Ill] 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 



- p+i)2_- (2)-i)2=^.4Z) = ^.A 

 4 4 4 



ir.D 



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 TT.D^ 



* : 100 : : : 



^ n /[ 



and p = ^^^^ . 



^ n .D 



Schneider's formula 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 



P~ ^ breadth of the present diameter ' 



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



18. 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 wiU 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 



^, i J a TT .d^ 



then p : 100 : : ir . rf . - — — 



and p = 200 X T . 



