HEIGHT MEASUEING. 



17 



In each of the above three cases two measurements are 

 required, unless the foot of the tree happens to be at the same 

 level as the eye of the observer. The horizontal distance D C 

 must be measured, and a c, h c and D c are read off upon the 

 instrument. 



The measurement of I) C can be avoided in the following 

 manner (Fig. 10) : — 



A staff M X, of a laiown length = I, is placed alongside the 

 tree, so that both its ends can be seen. In this way the 

 plumb-line gives two further points, m and u, and the similar 



B 



M 



Fig. 10. 



triangles D C M and I) c m, as well as D C N and Den, so 

 that the following equations hold good : — 



l> C : D c = A B : a h 



and 



hence, 

 and 



D C : D c = M X : m n ; 

 A B : ah = M X : m n 



A B = H 



a h X .V A^ _a h X I 



in n m ii 



The indirect determination of the distance by means of a 

 staff is less accurate than measuring it on the ground, as it is 

 F.M. c 



