928 
Journal of Agricultural Research 
Vol. XXXI, No. 10 
It appears, then, that a curve based on empirical data can neither 
be used backwards nor combined with other curves, without serious 
t liability of gross errors. It also appears that material should not be 
sorted for averaging in any way except on the basis of the independent 
variable. The seriousness of the errors depend largely on the degree 
of correlation between the variables. Yet in the literature of forestry 
may be found innumerable examples in which analogous processes are 
involved. The first error is more generally recognized and more 
generally avoided, although tree taper curves, for example, are still 
quite generally advocated for obtaining average heights to given 
D.B.H.-INCHES 
Fig. 6 —Curve of volume over diameter, obtained indirectly from curves of Figures 4 and 2, compared 
with actual averages 
diameter limits, whereas they give accurately only average diameters 
at given heights. The second error is probably more common than 
the third. It is exemplified in the study of uneven-aged stands by 
treating diameter classes as if they were age classes, when once the 
relation between age and diameter is worked out. In this case the 
correlation is obviously quite low, and one can but surmise how inac¬ 
curate the results thus obtained may be. A determination of the 
coefficient or index of correlation in such cases may suggest how ffreat 
the dangers in the indirect treatment are, but reliability can only be 
obtained by the simple direct method, laborious though it may prove 
to be. 
