in] MENSURATION AND INCREMENT 19 



17. Schneider's formula. 



Another very useful formula is Schneider's. Suppose that D 

 is the mean diameter of the sample tree at breast-height, and 

 that n is the number of annual rings in the last inch of radius, 

 and let us suppose also that the diameter D lies, not outside, 

 but in the middle of the i-inch zone of increment resulting from 

 the n years' growth. The area of this zone of increment is 



and the annual increment of this basal area will be - 



n ' 



then, assuming that the increment takes place half inside and 

 half outside the present diameter, 



TT.D 7T.D 2 



n 

 400 



p : 100 : : 



and p = 



n .D 



Schneider's iormula gives practically the same result as 

 Pressler's, for if in the latter n be taken as i year, the D d = 

 twice the breadth of the last ring, and D + d = twice the present 

 diameter, so 



breadth of the last ring 



Yj .4.OO X 



breadth of the present diameter ' 

 which is the same result as is given by Schneider's formula. 



1 8. Breymann's formula. 



A third formula of the same kind which is often useful for 

 purposes of investigation of increment is Breymann's. In this, 

 the width of the last annual increase of the diameter d is repre- 

 sented by a, so that -- represents the last annual increase of 



radius, and here again we will suppose that the diameter d lies 

 in the middle of this zone of increment. The superficial area of 

 the last annual zone of increment is 



7T ( / d\ f -. d\ } 7T d 



-x-nd-h- [a- -} V =-. 2 . a .d = ir.d x - 

 4 i\ r 2/ \ 2/ J 4 2 



then p : 100 ::v.d.- 



2 



and p = 200x5 



a 



7T 



2 4 



a 



2 2 



