39 



If the crop is irregular, the problem becomes more or less com- 

 plicated. Several stems of the different girth-classes present 

 must be examined, and when the respective ages of the several 

 classes have been determined, the question to be solved is how to 

 obtain the mean age of the crop from them. To take the mere 

 arithmetical mean of the several ages without reference to the 

 respective areas occupied by them, or to the quantity of material 

 each represents, would evidently be wrong. We now proceed to 

 investigate different methods for obtaining the true mean age 

 which may be defined as that age at which a crop of uniform age 

 would, under the same conditions of soil, locality and species, have 

 produced the same volume of material as the actual crop contains. 



Let v v v 2t t' 3 = respectively the volumes of the several 



classes aged, respectively, y v y 2 , y$ years, and Y = the re- 

 quired mean age = the age of the imaginary equivalent crop. By 

 hypothesis the mean annual increment of both crops is one and the 

 same ; let this increment = 7. Then 



1 V i 



II = V } + V 2 + t> 3 



and 1 = + .- ' + ; 



yi yt ys 



Hence f- + - + - 8 - I Y = 0, + v 9 -f v. . 



\y\ ya y ' 



and r = Vl + r * + *> Forraula(v). 



1 i *"3 i *J 



yT ~ ys y 3 



Expressed in words, the preceding formula would run thus: 

 To obtain the mean age of a crop composed of trees of diverse ages, 

 divide the total volume of material on the ground by the sum of the 

 mean annual increments of the several age-classes. 



Since the age of trees is, at least approximately, a function of 

 their girths, the girth-classes may be considered as coincident with 

 age-classes, and the words "girth-classes" may be substituted 

 for <l age-classes " in the above rule. 



Let us now investigate another formula' for the case in which 



the respective areas ot lt a 2 , 3 occupied by the diameter-classe 



are known. If i v i 2 , ? 3 - = respectively the meun annual 



increment per unit of surface in the different areas ,, s , a s , 



then we have 



"l *l '1 y\ > V 2 ~ 22 .'2 ' 3 "" 



