76 AGE OF TREES AND WOODS. 



By substituting this expression for I in the above equation, 

 the latter becomes : 



(1) l 



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 approxi- 

 mately proportionate 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 

 m l ; m z ; m s ; . . . . and the average annual increment 

 per acre by i 1 ; i 2 ; i^; . . . . then formula (1) can be 

 written in this way (after Gustav Heyer) : 



x % x a 1 _, ??i 2 x 2 X a 2 _, m 3 x % X a s 



or 



A _ m! x ij x E! + m 2 x i 2 x a 2 + m 3 x i 3 x a 3 + . . . 

 m.! x ^ + m 2 x i 2 + m 3 x i 3 + . . . 



If it is now assumed that : 



i 1 = i z = ?, 3 = . . . 



the above formula reduces to the following : 



m.! + m 2 + 10.3 + . . . 



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 the increment culminates, as it then 

 changes but slowly. 



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

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

 they are n 1 ; n z ; n s ; . . . . his formula would be : 



