HEIGHT MEASURING. 



15 



a. Geometrical Height Measuring. 



If a horizontal plane is drawn from the eye of the observer 

 to a tree, it will hit the same, according to the position of 

 the observer, either between the top and the foot of the tree, 

 thus dividing it into two parts, one of which is situated above, 

 and the other below the horizontal plane ; or above the top ; or 

 below the foot. If the observer holds a plumb-line at some 

 distance from his eye, it may be considered parallel to the axis 

 of the tree ; hence by looking at the top and foot of the tree 



o ,' 





Fig. 7. 



similar triangles are formed, which are used for the determina- 

 tion of the height of the tree. 



Let A B (Fig. 7) be the height of the tree. 



D B SL ray from the eye of the observer to the top of the 



tree. 



D A, ditto to the foot of the tree. 

 D C a horizontal line. 



a, b, and c the points where the three rays hit the plumb- 

 line. Then the height is determined as follows : 



The horizontal line hits the tree between the top and 

 foot. Here the following equation holds good : 

 B C :bc = D C : D c 



(1) 



