THE CONSTRUCTION OF YIELD TABLES 423 



the yields are given as for even-aged stands. Since it is seldom that 

 any species is so distributed in age classes and so free from major sources 

 of damage as never to be found in stands of even age, plots based on 

 age can be obtained under a greater range of conditions than is commonly 

 admitted. 



But when this method is apparently impracticable, there remains 

 one possibility for constructing a yield table based on age, which although 

 far from being accurate, is based on a fundamental law of growth of 

 stands. It was shown in § 274 that as trees develop, they require 

 increased crown space, and that this expansion of crown can be attained 

 only by the reduction of numbers of trees per acre. 



The diameters of crowns of trees is an index of the growing space 

 which they require though it seldom exactly measures this space. But 

 if it can be shown that the space occupied by trees of different diameters 

 is 'proportional to the diameter of their crowns, the relative number 

 of trees per acre of different diameters which can stand on an acre 

 can be determined. 



To obtain such data, crowns can be assumed as circular in shape, 

 (though the actual shape varies according to the light and growing 

 space available, especially in hardwoods), and that the space occupied 

 by each crown is in proportion to the square of its diameter or width 

 in feet. 



Measurement of Width of Crowns. To determine the average width 

 of crown for trees of different diameters, two men may work together. 

 One stations himself behind a plumb-bob suspended from a pole so to 

 hang clear from a height of about 8 feet. He lines in the second man 

 at a point below the outer edge of the crown of the tree, whose width is 

 then measured on the ground to the point intersecting the opposite 

 edge of crown. For this purpose a pole, marked in feet, can be used. 

 The distance measured must be at right angles to the lines of sight. A 

 record is made of the D.B.H. and crown width. ^ 



Areas of Crowns. To obtain a true average of crown area, each 

 crown width must be squared. The sum of the areas so obtained for 

 each diameter class is divided by the nmnber of trees in the class, to 

 get the average area of the square for that class. The square root, 

 or side of this square is the average width of the crown for the class. 

 Now, if it be assumed that the space occupied by this diameter squared 

 represents the actual growing space required by the tree, the number 

 of trees per acre for the diameter class is found by dividing the area 



1 No effort need be made to obtain the area of each cro^-n by two or more measure- 

 ments or by plotting the projected area of the crown. Reliance is placed on a large 

 number of measurements of one diameter, rapidly and accurately taken, to obtain 

 the true average diameter of crowns for each D.B.H. class. 



