EARTHWORK 197 



b 

 and x' = +sXd-sXy' (2) 



If the natural surface mem' is a level line, so that g, c, and 

 q' are at the same elevation, then y = o, :/ = o, and 



b 

 x = x > = ca==ca ' := - + s Xd (3) 



Formulas 1 and 2 are called slope-stake equations and formula 3 

 is called the level-section equation. The latter formula is 

 available when the ground is nearly level. When the ground 

 is sloping or irregular, formula 1 is employed, but not directly, 

 as the value of y is not known until after the stake has been 

 located. The distance x or A/ is determined by successive 

 trials. Suppose, for example, that, in Fig. 4, d = 6.3, and let 

 the rod reading on the point c be 5.9. Suppose, also, that 

 5 =1.5:1 and & =20. Then, if the ground were level, by for- 

 mula 3, 



ac = - [-1.5X6.3= 19.5 ft. 



To find the location of m, the rodman will hold the rod at 

 some point more than 19.5 from cr. Suppose that he holds 

 it at , 20 ft. from c r, and that the reading on the rod in this 

 position is 2.8. Then, the height of this point above c equals 

 the reading on c minus the reading on n, or 5.9 2.8 = 3.1 ft. 

 The computed distance from the rod to cr is by formula 1, 

 +1.5X6.3+1.5X3.1 = 24.1 ft. Since the measured distance 

 (20 ft.) is much smaller than this, the rod must be moved much 

 farther out. 



Suppose that the rod is carried out 7 ft. so that the measured 

 distance to cr is 27 ft., and suppose that the reading on the 

 rod in this position is .8 ft. The elevation of this trial point 

 above c will be 5.9 .8 = 5.1 ft., and by formula 1, the computed 

 distance x is ^+1.5X6.3+1.5X5.1 = 27.2 ft. This agrees 

 so closely with the measured distance that the slope stake 

 may be driven at this point. 



The lower slope stake at m' is set in the same manner as the 

 upper, except that the distance of each trial point below c is 

 measured, and formula 2 is used in computing the correspond- 

 ing value of x'. The distance of the trial point from c r will 



