approximate volume is 



V a = -(At+A t '-2T) 



Va=-\ (a+d)w+(a+d')iv > 



-2ab 



and the prismoidal correction is 



(d'-d) 



