24 INSTRUMENTS USED IN MENSURATION. 



The instrument is based upon the theory explained on page 

 17, which avoids the measurement of a base line. A staff of 

 known length = /, say 4 3'ards, is placed alongside the foot of 

 the tree. The instrument is then held in a vertical position 

 at some distance from the observer, and moved backward and 

 forward, until the top of the tree is seen along the upper edge 

 a, and the foot along the lower edge }> ; then the point is 

 marked on the instrument, where a ray from the eye to the 

 top of the staff hits the instrument at e. In this way 

 similar triangles are formed, in which the following equation 

 holds good : — 



he A B 



If now ah = 12 inches, and / = 4 yards, and successive values 

 for A B = height of tree, are introduced, corresponding values 

 oih c are obtained and can be marked on the instrument. In 

 this way the heights can be read off straight on the instrument. 

 For convenience sake, the marks on the instrument are cuts, so 

 that the place on the scale, where the top of the staff cuts in, 

 may be more easily seen. 



The instrument has the disadvantage that the marks are 

 very close one to another for heights over 30 yards. This 

 might be obviated to some extent by lengthening the instru- 

 ment and making it with a clasp in the middle, so that it 

 could be folded together when out of use. 



It is evident that, instead of using a staff 4 yards long, one 

 of, say, 2 yards can be used. In that case the height read 

 off on the instrument must be divided by 2. 



The instrument works well up to heights of 25, or at the 

 outside of 30, yards ; for higher trees it cannot be recommended 

 in its present shape. 



Brandis' Hiipsometer (Fig. 17) is based upon the trigono- 

 metrical method of height measuring. It consists of a tube 

 with an objective, 0, at one end and an eye-piece, e, in the shape 

 of a horizontal slit, at the other. Attached to this tube is a 



I'ibrarv 



