50 MEASUREMENT OF WHOLE WOODS. 



and 



s, It, J the basal area, height and form factoi' of the mean 

 tree of the classes thrown together, 

 then the following equation holds good : — 



T^ = »1 X Si X h X./l + »2 X So X //2 X /o + . . . 



= ("1 + "2 + • • •) X s X h X f. 

 If it is now assumed, that Iti Xf\ = ^o X J\ = h^ X f\ = . . 

 = // X /' then the a])Ove equation becomes : 



"1 X Si + ;/2 X 6'2 + • • . = ("1 + "2 + • . .) s, 



and 



S = "1 X Sl + Ho X 6-0 + • • •_ ^ 

 "1 + »2 + ■ • • A" 



where S = basal area of all trees of the group, and 

 A" = total number of trees ,, ,, 

 In words, the basal area of the average tree is equal to 

 the arithmetical mean of the basal area of all trees contained in 

 the group. 



The volume of the group is then : 

 T^ =- r X N, 

 where v represents the volume of the arithmetical mean sample 

 tree with a basal area = s. 



If no tree can be found with the basal area s, "another as 

 near as possible to it is chosen of a section s', and the volume 

 of the group is obtained by the formula : 



s' s' 



since s x X = S = the basal area of all trees in the group. 



If several approximately mean sample trees are taken, the 

 formula changes into the following : — 



V^ ( v^ + y" + y'" + . . .) X S 

 s' -I- s" + s'" ... 



The above method rests on the assumption, that hifi = 

 ^2 /2 = ^'3 .f3= • ■ ■ = It /• This, however, is not 

 absolutely correct, though it holds good approximately in 



