EARTHWORK 207 



prismoidal formula, is, therefore, 1,0493=1,046 cu. yd.; that 

 of the second, 1,602-11 = 1,591 cu. yd., etc. 



Now assume that the portion of the track just calculated 

 is on a 7 curve to the right. Applying the formula for C c 

 for stations of 100 ft. and in cubic yards, 



_ 100 VA t (wiw r ) A' t (w'iw' r )~\ 



C 3R [_ 2X27 2X27 J 



At Sta. 22, av=16.1, w r =30.2, and, hence, wi w r =16.1 



- 30.2 = - 14.1. At Sta. 23, w { '= 18.2, w r ' = 31.4, and, hence, 



Wl '-w r ' = 18.2- 31.4 =-13.2. The values of ; - and 



2X27 



are those already tabulated in column 7 (a); thus, 



2X27 



=579 and =767. Substituting all of these 

 2X27 2X27 



values, anc? xhe value of 2? = 819 for a 7 curve, 



C c = X(579X-14.1 + 767X-13.2)=-7cu. yd. 



3X819 



Since wi and wi' are smaller, respectively, than w r and w r ' t 

 the centers of gravity of the sections lie on the right of the 

 center line of the roadbed; and, as the curve turns to the right, 

 the centers of gravity lie inside of the center line, and the 

 correction is to be subtracted. The volume for this section 

 computed by the prismoidal formula is 1,049 3=1,046 cu. 

 yd., and, corrected for curvature, the final result is 1,0467 

 = 1,039 cu. yd. The curvature corrections for other sections 

 are figured in a similar manner, except for sections less than 

 100 ft. long, when the result must be multiplied by the ratio 

 of the length of the section to 100 ft. To find, for instance, 

 the curvature correction for the section between Sta. 24 and Sta. 

 24+35, determine, as before, the correction just as if the 

 station were 100 ft. long and multiply the result by tfo. Thus, 



C c = - (l,132X-15.6+684X-8.2)X3fo=-3cu. yd. 

 3X819 



As in the previous case, the actual volume is less than the 

 one computed for a straight track; therefore, the actual vol- 

 ume F = 532 -6- 3 = 523 cu. yd. 

 15 



