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 i-io, 1-20, 

 i - 80 years just before the fall in each 

 year, while immediately after the fall it 

 would be 0-9, 0-19, 0-79 years, and 

 at midsummer it would be J - 9^, J - 19^, 

 i~79i 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 



