HEIGHT MEASURING. 



17 



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

 level with the eye of the observer. The horizontal distance 

 D C must be measured, and a c, b c and D c are read off upon 

 the instrument in the same units in which D C has been 

 measured. 



The measurement of D C can be avoided in the following 

 manner (Fig. 10 on next page) : 



A staff M N, of a known 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 n, and the similar 

 triangles D C M and D c m, as well as D C N and D c n, so 

 that the following equations hold good : 



D G :Dc = A B :ab 

 and 



D G :D c = MN : mn ; 

 hence, 



and 



A B :a I = M N :mn 



= H = a - x M ~ N = ab x l 

 m n mn 



