76 AGE OF TREES AND WOODS. 



Bj' substituting this expression for I in the above equation 

 the latter becomes — 



A _ ^1 + ^2 + V3 + . . . 



^1 _|_ ^2 _^ _^3 



(1.) 



This formula is known as that of Smalian and C. Heyer. It 

 says in words: The mean age of a wood is obtained by dividing 

 the volume of the whole wood by the sum of the mean annual 

 increments of the several age classes. The method may be 

 simplified by assuming, that the age is approximately propor- 

 tionate to the diameter ; hence, the diameter classes may be 

 taken as the age classes. The above formula is chiefly used, 

 when the age classes are irregularly mixed over the area. 



If the areas of the several age classes are represented by 

 y«i ; 7//2 ; ni-i) .... and the average annual increment 

 per acre by ii\ H', i^\ • • • • then formula (1.) can be 

 written in this way (after Gustav Heyer): — 



J _ nil X /'i X (ii 4- ^^'2 X 12 X a.2 -\- ;»3 X /^ X ((^ -f" • • - 



nil X h X ^'1 _|_ 111-2 X i-2 X a-2 , 'ij'i X i^ X ('3 1 



or «i "2 «3 



^ _ mi X ii X ai + ^2 X ia X aa H- "^3 X is X a3 -|- . . . .g ) 



mj X ii + ma X 12 + mg X ig + . . . 



If it is now assumed, that — 



'1 = '2 = 'y = • ■ • 

 the above formula reduces to the following : 



. _ mi X ai + ma X aa + ma X aa + 



- . (3.) 



mi + mg + ma + . . . 



This formula was first given by Giimpel. It holds good 

 only, if the differences in age are small and the age itself is 

 close to that, at which tlie increment culminates, as it then 

 changes but slowly. 



Andre follows a yet different method. He bases the calcu- 

 lation upon the number of trees in the several age classes. If 

 they are Hi ; n^ ; »3 ; .... his formula would be: 



A = -^ X^i + n^ X aa + na X ag + . . . . ^^ ^ 



^1 + 112 + 113 + /. r 



