SUBSTITUTION OF VOLUME TABLES FOR TREE ANALYSIS 373 



the upper dimensions and volume of trees of a smaller size than those 

 which exist in a given stand. This is an advantage in case such 

 smaller sizes are lacking, but where present they may be directly meas- 

 ured. The volume which trees produce at given ages can thus be 

 obtained in one of two ways, either by measuring trees of different 

 ages directly for volume or by analyzing a single tree or a number of 

 trees in order to determine the past growth in volume. The latter 

 method alone will bring out the changes which take place in form, as 

 described above, due to altered conditions. In applying such growth 

 figures to answer the fundamental question of growth studies, namely, 

 what is the rate of growth in volume per acre, annually or for a given 

 period, not only must the growth of average rather than individual 

 trees be determined, but the relations of these average trees to the 

 number of trees which will survive on an acre at different ages must 

 also be known (§ 275). Since the recording and working up of growth 

 measurements to determine total volume growth is slow and expensive, 

 only a few trees may be taken. It is necessary that these trees have 

 the average form quotient for the stand to which their results will be 

 applied. This means either a careful selection or a chance of incurring 

 an error of from 10 to 15 per cent by the accidental selection of trees 

 which depart from this average in form. 



288. Substitution of Volume Tables for Tree Analysis. The growth 

 of an average tree is determined by the average growth in D.B.H., 

 the average height growth and the average growth in diameter at 

 upper sections, of which the most important is the diameter growth 

 at one -half of the height. The growth of upper diameters is usually 

 accompanied by a change in form, caused by a change in the length and 

 position of the crown. This is illustrated in Fig. 80 (§ 290) for 

 which tree both butt swelling and upper diameters increased faster 

 than growth at 8 feet. 



Relying upon the maintenance of a consistent tree form for average 

 trees, a method is in common use as a substitute for the analysis of 

 trees to determine their volume growth. This method depends upon 

 the use of volume tables to determine the volume of trees whose height 

 and diameter are known. Since a standard volume table expresses 

 the actual volume of average trees much more accurately than it can 

 1)6 obtained by the analysis of a few sample trees, the substitution 

 of a volume for the average tree taken from this table enables the investi- 

 gator to concentrate his effort on determining average growth in D.B.H. 

 and in height. The actual measurement of height growth involves 

 the counting of rings for determination of age of upper sections on at 

 least a few trees (§ 284), but dispenses with the measurement of diameter 

 growth on these upper sections, and requires from one-fifth to one-tenth 



