430 THE DETERMINATION OF GROWTH PER CENT 



sary. Let V ofiiuil volume at present, and v equal volume n years ago. 



V — V 



Then growth for one year equals . If it is assumed that this 



n 



growth for n years is laid on in equal annual installments, then the growth 



so obtained is considered that of the current year or for any year during 



the period. 



If the growth per cent is obtained on this basis, the result will vary 



according to the year in which the volume of the stand is taken as the 



basis. If for ten years ago, then the formula is. 



Growth per cent= (^^) 100. 



\ vn / 



But if the per cent is desired for the last or present year, 



Growth per cent = ( -^ — ) 100. 

 \ Vn I 



For an average year midway of the period, the capital or volume is 



2 ' 

 and growth per cent is 



Y-n 



100 



Y-v \ 200 



F+ V \F+ 



2 



This is known as Pressler's formula. 



329. Pressler's Formula Based on Relative Diameter. Further modifications 

 of this formula by Pressler are intended to reduce it to terms of diameter so that it 

 may be applied to measurements on standing trees taken at B.H. If height and form 

 factor do not change, then 



_ / D^-dA 200 



^~VD2+dV ~' 



In this formula D is the present D.B.H. and d is the diameter n years ago. D—d 



is then designated as a and — is called the relative diameter. By making — = g, 

 a a 



and substituting aq for D, and o{q — l) for d, he reduced the formula thus to 



■(g-l)A200 



g2+(g-l)2/ 



for which expressions values are computed in a table. 



To use this table the present diameter D is divided by twice the width of the 

 rings in the period 7i, thus indicating the relative diameter. The values in the table 

 give the per cent of volume growth for the period. This is then divided by the num- 

 ber of years in the period to get the current annual growth per cent.i 



1 This table is given in Principles of American Forestry, Samuel B, Green, John 

 Wiley & Sons, N. Y., 1903, p. 178. 



