METHOD OF DETERMINING THE DIMENSIONS OF A TREE 311 



difficult to get a tree which was actually an average for the stand, but 

 when the stand was divided into diameter groups, any required degree 

 of accuracy could be obtained, according to the number of groups made. 



In determining the diameter of the average tree, the arithmetical 

 mean of diameters gave too small a result since the volumes of trees 

 of uniform height are in proportion to T>' z . With a table of the areas of 

 circles, the total basal area or sum of the areas of the cross sections at 

 D.B.H. for all the trees on the plot was obtained and divided by the 

 number to obtain the average basal area. The diameter correspond- 

 ing to this basal area was that of the tree sought. Where a tree of this 

 exact diameter to ^-inch could not be found, a larger or smaller tree 

 was selected and the difference found by the proportion existing between 

 the basal areas of the tree measured and the tree desired. This method 

 is termed the Mean Sample Tree Method. 



In this country the application of these methods has been confined 

 to a few early investigations into the cubic volume of cordwood in second- 

 growth hardwoods. The difficulty of selecting a tree of average height 

 and form as well as basal area and the expense of felling and measuring 

 a tree makes the use of volume tables far preferable whenever these 

 are dependable, and their substitution is practically universal. 1 



242. Method of Determining the Dimensions of a Tree Contain- 

 ing the Average Board-foot Volume. Another use of sample trees is 

 in connection with the determination of the age and growth of stands 

 rather than to determine their volume. For this purpose, the volume 

 of the stand is first found from volume tables and the average tree then 

 determined. The volume sought is that of a tree which when multi- 

 plied by the number of trees on the plot, will give the total volume of 

 the plot in the unit of volume" which was used in estimating. 



1 A recent test, 1920, by J. Nelson Spaeth, Harvard Forest School, in second- 

 growth hardwoods, in which mean sample trees for each 3-inch diameter group 

 were measured, gave the following comparison of accuracy with the use of a standard 

 volume table, although the latter was for but one species, red maple, comprising but 

 15 per cent of the stand: 



The refinements of these methods, known as Draught's, Urich's and Hartig's 

 Methods, are set forth in Graves' Mensuration, pp. 224-242. For application to 

 American problems that of the Mean Sample Tree is probably sufficient. 



