ilu> center f 1h> inxtnu.H'itt to tlic rod the distance is 



c bein^ tin- distance from the ol.jectivc to tin- center .t' the ins; nniient. 



Since (c + /) is practically a constant it is usually denoted by the' sin-le letter C 

 and is known as the constant of the instrument." 



Fig. 3 



m 



When the line of sight is not level, but the stadia held at right angle to it, the 

 formula for the horizontal distance is : 

 (2) D = &.a.cos n-f-c-f-om. 



The member om 



- sin n ; for a 



24', n = 45 the value of om is but 8.4', and for 



a = 10' , n = 10 it is 0.86'; this shows that om in most cases may safely be omitted. 

 Some engineers let the rodman hold the staff perpendicularly to the line of sight ; 

 they accomplish this by different devices, as, a telescope or a pair of sights attached 

 at right angle to the staff. This method is not practicable, as it is very difficult, 

 especially in long distances, and with greater vertical angles for the rodman to see 

 the exact position of the telescopes, and furthermore, in some instances it is entirely 

 Impossible, when, for instance, the point to be ascertained is on a place where only 

 the staff can stand, but where there is no room for the man. The only correct way 

 to hold the staff is vertically. 



In this case we have the following : (Fig. 4) 



MF = c -f GF = c -f fc.C.D. 

 CD must be expressed by AB. 

 AB = a. AGB = 2m. 

 CD = 2GF tan.w. 

 And finally, after many transformations : 



D = c.cos n + a.fc.cos 2 ;* a.k.&ii\ 2 n tan*m. 



The third member of this equation may safely be neglected, as it is very small 

 even for long distances and large angles of elevation (for 1500', n = 45 and A- = 100, 

 it i? but 0.02'). Therefore, the final formula for distances, with a stadia kept ver- 

 tically, and with wires equi-distant from the center wire, is the following: 

 (3) D = c.cos n-{-a.k.co&n. 



The value of c.cos n is usually neglected, as it amounts to but 1 or 1 .r> feet : ir is 

 exact enough to add always 1.25' to the distance as derived from the formula 



D = a.fc.cos 2 rc 

 without considering the different values of the angle n. 



In order to make the subtraction of the readings of the upper and lower wire 

 quickly, place one of the latter on the division of a whole foot and count the parts 



