LEVELING 89 



Let this excess be denoted by e c , the radius of the earth (about 

 20,900,000 ft.) by r, and the horizontal distance between the 

 instrument station and the leveling point by d; then, 



Another source of error in leveling, due to atmospheric 

 refraction, tends to lessen the error due to curvature. Its 

 value e r can be figured from the formula 



d2 



e r =.071 

 r 



The combined error due to curvature and refraction is equal to 



3J2 

 e-ec-er- 



The errors due to curvature and refraction are very small 

 for a single sight of ordinary length, and their cumulation may 

 be eliminated by balancing backsights and foresights. 



Degree of Accuracy Required in Spirit Leveling. If M 

 denotes the length of a leveling circuit and E the permissible 

 error of closure, in feet that is the permissible divergence 

 between the elevation of a point as obtained at the beginning 

 of the circuit and the elevation of the same point as obtained 

 when ending the circuit then, for very accurate surveys, 

 = .012 >/Mto.029 VM 



For good average work of ordinary character, 

 = .05 Yfcf 



For preliminary railroad surveys, 



= .i VM 



EXAMPLE. Determine the error permissible in making the 

 preliminary survey for a railroad 100 mi. long. 



SOLUTION. By substituting a value of 100 for M in the 

 proper equation, 



= .1 VlOO=1.0ft. 



