204 EARTHWORK 



to add the two denominators at each station to obtain the 

 numbers in column 6. Thus, at Sta. 22, w= 16.1 + 30.2 

 = 46.3; at Sta. 23, w = 18.2+31.4 = 49.6 ft. 



To compute the value of V a between Sta. 22 and Sta. 23, 

 the proper values must be substituted in the formula for V a . 

 This gives 



X 7.3X22 = 579 +767 -297 =1,049 cu. yd. 



The number 579 is written in column 7 (a) opposite Sta. 22, 

 and 767 in the same column opposite Sta. 23. The result, 

 1,049 cu. yd., is written opposite Sta. 23, in column 7 (6). 



In a similar manner, for the volume of the prismoid between 

 Sta. 23 and Sta. 24, 



100 100 



X19.1X64 



The first term of this expression has already been computed, 

 and its value, 767 cu. yd. has been written in column 7 (a) 

 opposite Sta. 23. The last term is the constant volume 297 

 cu. yd. It is therefore necessary to compute the second term 

 only. Its value is found to be 1,132 cu. yd., and this is writ- 

 ten in column 7 (a) opposite Sta. 24. Then, V a = 767+ 1,132 

 297= 1,602 cu. yd., and this result is written in column 7 .(b). 



It is thus seen that, at each station, it is necessary to com- 

 pute but one term of the formula for V a ; this term is the value 



of - (a+d)w for that station. The value of this term for 



4 X t 



each station is written in column 7 (a). If the stations are 

 100 ft. apart, any number in column 7 (b) is obtained by 

 adding the number opposite and the one preceding it in column 

 7 (a) and subtracting 297 cu. yd. from the resulting sum. The 

 result so obtained is the value of V a for a prismoid 100 ft. long. 

 But if the two stations are less than 100 ft. apart, the result 

 must be multiplied by the ratio of their distance to 100 ft. 

 to obtain the volume of the prismoid. This volume is then 

 mitten in column 7 (6). For example, for the prismoid 



