or, combining coefficients: 



i 



S = + a^T + a2 . (8) 



This equation, for appropriate coefficients a^ and a^, has an analytical form similar to that 

 described by Richardson (1961). 



ANALYSIS OF DATA 



The above analysis applies to specific gravity of a single annual increment. A similar 

 functional form should also apply to the average specific gravity of a uniform number of annual 

 increments . Because the cores taken from the trees on the growth study plots were measured 

 for the specific gravity of the outer 20 years' increment, this period was used for the analysis 

 of the individual tree data . 



The specific gravity of the outer 20 annual rings of each disk was used to estimate the 

 three coefficients in (8) for each tree . 



These three coefficients formed the components of the dependent vector of a multiple 

 linear regression on the four independent variables: d.b.h., crown length, age, and crown 

 class of the sample tree. A test statistic for the predictive value of each of the independent 

 variables was computed. This statistic has the F- distribution with 3 and 103-q degrees of 

 freedom where q is the number of independent variables included in the multivariate regression. 

 In the first part of table 2, this statistic is indicated for each variable separately. 



After removing the effect of crown length, crown class still accounted for a significant 

 part of the remaining generalized variance, but d.b.h. did not. 



The regression equations for the coefficients of (8), finally expressed in terms of crow 

 length (L) and crown class (C), were: 



SiQ = 0.377 -0.000971 (L) +0.0628 (C) 



= 0.000552 -0.0000883 (L) +0.00229 (C) 



a^ = 0.0474 +0.000678 (L) -0.0223 (C). 



Curves predicted from these regressions are shown in figure 1 for two typical crown 

 lengths in each crown class . 



ESTIMATING INCREMENT SPECIFIC GRAVITY FROM 

 BREAST-HEIGHT CORE DATA 



The average specific gravity of the layer of wood produced in a 20-year period is the 

 weighted average of the ordinates of the curves in figure 1, where the weights are the cross- 

 sectional area of the increment at the corresponding distance from the apex. The specific 

 gravity of the outer 20 rings of the core taken at breast height provided the principal index to 

 relative position of the curve for a particular tree. 



6 



