86 THE THEORY AND PRACTICE OF WORKING PLANS 



'y = j,?!2^ = j)X.oi = ^,500,000 X.oi =35,000 feet board measure 



nv 



equals annual cut. 



This result is identical with that obtained by Von Mantel's 

 formula (No. 2) or by the Austrian formula (No. 5) modified 

 (as suggested under No. 6) by making the period of distribution 

 of excess or deficit equal half the rotation. 



(c) Value and Application. — This method, published by 

 Hundeshagen in 182 1, was really discovered by Paulsen in 1795, 

 though Hundeshagen never knew of the latter's work until 1830. 

 It presents no advantages over the methods already described 

 and some very substantial disadvantages: 



(i) The assumption that the actual cut is to the actual 

 growing stock as the normal cut is to the normal growing 

 stock is not always correct, especially not where there are over- 

 mature and deteriorating stands in the forest. 



(2) The value of v changes constantly, hence, to be strictly 

 accurate, y would have to be redetermined annually. 



(3) The method provides for no definite period for the dis- 

 tribution of surplus or saving of deficit in the growing stock. A 

 cutting plan is permissible, but does not affect the volume of 

 the cut as determined by the formula. Hence under the 

 method, overmature stands can be held through many years 

 if the growing stock is excessive, or immature stands cut off 

 though the growing stock is already deficient. 



The only real use of the formula in irregular, uneven-aged 

 stands is as a check on other methods. Its use in even-aged 

 stands presupposes normal yield tables and regulated conditions, 

 neither of which exist in America at present nor are apt to exist 

 for some time to come. 



8. BY VOLUME.— BASED ON GROWING STOCK AND INCREMENT. 

 BREYMANN'S METHOD. 



(a) Description of Method. — Based on Hundeshagen's for- 

 mula, Bre>Tnann assumed that the actual cut is to the normal 

 cut as the actual average age is to the normal average age of a 



