CLEAR CUTTING IN HIGH FOREST. 233 



volumes rise within each period of n years according to an 

 arithmetical series, that is to say, by adding the same amount 

 of volume each year. 



Let be volume in the year =0 cubic feet, 



JJ 5> >> '" " > 



j> ?i X fl - n ,, 



3 x n = < 



M 4 X 7i = r? ,, 



then : 



Total volume from yearo to year n minus a = (0 + a) x a 







,, ,, n ,, 2 X minus b = (a + b) X b 



a 



n \ 1 

 ,, ,, 2xw ,, 3 x n minus c = (b + c) x - c 1 



3x?^ 4X7Z 

 Total volume from o to 4 x ?i years = 



Normal Gr. Stock, Gr n = 



This is the calculation for autumn. 



If the oldest age gradation is cut away during winter the 

 normal growing stock in spring must be d cubic feet less than 

 that in autumn, that is to say : 



Gn in spring = n ( 



\ 



111 spring the growing stock consists only of a series of 

 gradations running from to (r 1) years old. In the course 

 of the summer (the growing season), the series is brought up 

 again to one running from 1 to r years old. If, therefore, the 

 calculation is made for the middle of summer, it may be 



