EARTHWORK 199 



COMPUTATION OF VOLUME 



In calculating the cubical contents of earthwork, the volumes 

 between two consecutive cross-sections are considered as 

 prismoids whose bases are such sections as mcm'l'l. Fig. 4, 

 and whose lengths are the distances between the cross- 

 sections. These are usually 100 ft., unless the surface of the 

 ground is rough and irregular, when sections at intervals of 

 less than 100 ft. are taken. If Ai and A* are the areas of the 

 bases of a prismoid, A m the area of a section midway between 

 the bases, and I the perpendicular distance between them, the 

 approximate volume Va of the prismoid, as figured by the end- 

 area method, is 



(1) 



and the true area, as figured by the prismoidal formula, is 



V = -(Ai+4A m +At) (2) 

 o 



Prismoidal Correction. Formula 1 will usually give fairly 

 good results; for accurate work, however, formula 2 is used. 

 This formula requires that the dimensions of the middle 

 section whose area is A m shall be determined. This may be 

 done by averaging the di- 

 mensions of the bases from 

 which A m might be com- 

 puted. It is much simpler, 

 however, to figure the ap- 

 proximate volume V a by 

 formula 1, and then, if 

 desired, apply a correction 



equal to the algebraic difference between the volume V and V a ; 

 the result obtained will be the same as if formula 2 were used. 

 This difference is called the prismoidal correction. 



Correction for a Triangular Prismoid. Fig. 5 shows a 

 triangular prismoid, the dimensions of which are marked. 

 Its approximate volume as computed by formula 1 is 



