246 INCREMENT, GROWING STOCK AND YIELD. 



to the old growing stock ; but that laid on during the last year 

 is not cut, but goes over to the second rotation, and so on. 

 This gives the following allotment, if the increment of one age 

 gradation during a year is called = i : 



Allotment of Increment to 



Old New 



Growing Stock. Growing Stock. 



Gradation now years old r x i . . 



1 = (r-l)t . . i 



2 = (r-2)t ., . 2 -i 



3 = (r-3)i . . 3 t 



(r-2) =[r-(r-2)]i . . (r-2) . t 

 (r-1) =[r-(r-l)]i . . (r-1) i 



The terms under each growing stock form arithmetical series, 

 and if added up, they come to the following : 



Placing now rxi = I, the above become : 

 Spring, oM = /r + 



If the calculation is made for autumn, then the positions of 

 the old and new growing stocks are reversed. Of the youngest 

 age gradation, now 1 year old, only (r l)xi goes to the old, 

 and i to the new stock ; of the second age gradation, now 2 years 

 old ; (r 2) x i goes to the old, and 2 x i to the new stock, and 

 so on. This gives 



Autumn, G old 



