THE THEORY AND J'RACTICE OF WORKING PLANS 93 



normal.* If the proportion is normal it will be possible to cut 

 the group of old trees, plus their increment, during the first 

 third of the rotation, the increment, of course, being figured 

 for only half of the third of the rotation. 



But, first of all, it is necessary to ascertain whether or not 

 the volume as a whole is too great or too small. This is done by 

 finding the total volume which there would be if half of the 

 entire area were covered with trees of just exploitable size f 

 (not of very large mature trees). In obtaining this volume the 

 number of exploitable trees per acre, called for above, is used. 

 The result should be approximately equal to the sum of the old 

 and medium trees. If the result is less the forest contains a 

 surplus; if more, it contains a deficit. There are five distinct 

 possibilities : 



(i) The volume of the old and volume of the medium trees 

 may be in the proportion of 5:3, and sum of their volumes 

 normal. In this case nothing further is necessary before the 

 actual calculation of the cut. 



(2) The volume of old and medium trees may be in the pro- 

 portion of 5 13, but their sum less than normal. In this case 

 it will be necessary to increase the growing stock. This can be 

 done by cutting, during the first third of the rotation, only the 

 old trees, without their increment, or, if the area is very badly 

 understocked, by cutting less than the old trees. 



(3) The volume of old and medium trees may not be in the 

 proportion of 5 13, and their sum nevertheless normal. This is 

 adjusted by transfers from the group which is too large to that 

 which is too small. 



* This ratio is based on the relative age of the old group and the medium 

 group; it will vary with the length of the rotation, the conditions of growth, 

 and the species. In the present instance, if the rotation age is 150, each group 

 covers 50 years, i.e., the old group 100-150, average 125; the medium group 

 50-100, average 75. Then the old group is to the medium group as 125 : 75 = 5 : 3. 



t In dealing with open stands, such as Western yellow pine in the South- 

 west, the area must be considered as fully stocked with exploitable trees, but 

 due allowance must be made for natural openings and bare places. 



