gg ROTATION FOB QUANTITATIVE EXPLOIT ABILITY. 



■^oetween the trees composing it, as they expand their crowns. 

 Moreover the produce of thinning operations is more considerable 

 during the first half of the life of the crop operated upon than during 

 the other half. The consequence is that they affect our calculations 

 as soon as the middle age of the crop has been reached, and they 

 do this, if not as a constant quantity divided by an increasing 

 number corresponding to the advancing age of the crop, at least as 

 a quantity increasing less rapidly than the age. Taken into account, 

 this produce has the effect of diminishing the mean annual rate of 

 growth during the years that succeed the most productive thinnings, 

 as compared with the mean annual rate of growth during the im- 

 mediately preceding years, and it thus hastens or even suffices of 

 itself to bring about the maximum mean annual production sought.^ 



The explanation of this is simple. It is an established fact 

 that differences in the annual sum of production in any complete 

 crop, from being well-marked during the first years, become slight 

 later on; and it is equally well known that thinnings scarcely, if at 



(1) We will illustrate by figures the meaning of this paragraph. 



Suppose a full-cropped acre aged 90 years to have jilst been thinned, the 

 stock left standing measuring 5040 c. ft. and the total outturn of all thinnings 

 made hitherto being 2520 c. ft.; then the average animal pi oduction per acre 

 5040+2520 



at 90 years = = 840 c. ft. 



90 



Similarly suppose the crop at 120 years just before being thinned to contain 

 6720 c. ft.; then. 



6720+2520 



Average annual production per acre at 120 years = =* 770 c. ft. 



120 



Thus although we have assumed the annual production to be constant, 

 the produce of the thinnings of itself suffices to reduce the average annual 

 production in the space of only 25 years from 840 to 770 cubic feet. If we 

 continued the series, the average annual production, supposing T to be a con- 

 stant, would be represented by the general expression 



T 



P+- 



n 



where P=! annual production, T>= total produce of thinnings. andn= age of crop. 

 But actually T is naturally not a constant and hence the thinnings cannot 

 aifect our calculations " as a constant divided by an increasing number cor- 

 responding to the advancing age of the crop." It is easy to show that they 

 must affect our calculations " as a quantity increasing less rapidly than the 

 age"; for if this quantity increased at least as rapidly as the age, then 



T 



— ot n 



n 



or T oc n* 

 i. e. T would have to increase in an absurdly impossible ratio (Translator.) 



