THE MEASUREMENT OF HEIGHTS 235 



193. The Measurement of Heights. While in measuring diameters 

 it is possible to use the instrument upon every tree as a practical measure 

 when necessary, the greater difficulty and time required in measuring 

 heights makes the general use of an instrument for even a large per 

 cent of the trees impossible. Only on small, permanent sample plots 

 will the height of each tree be actually measured. Height measures, 

 or so-called hypsometers, are commonly used to obtain the height 

 of average trees from which the average height of the remaining trees 

 is determined, or to check the eye when the merchantable heights of 

 all trees are recorded. 



In the latter case, ocular estimation of the number of merchantable 

 logs in each tree, or total merchantable height, is the only practical 

 means possible. It takes no longer to estimate the height of a tree 

 by eye than its diameter, but the measurement of height by hypsometer 

 takes about ten times as long as to caliper the tree. 



The eye is slightly more unreliable in measuring heights than diam- 

 eters. The height scale is more difficult to fix in the mind. Con- 

 sequently the tendency is to arrive at the height of trees by comparison 

 with other trees. The result is that the standard of height for all trees 

 tends to shift from day to day unless heights are carefully checked at 

 the beginning of each day's work in order to maintain this mental 

 basis or standard. In no other feature of ocular timber estimating 

 are such serious errors made even by experienced cruisers as in estimat- 

 ing heights, and the novice should never trust his judgment over- 

 night. 



194. Methods Based on the Similarity of Isoceles Triangles. 

 Measurement of heights is based on the principles of similar triangles. 

 From the observer's eye, the tree forms one side of a large triangle, 

 the other two sides of which are the lines of sight to the top and base 

 of the tree. The base of this triangle can be measured. The length 

 of the vertical side which is the height of the tree is the dimension 

 sought. To determine this inaccessible dimension, a smaller, measure- 

 able, similar triangle is used. 



Similar triangles must have their three sides proportional and the 

 three angles equal. This is secured when either two sides are propor- 

 tional and one angle equal, or one side is proportional and two angles 

 equal. 



The isosceles triangle with two sides of equal length forms the 

 simplest method of measuring the height of a standing tree. In this 

 triangle the base from the eye to the foot of the tree is equal to the 

 height of the tree and may be directly measured. The small triangle 

 in this case is used to find the point on the ground at which this base 

 will be equal to tree height. A triangle which has its own base and 



