62 



h, is a h, and ve Iiave tVie follotring formala Tvith regard to the oonstant or redneiog 

 f cactiun called tiie form-factor (f) and the true volame (c') of the stem : — 



,,'=/(C) (C) = ah; c'=/aAvf = ^=-(^ 



The value of/ is determined by felling a sufficient number of trees and by ascertaining 

 practically the value of -j^ , that is to say, the relation which subsists between the 

 ideal cylinder and the true volume of the stem. With the above explanation we 

 may proceed to prove the rules with regard to the selection of type-trees as 

 follows :— 



Let C=:the total volnme of all the trees in a size-class. 

 A=:the sum of the basal areas of all the stems. 

 H=:the average height of the tree. 

 i'=:the average form-factor of all the trees. 

 n=the number of trees in the size-class. 

 c'=tlie contents of the type-tree. 

 a=the basal area of the type-tree. 

 h=the height of the type-tree. 

 f=the form-factor of the type-tree. 



We require to find a, the basal area of the type-tree representing the size-elass. 

 By supposition C=A H F, and c' = a h f : also o' = — . 



D 



It follows that o' = ^-^ and, therefore, that a h f = *-iI. Therefore, as- 

 suming that h f = H P, a = -I or, expressed in words, that the sum of the basal 

 areas of all the trees in the class divided by the number of trees in that class egvals 

 tie basal area of the type-tree. 



As the basal area = ^ ( P+^ \ '. it follows that the mean diameter of the tree 



sjnght (— ^) is equal to the square root of the basal area of the type-tree, as calcn- 

 'ated above, divided by one-fontth the value of %, or the mean diameter — -*' • 

 This, in practice, would be found from a table. 



THE MEASUREMENT OF TREES AND LOGS. 



General rules.— The following directions in regard to 

 measuring trees are taken (with some considerable omis- 

 sions) from the treatise on the measurement of timber and 

 timber crops already referred to, 



The heights of standing trees are ascertained by means of 

 special instruments, designed for that purpose and known as 

 dendrometers and hypsometers. These instruments are of two 

 kinds — 



(i) those which give the height without calculation, 

 their construction being based on the principle 

 of similar triangles ; and 



