47 



and former diameters (D and d) are measured on each 

 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 prnc- 

 ticable only when the annual concentric rings are distin- 

 guishable. 



II. BY" MEASURING THE ACTUAL AND FORMER DIAMETRBS AT 



HALT THE'HEIGHT OP THE TREK YEARS AGO. The length 

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

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

 through the middle. The diameters D and d being now 

 measured, the increment sought 



= / = *^k (D*-d*). 



III. BY MEANS OF FORM FACTORS. In this case it is assume;! 



that during short periods the form factor does not vary 

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

 respectively the actual diameter, height and volume, and 

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



This method is suitable for standing trees, when II, 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 8 and A the corresponding increments 

 during this interval of years. ' Then we have 



r=*(d+$)* (J + A) /and* = I 

 Hence / = V v 



= * fd'l + ldU -r S 8 / + d*\ + 2</A8 +8A --< 



= * f(ZdM + d^)+ (5 s / + 5W5* + 8A) j/. 



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 



