264 OUR FORESTS AND WOODLANDS 
of a simple arithmetical progression. In the 
above examples the: series of portions of the 
crops would respectively be aged 1-10, I-20, 
1-80 years just before the fall in each 
year, while immediately after the fall it 
would be Oo-9, O-19, O-—79 years, and 
at midsummer it would be 4-94, 4-193, 
-4—794 years. Hence, by summarising these 
series, the necessary capital in growing stock will 
be found to be in the above cases respectively 
equal to five, ten, and forty times the amount 
of that portion of the crop which comes to 
the fall as the. harvest of each year; because 
what comes annually to the fall as the mature 
crop, leaving thinnings out of consideration, is 
the incorporation of the annual growths from 
time of formation of the crop up to ten, 
twenty, and eighty years respectively. The 
correctness of this can be easily represented 
graphically. Assuming that the total sum of 
the annual growths incorporated in the mature 
fall consists of equal annual increments (which 
is not in reality the case, though this fact 
does not affect the total volume), if a series be 
formed of the annual falls of equal breadth 
