THINNINGS. 115 



Some owners wish to know how many stems per acre they can 

 keep on foot at given ages in a regular crop. I have already 

 said that there is no formula. It is easy to show the absurdity of 

 expecting one. An oak pole-crop, aged 30 years, may comprise 

 1600 to 2000 stems per acre, but only about 400 really forming 

 the main crop. On cutting out the feeble and useless, there remain 

 400 stems suitably spaced. Ten years later, at the age of 40, half 

 may be cut, say 200 ; at 50, cut a third of the remainder • at 

 60, one-fourth, and so on at equal intervals, one-fifth, one-sixth, 

 one-seventh, one-eighth. Then, at the age of 100, there will 

 remain 400 x -| = 50 dominant oaks. Continuing as before, 

 there remain 

 at 



Now, do the same for a spruce forest aged 30 years, containing 

 1600 stems, all included in the region of practical politics. 



At 80 years old there will be 270. 



100 „ „ „ 202. 



120 „ „ „ 162. 



150 „ „ „ 121. 



A silver fir wood, aged 30, may contain 800 principal stems 

 Treated in the same way, it will, at different ages, contain one- 

 half the number that the spruce has. What sort of result is this 1 

 Finally, whatever the species and the number " M " of stems con- 

 tained at thirty yeai-s old in the complete crop, it may be thinned 

 by the formula 



M x i x f x f x ...... x U ^ = X. 



Under the definition by which this article begins, the number of 

 stems to be preserved at different ages is, therefore, fixed by the 

 formula 



X = — M. 



n 



The progression may be accelerated, or diminished, according 

 to the soil, by making intervals of six or eight, twelve or fourteen 

 years. The hyperbolic curve may be constr acted, directrices and 

 asymptotes marked out, and so on. What a treat for a mathema- 

 tician, turned forester by mistake. 



