96 STADIA AND PLANE-TABLE SURVEYING 



Inclined Sights. When the line of sight is inclined, the rod 

 is held vertical and the vertical angle that the line of sight 

 makes with a horizontal is measured. Denoting this angle 

 by V and using the previous notation, 



d=(sRcos F-H) cos V 



When V is less than 3, the angle is not considered and 

 formula on page 94 is used. 



Vertical Distances. For finding differences in elevation 

 the following formula is used: 



v = $sR sin 2V+i sin V 



In this formula, v is the difference in elevation between the 

 center of the instrument and the point of intersection of the 

 line of sight with the rod. 



To determine the difference in elevation between the point 

 on which the rod is held and the point over which the instru- 

 ment is set, add to the value of v , as obtained from the formula, 

 the height of the instrument, and from the result subtract 

 the reading of the middle cross-hair. To avoid these calcula- 

 tions, the middle cross-hair may be made to intersect the rod at 

 a point whose height above the ground is equal to that of the 

 instrument. The result obtained from the formula is then 

 the required difference in elevation. 



The stadia point is higher or lower than the instrument 

 point according as the angle V is one of elevation or depression, 



EXAMPLE. The length intercepted on the rod is 7 ft., and 

 the vertical angle when the line of sight intersects the rod at a ' 

 height equal to the height of the instrument is 18 23'. If 

 the stadia constant is 100 and the instrument constant 1 ft., 

 (a) what is the horizontal distance of the rod from the center 

 of the instrument? (&) what is the difference of elevation 

 between the center of transit and the point where the line of 

 sight intersects the rod, as indicated by the center cross-hair? 



SOLUTION. (a) Here 5=100, # = 7, *'=!, and cos F = cos 

 18 23' = .94897. Substituting these values in the formula for d, 

 d= (100X7X .94897+1) X .94897 = 631.3 ft. 



(b) Here sin F = sin 18 23' = .31537, and sin 2F = sin 

 350 46' = .59856. Substituting these values and those given 

 above in the formula for v , 



P-JX100X7X. 59856+ IX. 31537 = 209.8 ft. 



