18 



INSTRUMENTS USED IN MENSURATION. 



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

 smallness and the necessarily primitive arrangement of the 

 height measuring instruments. 



If the length oi ah = h can he 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, lying between the said rays, 

 are proportionate to the lengths of the rays. 



Let 1) A = L (Fig. 11) be the length of ray from the eye of 

 the observer to the foot of the tree, D a = l that from the eye 



1'j 



4c 



Fiff. 11. 



to the plumb line, A B = H the height of tlie tree, and a h=]t 

 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, 



Da: D A = a h : A B, or, I : L = h : II 



and 



A B = 5-i X a h, or, II = ^x h. 

 D a I 



In this case L can easily be measured following the surface of 

 the soil, whether it be level or slanting, while I and It are read 

 oft' on the instrument. 



The number of hypsometers based upon the above theories 

 is very large ; some being used with stands, others without. 



