18 MENSURATION AND INCREMENT [CH. 



V+v 

 the crop in the middle of the period of n years will be . 



V v V + v 

 If p is the percentage rate of increment, p : 100 : : : 



, V v 2 200 V v , T 



therefore p = 100 x -- x ^ = -- x ~ - . Now if as in 



n V+v n V+v 



practice is most probable the crop we are investigating is 

 a middle-aged one, and if the two periods are not separated 

 by a great number of years, say more than ten years, in 

 that case the height and the form-factor of the average sample 

 tree will remain unchanged throughout the entire period of 

 measurement, and the volumes will then be proportionate to 

 the basal areas of the average sample tree of the crop, and the 

 formula will take the form of 



200 D 2 -d* 



As the difference between the two diameters will be small, 

 D 2 + d 2 will be approximately the same as f (D + d) 2 , and so 

 the formula can be simplified to the form 



200 D d 



1 6. Pressler's formula. 



This formula of Pressler's is a very useful one, and may be relied 

 upon to give good results, provided that the crop be of middle 

 age, say, of at least sixty years old, and that n represents a small 

 number of years so that D and d do not differ greatly. 



In the case of standing timber, the radial increment of the 

 tree is readily ascertained by means of Pressler's borer. This is 

 a tool like a hollow gimlet, which is screwed into the sample tree 

 in a radial direction at right angles to the axis of the tree, and 

 which thereby extracts a round spill of wood about 2 inches in 

 length from the tree. To insure accuracy two, if not four, borings 

 at right angles to one another should be made at the same level 

 on each tree; the annual rings on the spills of wood extracted 

 will be carefully counted and measured, and the mean taken. 



