EARTHWORK 



Irregular Sections. When the cross-sections are irregular, 

 the process of determining the volume of earthwork is essen- 

 m tially the same as for 



three-level sections, ex- 

 cept that a more accu- 

 rate method for compu- 

 ting the areas of the 

 cross-sections is applied. 

 After the area has 

 been determined, the 

 volume by the end- 

 area method, and the 

 prismoidal and curva- 

 ture corrections are obtained just as if the figures were 

 three-level sections. 



Areas of Irregular Sections. Using the notation of Fig. 8, 

 the area npqgfckm is determined by the formula 

 A = 



FIG. 8 



ysx-i yyxi xiyz 

 This long expression for the area may be very easily formed 

 as follows: Write the successive slope-stake fractions in 

 order, in a horizontal row, beginning with the extreme left 



d 

 slope stake; and for the center stake write the fraction. At 



the beginning and end of the row, write the fraction . 

 Thus, the fraction for the stake at n is ; for the point m, it 

 is , etc.; so that the row of fractions for Fig. 8 will be as fol- 



XI 



lows: 



/ o 



Next, multiply each denominator by the numerator that 

 follows it and each numerator by the denominator that fol- 

 lows it, giving to those products connected with full lines 

 the -plus sign, and to those connected with dotted lines the 



