CLEAR CUTTING IN HIGH FOREST. 227 



Beginning with the calculation for autumn, 



let be volume in the year =0 cubic feet, 

 » = a „ „ 

 ^ X n = h „ „ 

 S X )i = c „ 

 ■i X II = d „ „ 



then — 



Total volume from year to year n minus a=: (0+^0 X -^ a 



n „ 2 X » minus h={a-\-b) X '^i^ — b 



*A 



„ 2 X n „ dXn minus c = {b-{-c) X '^- — c 



„ 3XH „ 4XH ={c-\-d)x'^. 



2 



Total volume from to 4 X » years = 



'l±i (O + 2 a + 2 /. + 2 c + d) - (^a + b + c) 



Normal Gr. Stock, &„ = n Ta + b + c + -") + -. 



This is the calculation for autamn. 



If the oldest age gradation is cut away during winter, the 

 normal growing stock in spring must be d cul)ic feet less than 

 that in autumn, that is to say : — 



!■„ in Spring =.n(^-\-\)-\-c-{- j — 



In spring the growing stock consists onh' 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 

 assumed, that one-half of the annual increment has been laid 



q2 



