Nov. 15, 1925 
Possible Errors in the Use of Curves 
925 
in diameter, but this is readily explainable on the ground that the 
trees of largest diameter were undoubtedly those which were standing 
isolated from their neighbors, and which were shorter than those 
growing in denser stands. It should be noted, also, that curve 2 
does not necessarily originate from the point 4.5 — 0, because it is 
neither a growth curve nor (what is very similar) a relationship 
curve for a strictly selection stand. 
If the two curves are carefully compared it will at once be seen 
that the one is not merely a reversal of the other. . The extent of the 
difference is best brought out by Figure 3. In this the curve of 
Figure 1 is replotted, while that of Figure 2 (the broken line) is turned 
on its side so that its axes coincide with those of curve 1. Through 
the central part of the curves the errors are relatively small, but the 
upper end is startlingly different, both in position, trend, and range 
D.B.H.-INCHES 
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JL 
Fig. 3.—Comparison of curves of height over diameter, and of diameter over height, for same data 
of values. It is clear that to reverse either curve and use it as a 
substitute for the other will result in errors which may be very 
serious. The approximate coincidence of the two curves for the 
central half of their range is an indication of quite high correlation, 
but in spite of this the distortion at the upper end is so great that 
the most interesting fact brought out by the upper part of curve 1 
is completely obliterated. 
A second type of transformation which seems equally plausible 
(and on which the texts are silent, if not actually misleading) suggests 
itself in a case such as the following. Let us assume we have at 
hand a curve of height over diameter at breast height (such as fig. 1) 
and one of volume over height (such as fig. 4). Let us also assume 
that we wish a curve showing the relation between volume and diam¬ 
eter. Apparently we can obtain this curve directly from the two 
already drawn without having to turn once more to the original data, 
a process which would involve a considerable amount of labor in 
