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5. Valuation Survey by means of the Average free, 

 *rhe aveK^e tree, according to our assumption, is that tree 

 whose height and form-faetor are the same as the average height 

 and form-faetor of the crop, considered as a whole. 



In order to obtain the average tree we must first of all deter- 

 mine what its girth is. This we shall know, if we know its 

 basal area. If c, a, h, and /, represent respectively the contents, 

 basal area, height, and form-factor of the average tree, then— 



c = a hf: 

 But by formulae (i) and (ii) 



A BF ^ 



Therefore a i f = 



and a = — (since by hypothesis if — HF) • 



That is to say, the average tree is that tree whose basal area is 

 the average basal area of all the trees of the crop. This being so, 

 we can find oxit the girth of the average tree as soon as we 

 know the number of stems composing the crop and their total basal 

 area. Having obtained this gfirth, we fell and cube several trees 

 of that girth, and the mean contents of these trees will be ihe 

 contents of the average tree. 



To obtain the above result, we have to assume that h f =. EF. 

 This assumption is, however, true only when (1) the heights and 

 form-factors of all the trees in the crop, or, at least, the products 

 of their heights and form-factors are equal, (2) these heights and 

 form-factoi-s, or, at least, their products, are proportional to tlie 

 errresponding basal areas, and (3) the mean of aU these heights 

 and form -factors may be taken respectively as the height and forra- 

 factor of the crop as a whole. These three conditions can obtain 

 only in very regular crops, and even in such crops as many as three 

 or four of the trees of the average girth must be felled and 

 measured in order to obtain a sufficiently close average for the 

 contents of the average tree. 



Resume. — "When this method of valuation survey can be adopted 

 the following procedure should be followed : — Measure and register 

 the trees in girth-gradations embracing a range of 1 inch. Then, 

 with the aid of tables, calculate the aggregate basal area of the 

 trees in each class, and total the whole. Divide this total by the 

 number of trees, and the quotient will be the basal area of the 



