47 



and former diameters [D and y^ are measured on eacli 

 section exclusive of the bark. The actual and former 

 contents of the stem can thus be calculated, and their 

 difference is the increment sought. This method is prac- 

 ticable only., when the annual concentric rings are distin- 

 guishable. 



II. By mbasuring the actual and poemee diameters at 



HALF THE HEIGHT OP THE TfiEE 91 TEARS AGO. The length 



of stem added on during the pastw years is removed, and 

 the remaining log (whose length = A) is then cut across 

 through the middle. The diameters D and d being now 

 measured, the increment sought 



= J. = ^-.a {D^-d^. 



III. Bt means of form factoes. — In this ease it is assumed 



that during short periods the form factor does not vary 

 in any appreciable manner. If D, fl^ and V denote 

 respectively the actual diameter, height and volume, and 

 d, h, and v the corresponding figures n years ago, then 



/„= r-v = 1- {Dm-d>h)f. 



This method is suitable for standing trees, when H, D and d 

 can be determined ; h must be estimated as accurately as 

 possible. 



IV. By means of the basal area and height. — Let d and 



I denote respectively the diameter and length or height 

 n years ago, and S and X the corresponding increments 

 during this interval of years. Then we have 



r =5(^+8)2 (;+X) /and» = Id^lf. 



Hence 7„ = V—v 



= l^(d + lY{l^x) - dH \f 



= \ (dH + IdU + m + d«A + ZrfxS +8*A — dH\f 



= 1^{UU + d'x)+ (IH + ZdU + 8«A)|/; 



Since n is always a small interval of years, the value of the 

 expression in the second bracket is so insignificant that 

 be it may be neglected, and we have, therefore 



