EARTHWORK 203 



In calculating the correction for curvature in three-level 

 section work, it is sufficiently accurate to use in the general 

 formula for curvature correction the values ei, ez and Ai, A 2 for 

 the full sections qcpn = A t instead of the actual area qcpmt. 

 The values of e\ and ez are then too small, and the resulting 

 error nearly neutralizes the one due to the inclusion in the 

 area of the triangle tmn. The eccentricity of the area qcpn 

 is ei = ^(w l w r ), and, using the same notation as before, the 

 curvature correction becomes 



-w' r ) \ 



The form in which the computation of volume should be 

 arranged when the cross-sections are three-level sections is 

 shown in the table on page 205. The figures in the first 

 four columns are written while the survey is being made; 

 those in columns 5, 6, and 7 are used for computing the average- 

 end area volume V a ; those in columns 8, 9, and 10 are employed 

 in computing the prismoidal correction; and the figures in 

 the last two columns are used for computing the correction 

 for curvature. 



The values of V a for the prismoids included between the 

 successive cross-sections are found as follows: Since the 

 results always are expressed in cubic yards, the preceding 

 formula for V a becomes, for the volume between two full 

 stations 



If the slope 5= 1J:1 and the width of the roadbed & = 22ft., 

 then a for all stations is 



= 7.3 ft. 



The sums of the constant depth a and the variable depths d 

 in the second column are written in the fifth column. Thus, 

 at Sta. 22, o+d = 7.3+6.2 = 13.5 ft.; at Sta. 23, a+d=7.3 

 +9.4 = 16.7 ft. The total width at each station is written 

 in the sixth column. Since, in Fig. 7, w = w l +w r , and since 

 the measured distances w l and w r are the denominators of the 

 fractions in columns 3 and 4 respectively, it is only necessary 



