50 VOLUME OF WHOLE WOODS. 



then the following equation holds good : 



V= Wj x j x 7^ x/!+ w 2 x s, x 7i 2 x/ 2 + . . . 



= (7*1 + ^2+ ) X 8 X /I X/. 



If it is now assumed that li X /i = 7i- 2 X / a = 7t s X / 3 

 = h X /then the above equation becomes : 



and 



. ~N 



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



N = total number of trees ,, ,, 

 In other 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 : 

 V=vxN, 



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 : 



since s X N = 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 + vf V" + -.)xS 



The above method rests on the assumption that h l f l = 

 fci/i -&/=...= hf. 



This, however, is not absolutely correct, though it holds 

 good approximately in all regularly-grown woods. It follows that 

 the degree of accuracy decreases with the increase in the number 

 of classes which are clubbed together into one group, the least 



