18 



INSTRUMENTS USED IN MENSURATION. 



This equation can easily be modified for the cases when the 

 horizontal plane lies above the top or below the foot of the 

 tree. 



The indirect determination of the distance by means of a 

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

 difficult to read off in n with sufficient accuracy, owing to its 

 smallness and the necessarily primitive arrangement of the 

 height measuring instruments. 



"*-- - 

 c. . 



** 



Fig. 10. 



If the length of a b = h can be read off at once, the business 

 becomes more simple, and may be expressed as follows : 



If two parallel objects are cut by diverging rays, then the 

 portions of the parallel objects tying between the said rays are 

 proportionate to the lengths of the rays. 



Let D A = L (Fig. 11) be the length of ray from the eye of 

 the observer to the foot of the tree, Da I that from the eye to 

 the plumb line, A B = H the height of the tree, and a b = h the 

 length of the plumb line between two rays going from the eye 

 of the observer to the top and foot of the tree, then, 



I :L = h :H 

 and 



x h. 



