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average tree. From this deduce the girth of such tree. Lastly, 

 fell several type trees of this girth, and find out their contents 

 accurately. The mean of their aggregate contents will be the 

 contents of the average tree, and this, multiplied by the number of 

 trees in the whole crop, or, which comes to the same thing, by the 

 ratio of the total basal areas to the basal area of the average tree, 

 will give the contents of the crop. 



6. Survey by Girth or Heighl-and Girth-Classes. 



In a forest crop there is never any constant relation between 

 the heights, girths, and form-factors of the component trees. Of 

 these three elements, two of them remaining the same, the widest 

 fluctuations are presented by the girth, the other two varying 

 within much narrower limits. In regular crops the average height 

 of the stems comprised in each class varies directly as the girth 

 of that class, the thicker stems being also the taller and vice versa ; 

 BO that we may consider the height as a function of the girth. 

 If the crop is very regular, the differences of height between the 

 component trees will be so small that the height of the crop may 

 be expressed by a single figure. In irregular forests, on the other 

 Land, there can never be any constant relation between height and 

 girth, for the thickest stem may be the shortest of all. 



As regards form-factor, it may be regarded as a function of 

 height and girth combined, for its variation depends on the same 

 circumstances which govern the variations of height and girth and 

 especially on the ratio of height to girth. Hence the form-factor 

 may be assumed as being nearly equal for trees of like girth and 

 height. But even in regular crops measurements of sample stems 

 of one and the same girths may give differences of from 4 to 6 and 

 even 10 per cent, in the form-factors'- 



We will now investigate the different conditions that may 

 present themselves in the survey of crops or of a group of trees 

 composing a girth-class, which may be regarded for the present 

 purpose as a small crop by itself. 



Starting with the element of girth, we have two broad cases : 

 The girths of the trees may either (A) be different, or (B) be 

 one and the same. 



A. GIRTHS DIFFERENT. Under this head we may have four 

 separate cases as follows :- 



(a) Height and form-factor constant, .*., form-factor a func- 



