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 



^ . (/)+I) i _ J . ( z)-i)2 = ?. 4 o = , . 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, 



7T.D 7T.D 2 







and 



n .D 



Schneider's tormula 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 



J* _ A r\r\ v/ __ ____ ____ _ _ O _ 



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 



2 



77 f/ 

 -x\( 

 4 \\ 



^+T) -U-~) \=^-.2.a.d = Tr.dx^ 



then p : 100 : : TT . d . - 



and ^> = 200 x ^ . 



2 2 



