HEIGHT MEASURING. 



15 



Z> .4, a ray from the eye of the observer to the foot of 



the tree. 

 D C, a horizontal hue. 



a, h, and c, the points where the three rays hit the phimb 

 line. Then the heiojht is determined as follows : — 



Fig. 7. 



(1.) The horizontal line hits the tree between the top and 

 foot. Here the following equation holds good : — 



B C :hc = DC '.Dc 

 and 



B C = ^ ^' ^ ^ ^ 

 D c 

 Again, 



A C : ac = D C : D c 

 and 



a c X D C 



AC ^ 



D 



Hence, 



B C + AC = AB = height of tree = (^ ^ + « ^) x ^ <^' . 

 ^ 1) c 



or, 



H = ah X 



D C 

 Dc' 



(2.) The horizontal plane passes below the foot of the tree. 

 In that case (Fig. 8) : — 



H = BC-AC = ^^^^^^AR^ = ahx^^ 



D c 



Dc' 



