89 



included between this and the other wire ; this multiply mentally by 100 (the con- 

 stant A;) which gives the direct distance D'. 



In cases where it is not possible to read with both stadia wires, it is the custom 

 to use but one of them in connection with the center wire, and then to double the 

 reading thus obtained. With very large vertical angles, this custom is not advis- 

 able, as the error may amount to 0.50 % . 



Fig*. 



To find the height of the point where the stadia stands above that one of the 

 instrument, simultaneously with the distance, we have the following: 



We assume in reference to figure 4, 



q = height of instrument point above datum. 



MP= D = horizontal distance as derived from formula (3). 



n = vertical angle. 



h = FE = stadia reading of the center wire. 



Q = height of stadia point above datum ; it is 



Q = g-fptanw h. 



The substraction of h can be made directly by the instrument, by sighting with 

 the center wire to that point of the rod, which is equal to the height of the telescope 

 above the ground (which is in most cases = 4.5.') ; q will be constant for one and 

 the same instrument point ; then the formula : 



Q = D tan n ; 

 this in connection with formula (3) gives 



Q = c sin n -\- a.k. cos n. sin n. 



or 



Q = c sin n 



sin 2 n 



The first term of the equation can be neglected, when the vertical angle is not too 

 large ; hence the final formula for the height is 



(5; r t _a.k. sin 2 n 



2 



The position of the stadia must be strictly vertical. 



The error increases with the height of m ; (m = height of center wire on the 

 rod) . In shorter distances the result is seven-fold better when the center wire is 

 placed as low as one foot than it is at 10' ; in longer distances this advantage is 

 only double. 



It is always better to place the center wire as low as possible. If the stadia is 

 provided with a good circular level, the rodmau ought to be able to hold it vertically 



